Merge branch 'main' into next

2023-04-25 12:34:26 +02:00 · 2023-04-25 12:34:26 +02:00 · fa78d806e3
commit fa78d806e3
parent 654999e254 a16eb7e4b8
202 changed files with 25943 additions and 2775 deletions
--- a/.envrc
+++ b/.envrc
@ -0,0 +1 @@
+use flake
--- a/.gitignore
+++ b/.gitignore
@ -3,3 +3,4 @@
 /pki
 **/*.rs.bk
 *.swp
+/.direnv
--- a/Cargo.lock
+++ b/Cargo.lock
--- a/Cargo.nix
+++ b/Cargo.nix
--- a/2
+++ b/2
@ -4,7 +4,7 @@ all:
 	clear; cargo build

 release:
-	nix-build --arg release true
+	nix-build --attr pkgs.amd64.release --no-build-output

 shell:
 	nix-shell
--- a/default.nix
+++ b/default.nix
@ -1,7 +1,4 @@
-{
-  system ? builtins.currentSystem,
-  git_version ? null,
-}:
+{ system ? builtins.currentSystem, git_version ? null, }:

 with import ./nix/common.nix;

@ -13,21 +10,20 @@ let
    debug = (compile {
      inherit system target git_version pkgsSrc cargo2nixOverlay;
      release = false;
-    }).workspace.garage {
-      compileMode = "build";
-    };
+    }).workspace.garage { compileMode = "build"; };

    release = (compile {
      inherit system target git_version pkgsSrc cargo2nixOverlay;
      release = true;
-    }).workspace.garage {
-      compileMode = "build";
-    };
+    }).workspace.garage { compileMode = "build"; };
  });

-  test = (rustPkgs: pkgs.symlinkJoin {
+  test = (rustPkgs:
+    pkgs.symlinkJoin {
      name = "garage-tests";
-    paths = builtins.map (key: rustPkgs.workspace.${key} { compileMode = "test"; }) (builtins.attrNames rustPkgs.workspace);
+      paths =
+        builtins.map (key: rustPkgs.workspace.${key} { compileMode = "test"; })
+        (builtins.attrNames rustPkgs.workspace);
    });

 in {
@ -55,8 +51,6 @@ in {
      inherit system git_version pkgsSrc cargo2nixOverlay;
      target = "x86_64-unknown-linux-musl";
      compiler = "clippy";
-    }).workspace.garage {
-      compileMode = "build";
-    };
+    }).workspace.garage { compileMode = "build"; };
  };
 }
--- a/doc/api/garage-admin-v0.yml
+++ b/doc/api/garage-admin-v0.yml
@ -678,10 +678,12 @@ paths:
                  properties:
                    maxSize: 
                      type: integer
+                      format: int64
                      nullable: true
                      example: 19029801
                    maxObjects:
                      type: integer
+                      format: int64
                      nullable: true
                      example: null

@ -1158,9 +1160,11 @@ components:
            $ref: '#/components/schemas/BucketKeyInfo'
        objects:
          type: integer
+          format: int64
          example: 14827
        bytes:
          type: integer
+          format: int64
          example: 13189855625
        unfinishedUploads:
          type: integer
@ -1171,10 +1175,12 @@ components:
            maxSize:
              nullable: true
              type: integer
+              format: int64
              example: null
            maxObjects:
              nullable: true
              type: integer
+              format: int64
              example: null


--- a/doc/book/connect/_index.md
+++ b/doc/book/connect/_index.md
@ -10,11 +10,12 @@ Garage implements the Amazon S3 protocol, which makes it compatible with many ex

 In particular, you will find here instructions to connect it with:

-  - [Browsing tools](@/documentation/connect/cli.md)
  - [Applications](@/documentation/connect/apps/index.md)
-  - [Website hosting](@/documentation/connect/websites.md)
-  - [Software repositories](@/documentation/connect/repositories.md)
+  - [Browsing tools](@/documentation/connect/cli.md)
  - [FUSE](@/documentation/connect/fs.md)
+  - [Observability](@/documentation/connect/observability.md)
+  - [Software repositories](@/documentation/connect/repositories.md)
+  - [Website hosting](@/documentation/connect/websites.md)

 ### Generic instructions

--- a/doc/book/connect/apps/index.md
+++ b/doc/book/connect/apps/index.md
@ -13,7 +13,7 @@ In this section, we cover the following web applications:
 | [Matrix](#matrix)     | ✅       |  Tested with `synapse-s3-storage-provider`    |
 | [Pixelfed](#pixelfed)     | ❓       |  Not yet tested    |
 | [Pleroma](#pleroma)     | ❓       |  Not yet tested    |
-| [Lemmy](#lemmy)     | ❓       |  Not yet tested    |
+| [Lemmy](#lemmy)     | ✅        |  Supported with pict-rs    |
 | [Funkwhale](#funkwhale)     | ❓       | Not yet tested     |
 | [Misskey](#misskey)     | ❓       | Not yet tested     |
 | [Prismo](#prismo)     | ❓       | Not yet tested     |
@ -484,7 +484,68 @@ And add a new line. For example, to run it every 10 minutes:

 ## Lemmy

-Lemmy uses pict-rs that [supports S3 backends](https://git.asonix.dog/asonix/pict-rs/commit/f9f4fc63d670f357c93f24147c2ee3e1278e2d97)
+Lemmy uses pict-rs that [supports S3 backends](https://git.asonix.dog/asonix/pict-rs/commit/f9f4fc63d670f357c93f24147c2ee3e1278e2d97).
+This feature requires `pict-rs >= 4.0.0`.
+
+### Creating your bucket
+
+This is the usual Garage setup:
+
+```bash
+garage key new --name pictrs-key
+garage bucket create pictrs-data
+garage bucket allow pictrs-data --read --write --key pictrs-key
+```
+
+Note the Key ID and Secret Key.
+
+### Migrating your data
+
+If your pict-rs instance holds existing data, you first need to migrate to the S3 bucket.
+
+Stop pict-rs, then run the migration utility from local filesystem to the bucket:
+
+```
+pict-rs \
+  filesystem -p /path/to/existing/files \
+  object-store \
+   -e my-garage-instance.mydomain.tld:3900 \
+   -b pictrs-data \
+   -r garage \
+   -a GK... \
+   -s abcdef0123456789...
+```
+
+This is pretty slow, so hold on while migrating.
+
+### Running pict-rs with an S3 backend
+
+Pict-rs supports both a configuration file and environment variables.
+
+Either set the following section in your `pict-rs.toml`:
+
+```
+[store]
+type = 'object_storage'
+endpoint = 'http://my-garage-instance.mydomain.tld:3900'
+bucket_name = 'pictrs-data'
+region = 'garage'
+access_key = 'GK...'
+secret_key = 'abcdef0123456789...'
+```
+
+... or set these environment variables:
+
+
+```
+PICTRS__STORE__TYPE=object_storage
+PICTRS__STORE__ENDPOINT=http:/my-garage-instance.mydomain.tld:3900
+PICTRS__STORE__BUCKET_NAME=pictrs-data
+PICTRS__STORE__REGION=garage
+PICTRS__STORE__ACCESS_KEY=GK...
+PICTRS__STORE__SECRET_KEY=abcdef0123456789...
+```
+

 ## Funkwhale

--- a/doc/book/connect/backup.md
+++ b/doc/book/connect/backup.md
@ -13,7 +13,41 @@ Borg Backup is very popular among the backup tools but it is not yet compatible
 We recommend using any other tool listed in this guide because they are all compatible with the S3 API.
 If you still want to use Borg, you can use it with `rclone mount`.

+## git-annex

+[git-annex](https://git-annex.branchable.com/) supports synchronizing files
+with its [S3 special remote](https://git-annex.branchable.com/special_remotes/S3/).
+
+Note that `git-annex` requires to be compiled with Haskell package version
+`aws-0.24` to work with Garage.
+
+```bash
+garage key new --name my-key
+garage bucket create my-git-annex
+garage bucket allow my-git-annex --read --write --key my-key
+```
+
+Register your Key ID and Secret key in your environment:
+
+```bash
+export AWS_ACCESS_KEY_ID=GKxxx
+export AWS_SECRET_ACCESS_KEY=xxxx
+```
+
+Within a git-annex enabled repository, configure your Garage S3 endpoint with
+the following command:
+
+```bash
+git annex initremote garage type=S3 encryption=none host=my-garage-instance.mydomain.tld protocol=https bucket=my-git-annex requeststyle=path region=garage signature=v4
+```
+
+Files can now be synchronized using the usual `git-annex` `copy` or `get`
+commands.
+
+Note that for simplicity - this example does not enable encryption for the files
+sent to Garage - please refer to the
+[git-annex encryption page](https://git-annex.branchable.com/encryption/) for
+how to configure this.

 ## Restic

--- a/doc/book/connect/cli.md
+++ b/doc/book/connect/cli.md
@ -12,6 +12,7 @@ These tools are particularly suitable for debug, backups, website deployments or
 | [AWS CLI](#aws-cli)     | ✅       | Recommended   |
 | [rclone](#rclone)     | ✅       |    |
 | [s3cmd](#s3cmd)     | ✅       |    |
+| [s5cmd](#s5cmd)     | ✅       |    |
 | [(Cyber)duck](#cyberduck)     | ✅       |    |
 | [WinSCP (libs3)](#winscp)     | ✅       | CLI instructions only   |
 | [sftpgo](#sftpgo)     | ✅       |    |
@ -178,59 +179,34 @@ s3cmd put /tmp/hello.txt s3://my-bucket/
 s3cmd get s3://my-bucket/hello.txt hello.txt
 ```

+## `s5cmd`
+
+Configure a credentials file as follows:
+
+```bash
+export AWS_ACCESS_KEY_ID=GK...
+export AWS_SECRET_ACCESS_KEY=
+export AWS_DEFAULT_REGION='garage'
+export AWS_ENDPOINT='http://localhost:3900'
+```
+
+After adding these environment variables in your shell, `s5cmd` can be used
+with:
+
+```bash
+s5cmd --endpoint-url=$AWS_ENDPOINT ls
+```
+
+See its usage output for other commands available.
+
 ## Cyberduck & duck {#cyberduck}

 Both Cyberduck (the GUI) and duck (the CLI) have a concept of "Connection Profiles" that contain some presets for a specific provider.
-We wrote the following connection profile for Garage:

-```xml
-<?xml version="1.0" encoding="UTF-8"?>
-<!DOCTYPE plist PUBLIC "-//Apple//DTD PLIST 1.0//EN" "http://www.apple.com/DTDs/PropertyList-1.0.dtd">
-<plist version="1.0">
-    <dict>
-        <key>Protocol</key>
-        <string>s3</string>
-        <key>Vendor</key>
-        <string>garage</string>
-        <key>Scheme</key>
-        <string>https</string>
-        <key>Description</key>
-        <string>GarageS3</string>
-        <key>Default Hostname</key>
-        <string>127.0.0.1</string>
-        <key>Default Port</key>
-        <string>4443</string>
-        <key>Hostname Configurable</key>
-        <false/>
-        <key>Port Configurable</key>
-        <false/>
-        <key>Username Configurable</key>
-        <true/>
-        <key>Username Placeholder</key>
-        <string>Access Key ID (GK...)</string>
-        <key>Password Placeholder</key>
-        <string>Secret Key</string>
-        <key>Properties</key>
-        <array>
-            <string>s3service.disable-dns-buckets=true</string>
-        </array>
-        <key>Region</key>
-        <string>garage</string>
-        <key>Regions</key>
-        <array>
-            <string>garage</string>
-        </array>
-    </dict>
-</plist>
-```
-
-*Note: If your garage instance is configured with vhost access style, you can remove `s3service.disable-dns-buckets=true`.*
-
-### Instructions for the GUI
-
-Copy the connection profile, and save it anywhere as `garage.cyberduckprofile`.
-Then find this file with your file explorer and double click on it: Cyberduck will open a connection wizard for this profile.
-Simply follow the wizard and you should be done!
+Within Cyberduck, a
+[Garage connection profile](https://docs.cyberduck.io/protocols/s3/garage/) is
+available within the `Preferences -> Profiles` section. This can enabled and
+then connections to Garage may be configured.

 ### Instuctions for the CLI

--- a/doc/book/connect/observability.md
+++ b/doc/book/connect/observability.md
@ -0,0 +1,57 @@
+++
+title = "Observability"
+weight = 25
+++
+
+An object store can be used as data storage location for metrics, and logs which
+can then be leveraged for systems observability.
+
+## Metrics
+
+### Prometheus
+
+Prometheus itself has no object store capabilities, however two projects exist
+which support storing metrics in an object store:
+
+ - [Cortex](https://cortexmetrics.io/)
+ - [Thanos](https://thanos.io/)
+
+## System logs
+
+### Vector
+
+[Vector](https://vector.dev/) natively supports S3 as a
+[data sink](https://vector.dev/docs/reference/configuration/sinks/aws_s3/)
+(and [source](https://vector.dev/docs/reference/configuration/sources/aws_s3/)).
+
+This can be configured with Garage with the following:
+
+```bash
+garage key new --name vector-system-logs
+garage bucket create system-logs
+garage bucket allow system-logs --read --write --key vector-system-logs
+```
+
+The `vector.toml` can then be configured as follows:
+
+```toml
+[sources.journald]
+type = "journald"
+current_boot_only = true
+
+[sinks.out]
+encoding.codec = "json"
+type = "aws_s3"
+inputs = [ "journald" ]
+bucket = "system-logs"
+key_prefix = "%F/"
+compression = "none"
+region = "garage"
+endpoint = "https://my-garage-instance.mydomain.tld"
+auth.access_key_id = ""
+auth.secret_access_key = ""
+```
+
+This is an example configuration - please refer to the Vector documentation for
+all configuration and transformation possibilities. Also note that Garage
+performs its own compression, so this should be disabled in Vector.
--- a/doc/book/cookbook/_index.md
+++ b/doc/book/cookbook/_index.md
@ -6,7 +6,7 @@ sort_by = "weight"
 +++

 A cookbook, when you cook, is a collection of recipes.
-Similarly, Garage's cookbook contains a collection of recipes that are known to works well!
+Similarly, Garage's cookbook contains a collection of recipes that are known to work well!
 This chapter could also be referred as "Tutorials" or "Best practices".

 - **[Multi-node deployment](@/documentation/cookbook/real-world.md):** This page will walk you through all of the necessary
@ -16,6 +16,10 @@ This chapter could also be referred as "Tutorials" or "Best practices".
  source in case a binary is not provided for your architecture, or if you want to
  hack with us!

+- **[Binary packages](@/documentation/cookbook/binary-packages.md):** This page
+  lists the different platforms that provide ready-built software packages for
+  Garage.
+
 - **[Integration with Systemd](@/documentation/cookbook/systemd.md):** This page explains how to run Garage
  as a Systemd service (instead of as a Docker container).

@ -26,6 +30,14 @@ This chapter could also be referred as "Tutorials" or "Best practices".

 - **[Configuring a reverse-proxy](@/documentation/cookbook/reverse-proxy.md):** This page explains how to configure a reverse-proxy to add TLS support to your S3 api endpoint.

+- **[Deploying on Kubernetes](@/documentation/cookbook/kubernetes.md):** This page explains how to deploy Garage on Kubernetes using our Helm chart.
+
+- **[Deploying with Ansible](@/documentation/cookbook/ansible.md):** This page lists available Ansible roles developed by the community to deploy Garage.
+
+- **[Monitoring Garage](@/documentation/cookbook/monitoring.md)** This page
+  explains the Prometheus metrics available for monitoring the Garage
+  cluster/nodes.
+
 - **[Recovering from failures](@/documentation/cookbook/recovering.md):** Garage's first selling point is resilience
  to hardware failures. This section explains how to recover from such a failure in the
  best possible way.
--- a/doc/book/cookbook/ansible.md
+++ b/doc/book/cookbook/ansible.md
@ -0,0 +1,51 @@
+++
+title = "Deploying with Ansible"
+weight = 35
+++
+
+While Ansible is not officially supported to deploy Garage, several community members
+have published Ansible roles.  We list them and compare them below.
+
+## Comparison of Ansible roles
+
+| Feature                            | [ansible-role-garage](#zorun-ansible-role-garage) | [garage-docker-ansible-deploy](#moan0s-garage-docker-ansible-deploy) |
+|------------------------------------|---------------------------------------------|---------------------------------------------------------------|
+| **Runtime**                        | Systemd                                     | Docker                                                        |
+| **Target OS**                      | Any Linux                                   | Any Linux                                                     |
+| **Architecture**                   | amd64, arm64, i686                          | amd64, arm64                                                  |
+| **Additional software**            | None                                        | Traefik                                                       |
+| **Automatic node connection**      | ❌                                          | ✅                                                            |
+| **Layout management**              | ❌                                          | ✅                                                            |
+| **Manage buckets & keys**          | ❌                                          | ✅ (basic)                                                    |
+| **Allow custom Garage config**     | ✅                                          | ❌                                                            |
+| **Facilitate Garage upgrades**     | ✅                                          | ❌                                                            |
+| **Multiple instances on one host** | ✅                                          | ✅                                                            |
+
+
+## zorun/ansible-role-garage
+
+[Source code](https://github.com/zorun/ansible-role-garage), [Ansible galaxy](https://galaxy.ansible.com/zorun/garage)
+
+This role is voluntarily simple: it relies on the official Garage static
+binaries and only requires Systemd.  As such, it should work on any
+Linux-based OS.
+
+To make things more flexible, the user has to provide a Garage
+configuration template.  This allows to customize Garage configuration in
+any way.
+
+Some more features might be added, such as a way to automatically connect
+nodes to each other or to define a layout.
+
+## moan0s/garage-docker-ansible-deploy
+
+[Source code](https://github.com/moan0s/garage-docker-ansible-deploy), [Blog post](https://hyteck.de/post/garage/)
+
+This role is based on the Docker image for Garage, and comes with
+"batteries included": it will additionally install Docker and Traefik. In
+addition, it is "opinionated" in the sense that it expects a particular
+deployment structure (one instance per disk, one gateway per host,
+structured DNS names, etc).
+
+As a result, this role makes it easier to start with Garage on Ansible,
+but is less flexible.
--- a/doc/book/cookbook/binary-packages.md
+++ b/doc/book/cookbook/binary-packages.md
@ -0,0 +1,28 @@
+++
+title = "Binary packages"
+weight = 11
+++
+
+Garage is also available in binary packages on:
+
+## Alpine Linux
+
+```bash
+apk install garage
+```
+
+## Arch Linux
+
+Garage is available in the [AUR](https://aur.archlinux.org/packages/garage).
+
+## FreeBSD
+
+```bash
+pkg install garage
+```
+
+## NixOS
+
+```bash
+nix-shell -p garage
+```
--- a/doc/book/cookbook/gateways.md
+++ b/doc/book/cookbook/gateways.md
@ -21,7 +21,7 @@ You can configure Garage as a gateway on all nodes that will consume your S3 API
 The instructions are similar to a regular node, the only option that is different is while configuring the node, you must set the `--gateway` parameter:

 ```bash
-garage layout assign --gateway --tag gw1 <node_id>
+garage layout assign --gateway --tag gw1 -z dc1 <node_id>
 garage layout show    # review the changes you are making
 garage layout apply   # once satisfied, apply the changes
 ```
--- a/doc/book/cookbook/kubernetes.md
+++ b/doc/book/cookbook/kubernetes.md
@ -48,6 +48,7 @@ garage:
  replicationMode: "2"

 # Start 4 instances (StatefulSets) of garage
+deployment:
  replicaCount: 4

 # Override default storage class and size
--- a/doc/book/cookbook/monitoring.md
+++ b/doc/book/cookbook/monitoring.md
@ -52,255 +52,6 @@ or make your own.
 We detail below the list of exposed metrics and their meaning.


-
 ## List of exported metrics

-
-### Metrics of the API endpoints
-
-#### `api_admin_request_counter` (counter)
-
-Counts the number of requests to a given endpoint of the administration API. Example:
-
-```
-api_admin_request_counter{api_endpoint="Metrics"} 127041
-```
-
-#### `api_admin_request_duration` (histogram)
-
-Evaluates the duration of API calls to the various administration API endpoint. Example:
-
-```
-api_admin_request_duration_bucket{api_endpoint="Metrics",le="0.5"} 127041
-api_admin_request_duration_sum{api_endpoint="Metrics"} 605.250344830999
-api_admin_request_duration_count{api_endpoint="Metrics"} 127041
-```
-
-#### `api_s3_request_counter` (counter)
-
-Counts the number of requests to a given endpoint of the S3 API. Example:
-
-```
-api_s3_request_counter{api_endpoint="CreateMultipartUpload"} 1
-```
-
-#### `api_s3_error_counter` (counter)
-
-Counts the number of requests to a given endpoint of the S3 API that returned an error. Example:
-
-```
-api_s3_error_counter{api_endpoint="GetObject",status_code="404"} 39
-```
-
-#### `api_s3_request_duration` (histogram)
-
-Evaluates the duration of API calls to the various S3 API endpoints. Example:
-
-```
-api_s3_request_duration_bucket{api_endpoint="CreateMultipartUpload",le="0.5"} 1
-api_s3_request_duration_sum{api_endpoint="CreateMultipartUpload"} 0.046340762
-api_s3_request_duration_count{api_endpoint="CreateMultipartUpload"} 1
-```
-
-#### `api_k2v_request_counter` (counter), `api_k2v_error_counter` (counter), `api_k2v_error_duration` (histogram)
-
-Same as for S3, for the K2V API.
-
-
-### Metrics of the Web endpoint
-
-
-#### `web_request_counter` (counter)
-
-Number of requests to the web endpoint
-
-```
-web_request_counter{method="GET"} 80
-```
-
-#### `web_request_duration` (histogram)
-
-Duration of requests to the web endpoint
-
-```
-web_request_duration_bucket{method="GET",le="0.5"} 80
-web_request_duration_sum{method="GET"} 1.0528433229999998
-web_request_duration_count{method="GET"} 80
-```
-
-#### `web_error_counter` (counter)
-
-Number of requests to the web endpoint resulting in errors
-
-```
-web_error_counter{method="GET",status_code="404 Not Found"} 64
-```
-
-
-### Metrics of the data block manager
-
-#### `block_bytes_read`, `block_bytes_written` (counter)
-
-Number of bytes read/written to/from disk in the data storage directory.
-
-```
-block_bytes_read 120586322022
-block_bytes_written 3386618077
-```
-
-#### `block_read_duration`, `block_write_duration` (histograms)
-
-Evaluates the duration of the reading/writing of individual data blocks in the data storage directory.
-
-```
-block_read_duration_bucket{le="0.5"} 169229
-block_read_duration_sum 2761.6902550310056
-block_read_duration_count 169240
-block_write_duration_bucket{le="0.5"} 3559
-block_write_duration_sum 195.59170078500006
-block_write_duration_count 3571
-```
-
-#### `block_delete_counter` (counter)
-
-Counts the number of data blocks that have been deleted from storage.
-
-```
-block_delete_counter 122
-```
-
-#### `block_resync_counter` (counter), `block_resync_duration` (histogram)
-
-Counts the number of resync operations the node has executed, and evaluates their duration.
-
-```
-block_resync_counter 308897
-block_resync_duration_bucket{le="0.5"} 308892
-block_resync_duration_sum 139.64204196100016
-block_resync_duration_count 308897
-```
-
-#### `block_resync_queue_length` (gauge)
-
-The number of block hashes currently queued for a resync.
-This is normal to be nonzero for long periods of time.
-
-```
-block_resync_queue_length 0
-```
-
-#### `block_resync_errored_blocks` (gauge)
-
-The number of block hashes that we were unable to resync last time we tried.
-**THIS SHOULD BE ZERO, OR FALL BACK TO ZERO RAPIDLY, IN A HEALTHY CLUSTER.**
-Persistent nonzero values indicate that some data is likely to be lost.
-
-```
-block_resync_errored_blocks 0
-```
-
-
-### Metrics related to RPCs (remote procedure calls) between nodes
-
-#### `rpc_netapp_request_counter` (counter)
-
-Number of RPC requests emitted
-
-```
-rpc_request_counter{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 176
-```
-
-#### `rpc_netapp_error_counter` (counter)
-
-Number of communication errors (errors in the Netapp library, generally due to disconnected nodes)
-
-```
-rpc_netapp_error_counter{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 354
-```
-
-#### `rpc_timeout_counter` (counter)
-
-Number of RPC timeouts, should be close to zero in a healthy cluster.
-
-```
-rpc_timeout_counter{from="<this node>",rpc_endpoint="garage_rpc/membership.rs/SystemRpc",to="<remote node>"} 1
-```
-
-#### `rpc_duration` (histogram)
-
-The duration of internal RPC calls between Garage nodes.
-
-```
-rpc_duration_bucket{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>",le="0.5"} 166
-rpc_duration_sum{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 35.172253716
-rpc_duration_count{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 174
-```
-
-
-### Metrics of the metadata table manager
-
-#### `table_gc_todo_queue_length` (gauge)
-
-Table garbage collector TODO queue length
-
-```
-table_gc_todo_queue_length{table_name="block_ref"} 0
-```
-
-#### `table_get_request_counter` (counter), `table_get_request_duration` (histogram)
-
-Number of get/get_range requests internally made on each table, and their duration.
-
-```
-table_get_request_counter{table_name="bucket_alias"} 315
-table_get_request_duration_bucket{table_name="bucket_alias",le="0.5"} 315
-table_get_request_duration_sum{table_name="bucket_alias"} 0.048509778000000024
-table_get_request_duration_count{table_name="bucket_alias"} 315
-```
-
-
-#### `table_put_request_counter` (counter), `table_put_request_duration` (histogram)
-
-Number of insert/insert_many requests internally made on this table, and their duration
-
-```
-table_put_request_counter{table_name="block_ref"} 677
-table_put_request_duration_bucket{table_name="block_ref",le="0.5"} 677
-table_put_request_duration_sum{table_name="block_ref"} 61.617528636
-table_put_request_duration_count{table_name="block_ref"} 677
-```
-
-#### `table_internal_delete_counter` (counter)
-
-Number of value deletions in the tree (due to GC or repartitioning)
-
-```
-table_internal_delete_counter{table_name="block_ref"} 2296
-```
-
-#### `table_internal_update_counter` (counter)
-
-Number of value updates where the value actually changes (includes creation of new key and update of existing key)
-
-```
-table_internal_update_counter{table_name="block_ref"} 5996
-```
-
-#### `table_merkle_updater_todo_queue_length` (gauge)
-
-Merkle tree updater TODO queue length (should fall to zero rapidly)
-
-```
-table_merkle_updater_todo_queue_length{table_name="block_ref"} 0
-```
-
-#### `table_sync_items_received`, `table_sync_items_sent` (counters)
-
-Number of data items sent to/recieved from other nodes during resync procedures
-
-```
-table_sync_items_received{from="<remote node>",table_name="bucket_v2"} 3
-table_sync_items_sent{table_name="block_ref",to="<remote node>"} 2
-```
-
-
+See our [dedicated page](@/documentation/reference-manual/monitoring.md) in the Reference manual section.
--- a/doc/book/cookbook/real-world.md
+++ b/doc/book/cookbook/real-world.md
@ -19,8 +19,12 @@ To run a real-world deployment, make sure the following conditions are met:

 - You have at least three machines with sufficient storage space available.

- Each machine has a public IP address which is reachable by other machines.
-  Running behind a NAT is likely to be possible but hasn't been tested for the latest version (TODO).
+- Each machine has a public IP address which is reachable by other machines. It
+  is highly recommended that you use IPv6 for this end-to-end connectivity. If
+  IPv6 is not available, then using a mesh VPN such as
+  [Nebula](https://github.com/slackhq/nebula) or
+  [Yggdrasil](https://yggdrasil-network.github.io/) are approaches to consider
+  in addition to building out your own VPN tunneling.

 - This guide will assume you are using Docker containers to deploy Garage on each node. 
  Garage can also be run independently, for instance as a [Systemd service](@/documentation/cookbook/systemd.md).
@ -345,5 +349,5 @@ and is covered in the [quick start guide](@/documentation/quick-start/_index.md)
 Remember also that the CLI is self-documented thanks to the `--help` flag and
 the `help` subcommand (e.g. `garage help`, `garage key --help`).

-Configuring S3-compatible applicatiosn to interact with Garage
+Configuring S3-compatible applications to interact with Garage
 is covered in the [Integrations](@/documentation/connect/_index.md) section.
--- a/doc/book/cookbook/reverse-proxy.md
+++ b/doc/book/cookbook/reverse-proxy.md
@ -168,40 +168,65 @@ Here is [a basic configuration file](https://doc.traefik.io/traefik/https/acme/#

 ### Add Garage service

-To add Garage on Traefik you should declare a new service using its IP address (or hostname) and port:
+To add Garage on Traefik you should declare two new services using its IP
+address (or hostname) and port, these are used for the S3, and web components
+of Garage:

 ```toml
 [http.services]
-  [http.services.my_garage_service.loadBalancer]
-    [[http.services.my_garage_service.loadBalancer.servers]]
+  [http.services.garage-s3-service.loadBalancer]
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://xxx.xxx.xxx.xxx"
      port = 3900
+
+  [http.services.garage-web-service.loadBalancer]
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://xxx.xxx.xxx.xxx"
+      port = 3902
 ```

 It's possible to declare multiple Garage servers as back-ends:

 ```toml
 [http.services]
-    [[http.services.my_garage_service.loadBalancer.servers]]
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://xxx.xxx.xxx.xxx"
      port = 3900
-    [[http.services.my_garage_service.loadBalancer.servers]]
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://yyy.yyy.yyy.yyy"
      port = 3900
-    [[http.services.my_garage_service.loadBalancer.servers]]
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://zzz.zzz.zzz.zzz"
      port = 3900
+
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://xxx.xxx.xxx.xxx"
+      port = 3902
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://yyy.yyy.yyy.yyy"
+      port = 3902
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://zzz.zzz.zzz.zzz"
+      port = 3902
 ```

 Traefik can remove unhealthy servers automatically with [a health check configuration](https://doc.traefik.io/traefik/routing/services/#health-check):

 ```
 [http.services]
-  [http.services.my_garage_service.loadBalancer]
-    [http.services.my_garage_service.loadBalancer.healthCheck]
-      path = "/"
-      interval = "60s"
-      timeout = "5s"
+  [http.services.garage-s3-service.loadBalancer]
+    [http.services.garage-s3-service.loadBalancer.healthCheck]
+      path = "/health"
+      port = "3903"
+      #interval = "15s"
+      #timeout = "2s"
+
+  [http.services.garage-web-service.loadBalancer]
+    [http.services.garage-web-service.loadBalancer.healthCheck]
+      path = "/health"
+      port = "3903"
+      #interval = "15s"
+      #timeout = "2s"
 ```

 ### Adding a website
@ -210,10 +235,15 @@ To add a new website, add the following declaration to your Traefik configuratio

 ```toml
 [http.routers]
+  [http.routers.garage-s3]
+    rule = "Host(`s3.example.org`)"
+    service = "garage-s3-service"
+    entryPoints = ["websecure"]
+
  [http.routers.my_website]
    rule = "Host(`yoururl.example.org`)"
-    service = "my_garage_service"
-    entryPoints = ["web"]
+    service = "garage-web-service"
+    entryPoints = ["websecure"]
 ```

 Enable HTTPS access to your website with the following configuration section ([documentation](https://doc.traefik.io/traefik/https/overview/)):
@ -226,7 +256,7 @@ Enable HTTPS access to your website with the following configuration section ([d
 ...
 ```

-### Adding gzip compression
+### Adding compression

 Add the following configuration section [to compress response](https://doc.traefik.io/traefik/middlewares/http/compress/) using [gzip](https://developer.mozilla.org/en-US/docs/Glossary/GZip_compression) before sending them to the client:

@ -234,10 +264,10 @@ Add the following configuration section [to compress response](https://doc.traef
 [http.routers]
  [http.routers.my_website]
    ...
-    middlewares = ["gzip_compress"]
+    middlewares = ["compression"]
    ...
 [http.middlewares]
-  [http.middlewares.gzip_compress.compress]
+  [http.middlewares.compression.compress]
 ```

 ### Add caching response
@ -262,27 +292,54 @@ Traefik's caching middleware is only available on [entreprise version](https://d
    entryPoint = "web"

 [http.routers]
+  [http.routers.garage-s3]
+    rule = "Host(`s3.example.org`)"
+    service = "garage-s3-service"
+    entryPoints = ["websecure"]
+
  [http.routers.my_website]
    rule = "Host(`yoururl.example.org`)"
-    service = "my_garage_service"
-    middlewares = ["gzip_compress"]
+    service = "garage-web-service"
+    middlewares = ["compression"]
    entryPoints = ["websecure"]

 [http.services]
-  [http.services.my_garage_service.loadBalancer]
-    [http.services.my_garage_service.loadBalancer.healthCheck]
-      path = "/"
-      interval = "60s"
-      timeout = "5s"
-    [[http.services.my_garage_service.loadBalancer.servers]]
+  [http.services.garage-s3-service.loadBalancer]
+    [http.services.garage-s3-service.loadBalancer.healthCheck]
+      path = "/health"
+      port = "3903"
+      #interval = "15s"
+      #timeout = "2s"
+
+  [http.services.garage-web-service.loadBalancer]
+    [http.services.garage-web-service.loadBalancer.healthCheck]
+      path = "/health"
+      port = "3903"
+      #interval = "15s"
+      #timeout = "2s"
+
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://xxx.xxx.xxx.xxx"
-    [[http.services.my_garage_service.loadBalancer.servers]]
+      port = 3900
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://yyy.yyy.yyy.yyy"
-    [[http.services.my_garage_service.loadBalancer.servers]]
+      port = 3900
+    [[http.services.garage-s3-service.loadBalancer.servers]]
      url = "http://zzz.zzz.zzz.zzz"
+      port = 3900
+
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://xxx.xxx.xxx.xxx"
+      port = 3902
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://yyy.yyy.yyy.yyy"
+      port = 3902
+    [[http.services.garage-web-service.loadBalancer.servers]]
+      url = "http://zzz.zzz.zzz.zzz"
+      port = 3902

 [http.middlewares]
-  [http.middlewares.gzip_compress.compress]
+  [http.middlewares.compression.compress]
 ```

 ## Caddy
@ -291,18 +348,83 @@ Your Caddy configuration can be as simple as:

 ```caddy
 s3.garage.tld, *.s3.garage.tld {
-	reverse_proxy localhost:3900 192.168.1.2:3900 example.tld:3900
+	reverse_proxy localhost:3900 192.168.1.2:3900 example.tld:3900 {
+        health_uri       /health
+        health_port      3903
+        #health_interval 15s
+        #health_timeout  5s
+    }
 }

 *.web.garage.tld {
-	reverse_proxy localhost:3902 192.168.1.2:3900 example.tld:3900
+	reverse_proxy localhost:3902 192.168.1.2:3902 example.tld:3902 {
+        health_uri       /health
+        health_port      3903
+        #health_interval 15s
+        #health_timeout  5s
+    }
 }

 admin.garage.tld {
-	reverse_proxy localhost:3903
+	reverse_proxy localhost:3903 {
+        health_uri       /health
+        health_port      3903
+        #health_interval 15s
+        #health_timeout  5s
+    }
 }
 ```

 But at the same time, the `reverse_proxy` is very flexible.
 For a production deployment, you should [read its documentation](https://caddyserver.com/docs/caddyfile/directives/reverse_proxy) as it supports features like DNS discovery of upstreams, load balancing with checks, streaming parameters, etc.

+### On-demand TLS
+
+Caddy supports a technique called
+[on-demand TLS](https://caddyserver.com/docs/automatic-https#on-demand-tls), by
+which one can configure the webserver to provision TLS certificates when a
+client first connects to it.
+
+In order to prevent an attack vector whereby domains are simply pointed at your
+webserver and certificates are requested for them - Caddy can be configured to
+ask Garage if a domain is authorized for web hosting, before it then requests
+a TLS certificate.
+
+This 'check' endpoint, which is on the admin port (3903 by default), can be
+configured in Caddy's global section as follows:
+
+```caddy
+{
+	...
+	on_demand_tls {
+		ask http://localhost:3903/check
+		interval 2m
+		burst 5
+	}
+	...
+}
+```
+
+The host section can then be configured with (note that this uses the web
+endpoint instead):
+
+```caddy
+# For a specific set of subdomains
+*.web.garage.tld {
+	tls {
+		on_demand
+	}
+
+	reverse_proxy localhost:3902 192.168.1.2:3902 example.tld:3902
+}
+
+# Accept all domains on HTTPS
+# Never configure this without global section above
+https:// {
+	tls {
+		on_demand
+	}
+
+	reverse_proxy localhost:3902 192.168.1.2:3902 example.tld:3902
+}
+```
--- a/doc/book/cookbook/upgrading.md
+++ b/doc/book/cookbook/upgrading.md
@ -6,45 +6,80 @@ weight = 60
 Garage is a stateful clustered application, where all nodes are communicating together and share data structures.
 It makes upgrade more difficult than stateless applications so you must be more careful when upgrading.
 On a new version release, there is 2 possibilities:
-  - protocols and data structures remained the same ➡️ this is a **straightforward upgrade**
-  - protocols or data structures changed  ➡️  this is an **advanced upgrade**
+  - protocols and data structures remained the same ➡️ this is a **minor upgrade**
+  - protocols or data structures changed  ➡️  this is a **major upgrade**

-You can quickly now what type of update you will have to operate by looking at the version identifier.
-Following the [SemVer ](https://semver.org/) terminology, if only the *patch* number changed, it will only need a straightforward upgrade.
-Example: an upgrade from v0.6.0 from v0.6.1 is a straightforward upgrade.
-If the *minor* or *major* number changed however, you will have to do an advanced upgrade. Example: from v0.6.1 to v0.7.0.
+You can quickly now what type of update you will have to operate by looking at the version identifier:
+when we require our users to do a major upgrade, we will always bump the first nonzero component of the version identifier
+(e.g. from v0.7.2 to v0.8.0).
+Conversely, for versions that only require a minor upgrade, the first nonzero component will always stay the same (e.g. from v0.8.0 to v0.8.1).

-Migrations are designed to be run only between contiguous versions (from a *major*.*minor* perspective, *patches* can be skipped).
-Example: migrations from v0.6.1 to v0.7.0 and from v0.6.0 to v0.7.0 are supported but migrations from v0.5.0 to v0.7.0 are not supported.
+Major upgrades are designed to be run only between contiguous versions.
+Example: migrations from v0.7.1 to v0.8.0 and from v0.7.0 to v0.8.2 are supported but migrations from v0.6.0 to v0.8.0 are not supported.

-## Straightforward upgrades
+The `garage_build_info`
+[Prometheus metric](@/documentation/reference-manual/monitoring.md) provides
+an overview for which Garage versions are currently in use within a cluster.

-Straightforward upgrades do not imply cluster downtime.
+## Minor upgrades
+
+Minor upgrades do not imply cluster downtime.
 Before upgrading, you should still read [the changelog](https://git.deuxfleurs.fr/Deuxfleurs/garage/releases) and ideally test your deployment on a staging cluster before.

 When you are ready, start by checking the health of your cluster.
-You can force some checks with `garage repair`, we recommend at least running `garage repair --all-nodes --yes` that is very quick to run (less than a minute).
-You will see that the command correctly terminated in the logs of your daemon.
+You can force some checks with `garage repair`, we recommend at least running `garage repair --all-nodes --yes tables` which is very quick to run (less than a minute).
+You will see that the command correctly terminated in the logs of your daemon, or using `garage worker list` (the repair workers should be in the `Done` state).

-Finally, you can simply upgrades nodes one by one. 
+Finally, you can simply upgrade nodes one by one.
 For each node: stop it, install the new binary, edit the configuration if needed, restart it.

-## Advanced upgrades
+## Major upgrades

-Advanced upgrades will imply cluster downtime.
+Major upgrades can be done with minimal downtime with a bit of preparation, but the simplest way is usually to put the cluster offline for the duration of the migration.
 Before upgrading, you must read [the changelog](https://git.deuxfleurs.fr/Deuxfleurs/garage/releases) and you must test your deployment on a staging cluster before.

-From a high level perspective, an advanced upgrade looks like this:
-  1. Make sure the health of your cluster is good (see `garage repair`)
-  2. Disable API access (comment the configuration in your reverse proxy)
-  3. Check that your cluster is idle
+We write guides for each major upgrade, they are stored under the "Working Documents" section of this documentation.
+
+### Major upgrades with full downtime
+
+From a high level perspective, a major upgrade looks like this:
+
+  1. Disable API access (for instance in your reverse proxy, or by commenting the corresponding section in your Garage configuration file and restarting Garage)
+  2. Check that your cluster is idle
+  3. Make sure the health of your cluster is good (see `garage repair`)
  4. Stop the whole cluster
-  5. Backup the metadata folder of all your nodes, so that you will be able to restore it quickly if the upgrade fails (blocks being immutable, they should not be impacted)
+  5. Back up the metadata folder of all your nodes, so that you will be able to restore it if the upgrade fails (data blocks being immutable, they should not be impacted)
  6. Install the new binary, update the configuration
  7. Start the whole cluster
  8. If needed, run the corresponding migration from `garage migrate`
  9. Make sure the health of your cluster is good
-  10. Enable API access (uncomment the configuration in your reverse proxy)
+  10. Enable API access (reverse step 1)
  11. Monitor your cluster while load comes back, check that all your applications are happy with this new version

-We write guides for each advanced upgrade, they are stored under the "Working Documents" section of this documentation.
+### Major upgarades with minimal downtime
+
+There is only one operation that has to be coordinated cluster-wide: the passage of one version of the internal RPC protocol to the next.
+This means that an upgrade with very limited downtime can simply be performed from one major version to the next by restarting all nodes
+simultaneously in the new version.
+The downtime will simply be the time required for all nodes to stop and start again, which should be less than a minute.
+If all nodes fail to stop and restart simultaneously, some nodes might be temporarily shut out from the cluster as nodes using different RPC protocol
+versions are prevented to talk to one another.
+
+The entire procedure would look something like this:
+
+1. Make sure the health of your cluster is good (see `garage repair`)
+
+2. Take each node offline individually to back up its metadata folder, bring them back online once the backup is done.
+  You can do all of the nodes in a single zone at once as that won't impact global cluster availability.
+  Do not try to make a backup of the metadata folder of a running node.
+
+3. Prepare your binaries and configuration files for the new Garage version
+
+4. Restart all nodes simultaneously in the new version
+
+5. If any specific migration procedure is required, it is usually in one of the two cases:
+
+  - It can be run on online nodes after the new version has started, during regular cluster operation.
+  - it has to be run offline
+
+   For this last step, please refer to the specific documentation pertaining to the version upgrade you are doing.
--- a/doc/book/design/_index.md
+++ b/doc/book/design/_index.md
@ -20,12 +20,16 @@ and could not do, etc.

 We love to talk and hear about Garage, that's why we keep a log here:

+  - [(en, 2023-01-18) Presentation of Garage with some details on CRDTs and data partitioning among nodes](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/commit/4cff37397f626ef063dad29e5b5e97ab1206015d/doc/talks/2023-01-18-tocatta/talk.pdf)
+
+  - [(fr, 2022-11-19) De l'auto-hébergement à l'entre-hébergement : Garage, pour conserver ses données ensemble](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/commit/4cff37397f626ef063dad29e5b5e97ab1206015d/doc/talks/2022-11-19-Capitole-du-Libre/pr%C3%A9sentation.pdf)
+
+  - [(en, 2022-06-23) General presentation of Garage](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/commit/4cff37397f626ef063dad29e5b5e97ab1206015d/doc/talks/2022-06-23-stack/talk.pdf)
+
  - [(fr, 2021-11-13, video) Garage : Mille et une façons de stocker vos données](https://video.tedomum.net/w/moYKcv198dyMrT8hCS5jz9) and [slides (html)](https://rfid.deuxfleurs.fr/presentations/2021-11-13/garage/) - during [RFID#1](https://rfid.deuxfleurs.fr/programme/2021-11-13/) event

-  - [(en, 2021-04-28) Distributed object storage is centralised](https://git.deuxfleurs.fr/Deuxfleurs/garage/raw/commit/b1f60579a13d3c5eba7f74b1775c84639ea9b51a/doc/talks/2021-04-28_spirals-team/talk.pdf)
+  - [(en, 2021-04-28) Distributed object storage is centralised](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/commit/b1f60579a13d3c5eba7f74b1775c84639ea9b51a/doc/talks/2021-04-28_spirals-team/talk.pdf)

-  - [(fr, 2020-12-02) Garage : jouer dans la cour des grands quand on est un hébergeur associatif](https://git.deuxfleurs.fr/Deuxfleurs/garage/raw/commit/b1f60579a13d3c5eba7f74b1775c84639ea9b51a/doc/talks/2020-12-02_wide-team/talk.pdf)
-
-*Did you write or talk about Garage? [Open a pull request](https://git.deuxfleurs.fr/Deuxfleurs/garage/) to add a link here!*
+  - [(fr, 2020-12-02) Garage : jouer dans la cour des grands quand on est un hébergeur associatif](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/commit/b1f60579a13d3c5eba7f74b1775c84639ea9b51a/doc/talks/2020-12-02_wide-team/talk.pdf)


--- a/doc/book/design/related-work.md
+++ b/doc/book/design/related-work.md
@ -72,8 +72,7 @@ We considered there v2's design but concluded that it does not fit both our *Sel
 **[Riak CS](https://docs.riak.com/riak/cs/2.1.1/index.html):**
 *Not written yet*

-**[IPFS](https://ipfs.io/):**
-*Not written yet*
+**[IPFS](https://ipfs.io/):** IPFS has design goals radically different from Garage, we have [a blog post](@/blog/2022-ipfs/index.md) talking about it.

 ## Specific research papers

--- a/doc/book/development/devenv.md
+++ b/doc/book/development/devenv.md
@ -39,7 +39,7 @@ Now you can enter our nix-shell, all the required packages will be downloaded bu
 nix-shell
 ```

-You can use the traditionnal Rust development workflow:
+You can use the traditional Rust development workflow:

 ```bash
 cargo build  # compile the project
--- a/doc/book/development/release-process.md
+++ b/doc/book/development/release-process.md
@ -11,7 +11,7 @@ We define them as our release process.
 While we run some tests on every commits, we do not make a release for all of them.

 A release can be triggered manually by "promoting" a successful build.
-Otherwise, every weeks, a release build is triggered on the `main` branch.
+Otherwise, every night, a release build is triggered on the `main` branch.

 If the build is from a tag following the regex: `v[0-9]+\.[0-9]+\.[0-9]+`, it will be listed as stable.
 If it is a tag but with a different format, it will be listed as Extra.
--- a/doc/book/quick-start/_index.md
+++ b/doc/book/quick-start/_index.md
@ -290,13 +290,13 @@ sourcing the right file.*
 aws s3 ls

 # list objects of a bucket
-aws s3 ls s3://my_files
+aws s3 ls s3://nextcloud-bucket

 # copy from your filesystem to garage
-aws s3 cp /proc/cpuinfo s3://my_files/cpuinfo.txt
+aws s3 cp /proc/cpuinfo s3://nextcloud-bucket/cpuinfo.txt

 # copy from garage to your filesystem
-aws s3 cp s3/my_files/cpuinfo.txt /tmp/cpuinfo.txt
+aws s3 cp s3://nextcloud-bucket/cpuinfo.txt /tmp/cpuinfo.txt
 ```

 Note that you can use `awscli` for more advanced operations like
--- a/doc/book/reference-manual/admin-api.md
+++ b/doc/book/reference-manual/admin-api.md
@ -1,6 +1,6 @@
 +++
 title = "Administration API"
-weight = 60
+weight = 40
 +++

 The Garage administration API is accessible through a dedicated server whose
--- a/doc/book/reference-manual/configuration.md
+++ b/doc/book/reference-manual/configuration.md
@ -3,6 +3,8 @@ title = "Configuration file format"
 weight = 20
 +++

+## Full example
+
 Here is an example `garage.toml` configuration file that illustrates all of the possible options:

 ```toml
@ -96,7 +98,7 @@ Performance characteristics of the different DB engines are as follows:

 - Sled: the default database engine, which tends to produce
  large data files and also has performance issues, especially when the metadata folder
-  is on a traditionnal HDD and not on SSD.
+  is on a traditional HDD and not on SSD.
 - LMDB: the recommended alternative on 64-bit systems,
  much more space-efficiant and slightly faster. Note that the data format of LMDB is not portable
  between architectures, so for instance the Garage database of an x86-64
@ -259,13 +261,17 @@ Compression is done synchronously, setting a value too high will add latency to
 This value can be different between nodes, compression is done by the node which receive the
 API call.

-### `rpc_secret`
+### `rpc_secret`, `rpc_secret_file` or `GARAGE_RPC_SECRET` (env)

-Garage uses a secret key that is shared between all nodes of the cluster
-in order to identify these nodes and allow them to communicate together.
-This key should be specified here in the form of a 32-byte hex-encoded
-random string. Such a string can be generated with a command
-such as `openssl rand -hex 32`.
+Garage uses a secret key, called an RPC secret, that is shared between all
+nodes of the cluster in order to identify these nodes and allow them to
+communicate together. The RPC secret is a 32-byte hex-encoded random string,
+which can be generated with a command such as `openssl rand -hex 32`.
+
+The RPC secret should be specified in the `rpc_secret` configuration variable.
+Since Garage `v0.8.2`, the RPC secret can also be stored in a file whose path is
+given in the configuration variable `rpc_secret_file`, or specified as an
+environment variable `GARAGE_RPC_SECRET`.

 ### `rpc_bind_addr`

@ -407,24 +413,30 @@ If specified, Garage will bind an HTTP server to this port and address, on
 which it will listen to requests for administration features.
 See [administration API reference](@/documentation/reference-manual/admin-api.md) to learn more about these features.

-### `metrics_token` (since version 0.7.2)
+### `metrics_token`, `metrics_token_file` or `GARAGE_METRICS_TOKEN` (env)

-The token for accessing the Metrics endpoint. If this token is not set in
-the config file, the Metrics endpoint can be accessed without access
-control.
+The token for accessing the Metrics endpoint. If this token is not set, the
+Metrics endpoint can be accessed without access control.

 You can use any random string for this value. We recommend generating a random token with `openssl rand -hex 32`.

-### `admin_token` (since version 0.7.2)
+`metrics_token` was introduced in Garage `v0.7.2`.
+`metrics_token_file` and the `GARAGE_METRICS_TOKEN` environment variable are supported since Garage `v0.8.2`.
+
+
+### `admin_token`, `admin_token_file` or `GARAGE_ADMIN_TOKEN` (env)

 The token for accessing all of the other administration endpoints.  If this
-token is not set in the config file, access to these endpoints is disabled
-entirely.
+token is not set, access to these endpoints is disabled entirely.

 You can use any random string for this value. We recommend generating a random token with `openssl rand -hex 32`.

+`admin_token` was introduced in Garage `v0.7.2`.
+`admin_token_file` and the `GARAGE_ADMIN_TOKEN` environment variable are supported since Garage `v0.8.2`.
+
+
 ### `trace_sink`

-Optionnally, the address of an Opentelemetry collector.  If specified,
-Garage will send traces in the Opentelemetry format to this endpoint. These
+Optionally, the address of an OpenTelemetry collector.  If specified,
+Garage will send traces in the OpenTelemetry format to this endpoint. These
 trace allow to inspect Garage's operation when it handles S3 API requests.
--- a/doc/book/reference-manual/k2v.md
+++ b/doc/book/reference-manual/k2v.md
@ -1,6 +1,6 @@
 +++
 title = "K2V"
-weight = 70
+weight = 100
 +++

 Starting with version 0.7.2, Garage introduces an optionnal feature, K2V,
@ -16,7 +16,7 @@ the `k2v` feature flag enabled can be obtained from our download page under
 with `-k2v` (example: `v0.7.2-k2v`).

 The specification of the K2V API can be found
-[here](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/branch/k2v/doc/drafts/k2v-spec.md).
+[here](https://git.deuxfleurs.fr/Deuxfleurs/garage/src/branch/main/doc/drafts/k2v-spec.md).
 This document also includes a high-level overview of K2V's design.

 The K2V API uses AWSv4 signatures for authentification, same as the S3 API.
--- a/doc/book/reference-manual/monitoring.md
+++ b/doc/book/reference-manual/monitoring.md
@ -0,0 +1,285 @@
+
+++
+title = "Monitoring"
+weight = 60
+++
+
+
+For information on setting up monitoring, see our [dedicated page](@/documentation/cookbook/monitoring.md) in the Cookbook section.
+
+## List of exported metrics
+
+### Garage system metrics
+
+#### `garage_build_info` (counter)
+
+Exposes the Garage version number running on a node.
+
+```
+garage_build_info{version="1.0"} 1
+```
+
+#### `garage_replication_factor` (counter)
+
+Exposes the Garage replication factor configured on the node
+
+```
+garage_replication_factor 3
+```
+
+### Metrics of the API endpoints
+
+#### `api_admin_request_counter` (counter)
+
+Counts the number of requests to a given endpoint of the administration API. Example:
+
+```
+api_admin_request_counter{api_endpoint="Metrics"} 127041
+```
+
+#### `api_admin_request_duration` (histogram)
+
+Evaluates the duration of API calls to the various administration API endpoint. Example:
+
+```
+api_admin_request_duration_bucket{api_endpoint="Metrics",le="0.5"} 127041
+api_admin_request_duration_sum{api_endpoint="Metrics"} 605.250344830999
+api_admin_request_duration_count{api_endpoint="Metrics"} 127041
+```
+
+#### `api_s3_request_counter` (counter)
+
+Counts the number of requests to a given endpoint of the S3 API. Example:
+
+```
+api_s3_request_counter{api_endpoint="CreateMultipartUpload"} 1
+```
+
+#### `api_s3_error_counter` (counter)
+
+Counts the number of requests to a given endpoint of the S3 API that returned an error. Example:
+
+```
+api_s3_error_counter{api_endpoint="GetObject",status_code="404"} 39
+```
+
+#### `api_s3_request_duration` (histogram)
+
+Evaluates the duration of API calls to the various S3 API endpoints. Example:
+
+```
+api_s3_request_duration_bucket{api_endpoint="CreateMultipartUpload",le="0.5"} 1
+api_s3_request_duration_sum{api_endpoint="CreateMultipartUpload"} 0.046340762
+api_s3_request_duration_count{api_endpoint="CreateMultipartUpload"} 1
+```
+
+#### `api_k2v_request_counter` (counter), `api_k2v_error_counter` (counter), `api_k2v_error_duration` (histogram)
+
+Same as for S3, for the K2V API.
+
+
+### Metrics of the Web endpoint
+
+
+#### `web_request_counter` (counter)
+
+Number of requests to the web endpoint
+
+```
+web_request_counter{method="GET"} 80
+```
+
+#### `web_request_duration` (histogram)
+
+Duration of requests to the web endpoint
+
+```
+web_request_duration_bucket{method="GET",le="0.5"} 80
+web_request_duration_sum{method="GET"} 1.0528433229999998
+web_request_duration_count{method="GET"} 80
+```
+
+#### `web_error_counter` (counter)
+
+Number of requests to the web endpoint resulting in errors
+
+```
+web_error_counter{method="GET",status_code="404 Not Found"} 64
+```
+
+
+### Metrics of the data block manager
+
+#### `block_bytes_read`, `block_bytes_written` (counter)
+
+Number of bytes read/written to/from disk in the data storage directory.
+
+```
+block_bytes_read 120586322022
+block_bytes_written 3386618077
+```
+
+#### `block_compression_level` (counter)
+
+Exposes the block compression level configured for the Garage node.
+
+```
+block_compression_level 3
+```
+
+#### `block_read_duration`, `block_write_duration` (histograms)
+
+Evaluates the duration of the reading/writing of individual data blocks in the data storage directory.
+
+```
+block_read_duration_bucket{le="0.5"} 169229
+block_read_duration_sum 2761.6902550310056
+block_read_duration_count 169240
+block_write_duration_bucket{le="0.5"} 3559
+block_write_duration_sum 195.59170078500006
+block_write_duration_count 3571
+```
+
+#### `block_delete_counter` (counter)
+
+Counts the number of data blocks that have been deleted from storage.
+
+```
+block_delete_counter 122
+```
+
+#### `block_resync_counter` (counter), `block_resync_duration` (histogram)
+
+Counts the number of resync operations the node has executed, and evaluates their duration.
+
+```
+block_resync_counter 308897
+block_resync_duration_bucket{le="0.5"} 308892
+block_resync_duration_sum 139.64204196100016
+block_resync_duration_count 308897
+```
+
+#### `block_resync_queue_length` (gauge)
+
+The number of block hashes currently queued for a resync.
+This is normal to be nonzero for long periods of time.
+
+```
+block_resync_queue_length 0
+```
+
+#### `block_resync_errored_blocks` (gauge)
+
+The number of block hashes that we were unable to resync last time we tried.
+**THIS SHOULD BE ZERO, OR FALL BACK TO ZERO RAPIDLY, IN A HEALTHY CLUSTER.**
+Persistent nonzero values indicate that some data is likely to be lost.
+
+```
+block_resync_errored_blocks 0
+```
+
+
+### Metrics related to RPCs (remote procedure calls) between nodes
+
+#### `rpc_netapp_request_counter` (counter)
+
+Number of RPC requests emitted
+
+```
+rpc_request_counter{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 176
+```
+
+#### `rpc_netapp_error_counter` (counter)
+
+Number of communication errors (errors in the Netapp library, generally due to disconnected nodes)
+
+```
+rpc_netapp_error_counter{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 354
+```
+
+#### `rpc_timeout_counter` (counter)
+
+Number of RPC timeouts, should be close to zero in a healthy cluster.
+
+```
+rpc_timeout_counter{from="<this node>",rpc_endpoint="garage_rpc/membership.rs/SystemRpc",to="<remote node>"} 1
+```
+
+#### `rpc_duration` (histogram)
+
+The duration of internal RPC calls between Garage nodes.
+
+```
+rpc_duration_bucket{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>",le="0.5"} 166
+rpc_duration_sum{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 35.172253716
+rpc_duration_count{from="<this node>",rpc_endpoint="garage_block/manager.rs/Rpc",to="<remote node>"} 174
+```
+
+
+### Metrics of the metadata table manager
+
+#### `table_gc_todo_queue_length` (gauge)
+
+Table garbage collector TODO queue length
+
+```
+table_gc_todo_queue_length{table_name="block_ref"} 0
+```
+
+#### `table_get_request_counter` (counter), `table_get_request_duration` (histogram)
+
+Number of get/get_range requests internally made on each table, and their duration.
+
+```
+table_get_request_counter{table_name="bucket_alias"} 315
+table_get_request_duration_bucket{table_name="bucket_alias",le="0.5"} 315
+table_get_request_duration_sum{table_name="bucket_alias"} 0.048509778000000024
+table_get_request_duration_count{table_name="bucket_alias"} 315
+```
+
+
+#### `table_put_request_counter` (counter), `table_put_request_duration` (histogram)
+
+Number of insert/insert_many requests internally made on this table, and their duration
+
+```
+table_put_request_counter{table_name="block_ref"} 677
+table_put_request_duration_bucket{table_name="block_ref",le="0.5"} 677
+table_put_request_duration_sum{table_name="block_ref"} 61.617528636
+table_put_request_duration_count{table_name="block_ref"} 677
+```
+
+#### `table_internal_delete_counter` (counter)
+
+Number of value deletions in the tree (due to GC or repartitioning)
+
+```
+table_internal_delete_counter{table_name="block_ref"} 2296
+```
+
+#### `table_internal_update_counter` (counter)
+
+Number of value updates where the value actually changes (includes creation of new key and update of existing key)
+
+```
+table_internal_update_counter{table_name="block_ref"} 5996
+```
+
+#### `table_merkle_updater_todo_queue_length` (gauge)
+
+Merkle tree updater TODO queue length (should fall to zero rapidly)
+
+```
+table_merkle_updater_todo_queue_length{table_name="block_ref"} 0
+```
+
+#### `table_sync_items_received`, `table_sync_items_sent` (counters)
+
+Number of data items sent to/recieved from other nodes during resync procedures
+
+```
+table_sync_items_received{from="<remote node>",table_name="bucket_v2"} 3
+table_sync_items_sent{table_name="block_ref",to="<remote node>"} 2
+```
+
+
--- a/doc/book/reference-manual/s3-compatibility.md
+++ b/doc/book/reference-manual/s3-compatibility.md
@ -1,6 +1,6 @@
 +++
 title = "S3 Compatibility status"
-weight = 40
+weight = 70
 +++

 ## DISCLAIMER
--- a/doc/book/working-documents/migration-08.md
+++ b/doc/book/working-documents/migration-08.md
@ -12,13 +12,15 @@ back up all your data before attempting it!**
 Garage v0.8 introduces new data tables that allow the counting of objects in buckets in order to implement bucket quotas.
 A manual migration step is required to first count objects in Garage buckets and populate these tables with accurate data.

+## Simple migration procedure (takes cluster offline for a while)
+
 The migration steps are as follows:

 1. Disable API and web access. Garage v0.7 does not support disabling
   these endpoints but you can change the port number or stop your reverse proxy for instance.
 2. Do `garage repair --all-nodes --yes tables` and `garage repair --all-nodes --yes blocks`,
   check the logs and check that all data seems to be synced correctly between
-   nodes. If you have time, do additional checks (`scrub`, `block_refs`, etc.)
+   nodes. If you have time, do additional checks (`versions`, `block_refs`, etc.)
 3. Check that queues are empty: run `garage stats` to query them or inspect metrics in the Grafana dashboard.
 4. Turn off Garage v0.7
 5. **Backup the metadata folder of all your nodes!** For instance, use the following command
@ -32,3 +34,24 @@ The migration steps are as follows:
 10. Your upgraded cluster should be in a working state. Re-enable API and Web
    access and check that everything went well.
 11. Monitor your cluster in the next hours to see if it works well under your production load, report any issue.
+
+## Minimal downtime migration procedure
+
+The migration to Garage v0.8 can be done with almost no downtime,
+by restarting all nodes at once in the new version. The only limitation with this
+method is that bucket sizes and item counts will not be estimated correctly
+until all nodes have had a chance to run their offline migration procedure.
+
+The migration steps are as follows:
+
+1. Do `garage repair --all-nodes --yes tables` and `garage repair --all-nodes --yes blocks`,
+   check the logs and check that all data seems to be synced correctly between
+   nodes. If you have time, do additional checks (`versions`, `block_refs`, etc.)
+
+2. Turn off each node individually; back up its metadata folder (see above); turn it back on again. This will allow you to take a backup of all nodes without impacting global cluster availability. You can do all nodes of a single zone at once as this does not impact the availability of Garage.
+
+3. Prepare your binaries and configuration files for Garage v0.8
+
+4. Shut down all v0.7 nodes simultaneously, and restart them all simultaneously in v0.8. Use your favorite deployment tool (Ansible, Kubernetes, Nomad) to achieve this as fast as possible.
+
+5. At this point, Garage will indicate invalid values for the size and number of objects in each bucket (most likely, it will indicate zero). To fix this, take each node offline individually to do the offline migration step: `garage offline-repair --yes object_counters`. Again you can do all nodes of a single zone at once.
--- a/doc/drafts/k2v-spec.md
+++ b/doc/drafts/k2v-spec.md
@ -706,6 +706,73 @@ HTTP/1.1 200 OK
 ]
 ```

+**PollRange: `POST /<bucket>/<partition key>?poll_range`**, or alternatively<br/>
+**PollRange: `SEARCH /<bucket>/<partition key>?poll_range`**
+
+Polls a range of items for changes.
+
+The query body is a JSON object consisting of the following fields:
+
+| name            | default value | meaning                                                                                |
+|-----------------|---------------|----------------------------------------------------------------------------------------|
+| `prefix`        | `null`        | Restrict items to poll to those whose sort keys start with this prefix                 |
+| `start`         | `null`        | The sort key of the first item to poll                                                 |
+| `end`           | `null`        | The sort key of the last item to poll (excluded)                                       |
+| `timeout`       | 300           | The timeout before 304 NOT MODIFIED is returned if no value in the range is updated    |
+| `seenMarker`    | `null`        | An opaque string returned by a previous PollRange call, that represents items already seen |
+
+The timeout can be set to any number of seconds, with a maximum of 600 seconds (10 minutes).
+
+The response is either:
+
+- A HTTP 304 NOT MODIFIED response with an empty body, if the timeout expired and no changes occurred
+
+- A HTTP 200 response, indicating that some changes have occurred since the last PollRange call, in which case a JSON object is returned in the body with the following fields:
+
+| name            | meaning                                                                                |
+|-----------------|----------------------------------------------------------------------------------------|
+| `seenMarker`    | An opaque string that represents items already seen for future PollRange calls         |
+| `items`         | The list of items that have changed since last PollRange call, in the same format as ReadBatch |
+
+If no seen marker is known by the caller, it can do a PollRange call
+without specifying `seenMarker`. In this case, the PollRange call will
+complete immediately, and return the current content of the range (which
+can be empty) and a seen marker to be used in further PollRange calls. This
+is the only case in which PollRange might return an HTTP 200 with an empty
+set of items.
+
+A seen marker returned as a response to a PollRange query can be used for further PollRange
+queries on the same range, or for PollRange queries in a subrange of the initial range.
+It may not be used for PollRange queries on ranges larger or outside of the initial range.
+
+Example query:
+
+```json
+SEARCH /my_bucket?poll_range HTTP/1.1
+
+{
+  "prefix": "0391.",
+  "start": "0391.000001973107",
+  "seenMarker": "opaquestring123",
+}
+```
+
+
+Example response:
+
+```json
+HTTP/1.1 200 OK
+Content-Type: application/json
+
+{
+  "seenMarker": "opaquestring456",
+  "items": [
+    { sk: "0391.000001973221", ct: "opaquetoken123", v: ["b64cryptoblob123", "b64cryptoblob'123"] },
+    { sk: "0391.000001974191", ct: "opaquetoken456", v: ["b64cryptoblob456", "b64cryptoblob'456"] },
+  ]
+}
+```
+

 ## Internals: causality tokens

--- a/doc/logo/garage_hires_crop.png
+++ b/doc/logo/garage_hires_crop.png
--- a/doc/sticker/Garage.svg
+++ b/doc/sticker/Garage.svg
--- a/doc/sticker/Garage_NGI.pdf
+++ b/doc/sticker/Garage_NGI.pdf
--- a/doc/sticker/Garage_NGI.png
+++ b/doc/sticker/Garage_NGI.png
--- a/doc/sticker/Garage_NGI.svg
+++ b/doc/sticker/Garage_NGI.svg
--- a/doc/talks/.envrc
+++ b/doc/talks/.envrc
@ -0,0 +1 @@
+use_nix
--- a/doc/talks/2023-01-18-tocatta/.gitignore
+++ b/doc/talks/2023-01-18-tocatta/.gitignore
@ -0,0 +1,17 @@
+*
+
+!*.txt
+!*.md
+
+!assets
+
+!.gitignore
+!*.svg
+!*.png
+!*.jpg
+!*.tex
+!Makefile
+!.gitignore
+!assets/*.drawio.pdf
+
+!talk.pdf
--- a/doc/talks/2023-01-18-tocatta/Makefile
+++ b/doc/talks/2023-01-18-tocatta/Makefile
@ -0,0 +1,34 @@
+ASSETS=assets/consistent_hashing_1.pdf \
+	   assets/consistent_hashing_2.pdf \
+	   assets/consistent_hashing_3.pdf \
+	   assets/consistent_hashing_4.pdf \
+	   assets/garage_tables.pdf \
+	   assets/consensus.pdf_tex \
+	   assets/lattice1.pdf_tex \
+	   assets/lattice2.pdf_tex \
+	   assets/lattice3.pdf_tex \
+	   assets/lattice4.pdf_tex \
+	   assets/lattice5.pdf_tex \
+	   assets/lattice6.pdf_tex \
+	   assets/lattice7.pdf_tex \
+	   assets/lattice8.pdf_tex \
+	   assets/latticeB_1.pdf_tex \
+	   assets/latticeB_2.pdf_tex \
+	   assets/latticeB_3.pdf_tex \
+	   assets/latticeB_4.pdf_tex \
+	   assets/latticeB_5.pdf_tex \
+	   assets/latticeB_6.pdf_tex \
+	   assets/latticeB_7.pdf_tex \
+	   assets/latticeB_8.pdf_tex \
+	   assets/latticeB_9.pdf_tex \
+	   assets/latticeB_10.pdf_tex \
+	   assets/deuxfleurs.pdf
+
+talk.pdf: talk.tex $(ASSETS)
+	pdflatex talk.tex
+
+assets/%.pdf: assets/%.svg
+	inkscape -D -z --file=$^ --export-pdf=$@
+
+assets/%.pdf_tex: assets/%.svg
+	inkscape -D -z --file=$^ --export-pdf=$@ --export-latex
--- a/doc/talks/2023-01-18-tocatta/abstract.md
+++ b/doc/talks/2023-01-18-tocatta/abstract.md
@ -0,0 +1,39 @@
+### (fr) Garage, un système de stockage de données géo-distribué léger et robuste
+
+Garage est un système de stockage de données léger, géo-distribué, qui
+implémente le protocole de stockage S3 de Amazon. Garage est destiné
+principalement à l'auto-hébergement sur du matériel courant d'occasion. À ce
+titre, il doit tolérer un grand nombre de pannes: coupures de courant, coupures
+de connexion Internet, pannes de machines, ... Il doit également être facile à
+déployer et à maintenir, afin de pouvoir être facilement utilisé par des
+amateurs ou des petites organisations.
+
+Cette présentation vous proposera un aperçu de Garage et du choix technique
+principal qui rend un système comme Garage possible: le refus d'utiliser des
+algorithmes de consensus, remplacés avantageusement par des méthodes à
+cohérence faible.  Notre modèle est fortement inspiré de la base de donnée
+Dynamo (DeCandia et al, 2007), et fait usage des types de données CRDT (Shapiro
+et al, 2011).  Nous exploreront comment ces méthodes s'appliquent à la
+construction de l'abstraction "stockage objet" dans un système distribué, et
+quelles autres abstractions peuvent ou ne peuvent pas être construites dans ce
+modèle.
+
+### (en) Garage, a lightweight and robust geo-distributed data storage system
+
+Garage is a lightweight geo-distributed data store that implements the Amazon
+S3 object storage protocol.  Garage is meant primarily for self-hosting at home
+on second-hand commodity hardware, meaning it has to tolerate a wide variety of
+failure scenarios such as power cuts, Internet disconnections and machine
+crashes. It also has to be easy to deploy and maintain, so that hobbyists and
+small organizations can use it without trouble. 
+
+This talk will present Garage and the key technical choice that made Garage
+possible: refusing to use consensus algorithms and using instead weak
+consistency methods, with a model that is loosely based on that of the Dynamo
+database (DeCandia et al, 2007) and that makes heavy use of conflict-free
+replicated data types (Shapiro et al, 2011).  We will explore how these methods
+are suited to building the "object store" abstraction in a distributed system,
+and what other abstractions are possible or impossible to build in this model.
+
+
+
--- a/doc/talks/2023-01-18-tocatta/assets/AGPLv3_Logo.png
+++ b/doc/talks/2023-01-18-tocatta/assets/AGPLv3_Logo.png
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme.png
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme.png
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme.svg
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_components1.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_components1.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_components1.png
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_components1.png
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_components2.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_components2.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_components2.png
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_components2.png
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_datatype.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_datatype.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_datatype.png
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_datatype.png
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_keys.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_keys.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/aerogramme_keys.png
+++ b/doc/talks/2023-01-18-tocatta/assets/aerogramme_keys.png
--- a/doc/talks/2023-01-18-tocatta/assets/alex.jpg
+++ b/doc/talks/2023-01-18-tocatta/assets/alex.jpg
--- a/doc/talks/2023-01-18-tocatta/assets/atuin.jpg
+++ b/doc/talks/2023-01-18-tocatta/assets/atuin.jpg
--- a/doc/talks/2023-01-18-tocatta/assets/compatibility.png
+++ b/doc/talks/2023-01-18-tocatta/assets/compatibility.png
--- a/doc/talks/2023-01-18-tocatta/assets/consensus.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/consensus.svg
@ -0,0 +1,137 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="800"
+   height="300"
+   viewBox="0 0 211.66666 79.374999"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="consensus.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="310.49139"
+     inkscape:cy="179.1688"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer1" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <g
+       id="g1218"
+       transform="translate(-8.9161476,-12.502301)">
+      <circle
+         style="fill:#ffffff;stroke:#000000;stroke-width:1;stroke-dasharray:none;stroke-opacity:1"
+         id="path111"
+         cx="38.904896"
+         cy="37.936272"
+         r="13.474442" />
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="38.879501"
+         y="40.908073"
+         id="text1105"><tspan
+           sodipodi:role="line"
+           id="tspan1103"
+           style="stroke-width:0.264583;fill:#000000"
+           x="38.879501"
+           y="40.908073">$\bot$</tspan></text>
+    </g>
+    <g
+       id="g1218-3"
+       transform="translate(127.41938,-12.502301)">
+      <circle
+         style="fill:#ffffff;stroke:#000000;stroke-width:1;stroke-dasharray:none;stroke-opacity:1"
+         id="path111-5"
+         cx="38.904896"
+         cy="37.936272"
+         r="13.474442" />
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="38.879501"
+         y="40.908073"
+         id="text1105-6"><tspan
+           sodipodi:role="line"
+           id="tspan1103-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="38.879501"
+           y="40.908073">$x$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 44.289635,25.433971 H 145.90576"
+       id="path1414"
+       sodipodi:nodetypes="cc" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="92.729836"
+       y="21.781803"
+       id="text2092"><tspan
+         sodipodi:role="line"
+         id="tspan2090"
+         style="stroke-width:0.264583;fill:#000000"
+         x="92.729836"
+         y="21.781803">$propose(x) / x$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="166.29887"
+       y="69.89299"
+       id="text2092-9"><tspan
+         sodipodi:role="line"
+         id="tspan2090-1"
+         style="stroke-width:0.264583;fill:#000000"
+         x="166.29887"
+         y="69.89299">$propose(y) / x$</tspan></text>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="m 155.82329,35.899857 c -8.35129,12.319651 0.54055,24.640898 11.72797,24.072085 8.65403,-0.440005 18.59818,-11.705963 11.8146,-20.570891"
+       id="path2150"
+       sodipodi:nodetypes="csc" />
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_1.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_1.svg
--- a/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_2.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_2.svg
--- a/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_3.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_3.svg
--- a/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_4.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/consistent_hashing_4.svg
--- a/doc/talks/2023-01-18-tocatta/assets/deuxfleurs.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/deuxfleurs.svg
@ -0,0 +1,91 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg
+   viewBox="0 0 70.424515 70.300102"
+   version="1.1"
+   id="svg8"
+   sodipodi:docname="logo.svg"
+   inkscape:version="1.1 (c68e22c387, 2021-05-23)"
+   inkscape:export-filename="/home/quentin/Documents/dev/deuxfleurs/site/src/img/logo.png"
+   inkscape:export-xdpi="699.30194"
+   inkscape:export-ydpi="699.30194"
+   width="70.424515"
+   height="70.300102"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <defs
+     id="defs12" />
+  <sodipodi:namedview
+     id="namedview10"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:pageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     showgrid="false"
+     inkscape:zoom="12.125"
+     inkscape:cx="43.092783"
+     inkscape:cy="48.082474"
+     inkscape:window-width="3072"
+     inkscape:window-height="1659"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="svg8" />
+  <g
+     id="g79969"
+     transform="translate(-0.827,34.992103)">
+    <path
+       fill="#ffffff"
+       d="m 15.632,34.661 c -0.799,-0.597 -1.498,-1.484 -2.035,-2.592 l -0.228,-0.47 -0.46,0.249 c -0.975,0.528 -1.913,0.858 -2.744,0.969 L 9.963,29.061 6.327,30.029 C 6.17,29.175 6.202,28.142 6.423,27.007 L 6.526,26.482 5.994,26.416 C 4.752,26.262 3.688,25.891 2.89,25.336 L 4.411,22.419 1.423,20.896 C 1.742,19.952 2.371,19.014 3.257,18.161 L 3.634,17.798 3.255,17.438 C 2.452,16.674 1.847,15.884 1.485,15.127 L 4.995,13.774 2.95,10.615 C 3.69,10.213 4.643,9.929 5.739,9.783 L 6.258,9.715 6.167,9.201 C 5.952,7.99 5.995,6.863 6.291,5.913 l 3.308,0.523 0.524,-3.308 c 0.988,0.013 2.08,0.326 3.164,0.907 L 13.749,4.283 13.975,3.81 C 14.454,2.807 15.019,1.986 15.628,1.406 L 18,4.326 20.372,1.406 c 0.609,0.58 1.175,1.401 1.653,2.404 l 0.226,0.473 0.462,-0.247 C 23.798,3.455 24.891,3.142 25.877,3.13 L 26.4,6.438 29.71,5.913 c 0.296,0.951 0.34,2.078 0.124,3.288 l -0.092,0.515 0.518,0.069 c 1.095,0.145 2.048,0.43 2.788,0.832 l -2.046,3.156 3.511,1.355 c -0.361,0.757 -0.966,1.547 -1.77,2.311 l -0.379,0.36 0.377,0.363 c 0.888,0.854 1.516,1.793 1.835,2.736 l -2.984,1.52 1.521,2.984 c -0.812,0.574 -1.871,0.964 -3.094,1.134 l -0.518,0.072 0.096,0.514 c 0.201,1.089 0.226,2.083 0.073,2.909 l -3.634,-0.97 -0.204,3.757 c -0.83,-0.11 -1.768,-0.44 -2.742,-0.968 l -0.459,-0.249 -0.228,0.47 c -0.539,1.107 -1.237,1.994 -2.036,2.591 L 18,32.293 Z"
+       id="path2" />
+    <path
+       d="M 7.092,10.678 C 6.562,9.189 6.394,7.708 6.66,6.478 l 2.368,0.375 0.987,0.156 0.157,-0.988 0.375,-2.368 C 11.808,3.78 13.16,4.396 14.409,5.359 14.527,5.022 14.653,4.696 14.791,4.392 13.24,3.257 11.568,2.629 10.061,2.629 9.938,2.629 9.816,2.633 9.695,2.642 L 9.184,5.865 5.96,5.354 C 5.36,6.841 5.395,8.769 6.045,10.747 6.38,10.71 6.729,10.686 7.092,10.678 Z M 21.593,5.359 c 1.248,-0.962 2.6,-1.578 3.86,-1.705 l 0.376,2.368 0.156,0.988 0.987,-0.157 2.369,-0.376 c 0.266,1.23 0.098,2.71 -0.432,4.2 0.361,0.009 0.711,0.032 1.046,0.07 C 30.606,8.769 30.64,6.841 30.04,5.353 L 26.815,5.865 26.304,2.641 c -0.12,-0.008 -0.242,-0.012 -0.365,-0.012 -1.507,0 -3.179,0.628 -4.73,1.762 0.14,0.306 0.266,0.631 0.384,0.968 z M 7.368,27 h 0.035 c 0.067,0 0.157,-0.604 0.26,-0.947 -0.098,0.004 -0.197,0.046 -0.294,0.046 -1.496,0 -2.826,-0.303 -3.83,-0.89 L 4.628,23.081 5.082,22.194 4.191,21.742 2.055,20.654 C 2.563,19.503 3.57,18.404 4.873,17.511 4.586,17.292 4.312,17.07 4.063,16.842 2.376,18.059 1.217,19.597 0.828,21.152 l 2.908,1.483 -1.482,2.843 C 3.475,26.501 5.303,27 7.368,27 Z m 27.806,-5.846 c -0.39,-1.555 -1.548,-3.093 -3.234,-4.311 -0.25,0.228 -0.523,0.451 -0.81,0.669 1.304,0.893 2.31,1.992 2.817,3.145 l -2.136,1.088 -0.891,0.453 0.454,0.892 1.089,2.137 c -1.004,0.587 -2.332,0.904 -3.828,0.904 -0.099,0 -0.199,-0.01 -0.299,-0.013 0.103,0.344 0.192,0.683 0.26,1.011 l 0.039,0.002 c 2.066,0 3.892,-0.563 5.112,-1.587 l -1.482,-2.908 z m -12.653,9.182 c -0.447,1.517 -1.181,2.812 -2.119,3.651 L 18.707,32.293 18,31.586 l -0.707,0.707 -1.695,1.694 c -0.938,-0.839 -1.673,-2.136 -2.12,-3.652 -0.296,0.206 -0.593,0.397 -0.886,0.563 0.636,1.98 1.741,3.559 3.1,4.409 L 18,33 l 2.308,2.308 c 1.358,-0.851 2.464,-2.428 3.101,-4.408 -0.295,-0.168 -0.591,-0.359 -0.888,-0.564 z"
+       fill="#ea596e"
+       id="path4" />
+    <path
+       fill="#ea596e"
+       d="m 20.118,5.683 c 0.426,1.146 0.748,2.596 0.841,4.284 l 0.2,3.683 3.564,-0.946 c 1.32,-0.351 2.655,-0.536 3.86,-0.536 0.16,0 0.318,0.003 0.474,0.01 l -1.827,2.819 3.139,1.211 c -0.958,0.759 -2.237,1.514 -3.814,2.123 l -3.441,1.328 2.001,3.099 c 0.918,1.42 1.509,2.782 1.838,3.96 L 23.709,25.853 23.527,29.21 C 22.508,28.533 21.395,27.55 20.329,26.237 L 18,23.374 15.672,26.236 c -1.066,1.312 -2.179,2.295 -3.198,2.972 l -0.18,-3.354 -3.248,0.864 c 0.329,-1.178 0.921,-2.54 1.839,-3.961 L 12.889,19.658 9.447,18.33 C 7.87,17.721 6.591,16.967 5.633,16.208 L 8.768,15 6.941,12.177 c 0.155,-0.006 0.313,-0.01 0.473,-0.01 1.206,0 2.541,0.185 3.861,0.536 l 3.564,0.947 0.202,-3.683 c 0.092,-1.688 0.415,-3.138 0.84,-4.284 L 18,8.292 20.118,5.683 M 20.308,0.692 18,3.533 15.692,0.692 C 13.703,2.224 12.271,5.684 12.046,9.804 10.429,9.374 8.854,9.167 7.414,9.167 c -2.11,0 -3.929,0.445 -5.161,1.289 l 1.989,3.073 -3.415,1.316 c 0.842,2.366 3.69,4.797 7.54,6.283 -2.241,3.465 -3.116,7.106 -2.407,9.516 l 3.537,-0.941 0.196,3.654 c 2.512,-0.07 5.703,-2.027 8.307,-5.228 2.603,3.201 5.796,5.158 8.306,5.228 l 0.198,-3.655 3.535,0.943 c 0.71,-2.411 -0.165,-6.05 -2.404,-9.517 3.849,-1.485 6.696,-3.918 7.538,-6.283 l -3.415,-1.318 1.99,-3.07 c -1.233,-0.844 -3.053,-1.29 -5.164,-1.29 -1.438,0 -3.013,0.207 -4.63,0.636 C 23.729,5.684 22.297,2.224 20.308,0.692 Z"
+       id="path6" />
+  </g>
+  <g
+     id="g79964"
+     transform="translate(-1.043816,35.993714)">
+    <path
+       fill="#ffffff"
+       d="m 51.92633,-2.0247139 c -0.799,-0.597 -1.498,-1.484 -2.035,-2.592 l -0.228,-0.47 -0.46,0.249 c -0.975,0.528 -1.913,0.858 -2.744,0.969 l -0.202,-3.7560001 -3.636,0.968 c -0.157,-0.854 -0.125,-1.887 0.096,-3.022 l 0.103,-0.525 -0.532,-0.066 c -1.242,-0.154 -2.306,-0.525 -3.104,-1.08 l 1.521,-2.917 -2.988,-1.523 c 0.319,-0.944 0.948,-1.882 1.834,-2.735 l 0.377,-0.363 -0.379,-0.36 c -0.803,-0.764 -1.408,-1.554 -1.77,-2.311 l 3.51,-1.353 -2.045,-3.159 c 0.74,-0.402 1.693,-0.686 2.789,-0.832 l 0.519,-0.068 -0.091,-0.514 c -0.215,-1.211 -0.172,-2.338 0.124,-3.288 l 3.308,0.523 0.524,-3.308 c 0.988,0.013 2.08,0.326 3.164,0.907 l 0.462,0.248 0.226,-0.473 c 0.479,-1.003 1.044,-1.824 1.653,-2.404 l 2.372,2.92 2.372,-2.92 c 0.609,0.58 1.175,1.401 1.653,2.404 l 0.226,0.473 0.462,-0.247 c 1.085,-0.581 2.178,-0.894 3.164,-0.906 l 0.523,3.308 3.31,-0.525 c 0.296,0.951 0.34,2.078 0.124,3.288 l -0.092,0.515 0.518,0.069 c 1.095,0.145 2.048,0.43 2.788,0.832 l -2.046,3.156 3.511,1.355 c -0.361,0.757 -0.966,1.547 -1.77,2.311 l -0.379,0.36 0.377,0.363 c 0.888,0.854 1.516,1.793 1.835,2.736 l -2.984,1.52 1.521,2.984 c -0.812,0.574 -1.871,0.964 -3.094,1.134 l -0.518,0.072 0.096,0.514 c 0.201,1.089 0.226,2.083 0.073,2.909 l -3.634,-0.97 -0.204,3.7570001 c -0.83,-0.11 -1.768,-0.44 -2.742,-0.968 l -0.459,-0.249 -0.228,0.47 c -0.539,1.107 -1.237,1.994 -2.036,2.591 l -2.367,-2.369 z"
+       id="path2-9" />
+    <path
+       d="m 43.38633,-26.007714 c -0.53,-1.489 -0.698,-2.97 -0.432,-4.2 l 2.368,0.375 0.987,0.156 0.157,-0.988 0.375,-2.368 c 1.261,0.127 2.613,0.743 3.862,1.706 0.118,-0.337 0.244,-0.663 0.382,-0.967 -1.551,-1.135 -3.223,-1.763 -4.73,-1.763 -0.123,0 -0.245,0.004 -0.366,0.013 l -0.511,3.223 -3.224,-0.511 c -0.6,1.487 -0.565,3.415 0.085,5.393 0.335,-0.037 0.684,-0.061 1.047,-0.069 z m 14.501,-5.319 c 1.248,-0.962 2.6,-1.578 3.86,-1.705 l 0.376,2.368 0.156,0.988 0.987,-0.157 2.369,-0.376 c 0.266,1.23 0.098,2.71 -0.432,4.2 0.361,0.009 0.711,0.032 1.046,0.07 0.651,-1.978 0.685,-3.906 0.085,-5.394 l -3.225,0.512 -0.511,-3.224 c -0.12,-0.008 -0.242,-0.012 -0.365,-0.012 -1.507,0 -3.179,0.628 -4.73,1.762 0.14,0.306 0.266,0.631 0.384,0.968 z m -14.225,21.641 h 0.035 c 0.067,0 0.157,-0.604 0.26,-0.947 -0.098,0.004 -0.197,0.046 -0.294,0.046 -1.496,0 -2.826,-0.303 -3.83,-0.89 l 1.089,-2.128 0.454,-0.887 -0.891,-0.452 -2.136,-1.088 c 0.508,-1.151 1.515,-2.25 2.818,-3.143 -0.287,-0.219 -0.561,-0.441 -0.81,-0.669 -1.687,1.217 -2.846,2.755 -3.235,4.31 l 2.908,1.483 -1.482,2.843 c 1.221,1.023 3.049,1.522 5.114,1.522 z m 27.806,-5.846 c -0.39,-1.555 -1.548,-3.093 -3.234,-4.311 -0.25,0.228 -0.523,0.451 -0.81,0.669 1.304,0.893 2.31,1.992 2.817,3.145 l -2.136,1.088 -0.891,0.453 0.454,0.892 1.089,2.137 c -1.004,0.587 -2.332,0.904 -3.828,0.904 -0.099,0 -0.199,-0.01 -0.299,-0.013 0.103,0.344 0.192,0.683 0.26,1.011 l 0.039,0.002 c 2.066,0 3.892,-0.563 5.112,-1.587 l -1.482,-2.908 z m -12.653,9.182 c -0.447,1.5170001 -1.181,2.8120001 -2.119,3.6510001 l -1.695,-1.694 -0.707,-0.707 -0.707,0.707 -1.695,1.694 c -0.938,-0.839 -1.673,-2.136 -2.12,-3.6520001 -0.296,0.2060001 -0.593,0.3970001 -0.886,0.5630001 0.636,1.98 1.741,3.559 3.1,4.409 l 2.308,-2.307 2.308,2.308 c 1.358,-0.851 2.464,-2.428 3.101,-4.408 -0.295,-0.168 -0.591,-0.359 -0.888,-0.5640001 z"
+       fill="#ea596e"
+       id="path4-3" />
+    <path
+       fill="#ea596e"
+       d="m 56.41233,-31.002714 c 0.426,1.146 0.748,2.596 0.841,4.284 l 0.2,3.683 3.564,-0.946 c 1.32,-0.351 2.655,-0.536 3.86,-0.536 0.16,0 0.318,0.003 0.474,0.01 l -1.827,2.819 3.139,1.211 c -0.958,0.759 -2.237,1.514 -3.814,2.123 l -3.441,1.328 2.001,3.099 c 0.918,1.42 1.509,2.782 1.838,3.96 l -3.244,-0.865 -0.182,3.357 c -1.019,-0.677 -2.132,-1.66 -3.198,-2.973 l -2.329,-2.863 -2.328,2.862 c -1.066,1.312 -2.179,2.295 -3.198,2.972 l -0.18,-3.354 -3.248,0.864 c 0.329,-1.178 0.921,-2.54 1.839,-3.961 l 2.004,-3.099 -3.442,-1.328 c -1.577,-0.609 -2.856,-1.363 -3.814,-2.122 l 3.135,-1.208 -1.827,-2.823 c 0.155,-0.006 0.313,-0.01 0.473,-0.01 1.206,0 2.541,0.185 3.861,0.536 l 3.564,0.947 0.202,-3.683 c 0.092,-1.688 0.415,-3.138 0.84,-4.284 l 2.119,2.609 2.118,-2.609 m 0.19,-4.991 -2.308,2.841 -2.308,-2.841 c -1.989,1.532 -3.421,4.992 -3.646,9.112 -1.617,-0.43 -3.192,-0.637 -4.632,-0.637 -2.11,0 -3.929,0.445 -5.161,1.289 l 1.989,3.073 -3.415,1.316 c 0.842,2.366 3.69,4.797 7.54,6.283 -2.241,3.465 -3.116,7.106 -2.407,9.5160001 l 3.537,-0.9410001 0.196,3.6540001 c 2.512,-0.07 5.703,-2.027 8.307,-5.2280001 2.603,3.2010001 5.796,5.1580001 8.306,5.2280001 l 0.198,-3.6550001 3.535,0.9430001 c 0.71,-2.4110001 -0.165,-6.0500001 -2.404,-9.5170001 3.849,-1.485 6.696,-3.918 7.538,-6.283 l -3.415,-1.318 1.99,-3.07 c -1.233,-0.844 -3.053,-1.29 -5.164,-1.29 -1.438,0 -3.013,0.207 -4.63,0.636 -0.225,-4.119 -1.657,-7.579 -3.646,-9.111 z"
+       id="path6-6" />
+  </g>
+  <text
+     xml:space="preserve"
+     style="font-style:normal;font-weight:normal;font-size:42.6667px;line-height:1.25;font-family:sans-serif;fill:#ea596e;fill-opacity:1;stroke:none"
+     x="2.2188232"
+     y="31.430677"
+     id="text46212"><tspan
+       sodipodi:role="line"
+       id="tspan46210"
+       x="2.2188232"
+       y="31.430677"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:42.6667px;font-family:'TeX Gyre Termes';-inkscape-font-specification:'TeX Gyre Termes'">D</tspan></text>
+  <text
+     xml:space="preserve"
+     style="font-style:normal;font-weight:normal;font-size:42.6667px;line-height:1.25;font-family:sans-serif;fill:#ea596e;fill-opacity:1;stroke:none"
+     x="41.347008"
+     y="67.114784"
+     id="text46212-1"><tspan
+       sodipodi:role="line"
+       id="tspan46210-5"
+       x="41.347008"
+       y="67.114784"
+       style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:42.6667px;font-family:'TeX Gyre Termes';-inkscape-font-specification:'TeX Gyre Termes'">F</tspan></text>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/endpoint-latency-dc.png
+++ b/doc/talks/2023-01-18-tocatta/assets/endpoint-latency-dc.png
--- a/doc/talks/2023-01-18-tocatta/assets/garage.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/garage.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/garage.drawio.png
+++ b/doc/talks/2023-01-18-tocatta/assets/garage.drawio.png
--- a/doc/talks/2023-01-18-tocatta/assets/garage2.drawio.png
+++ b/doc/talks/2023-01-18-tocatta/assets/garage2.drawio.png
--- a/doc/talks/2023-01-18-tocatta/assets/garage2a.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/garage2a.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/garage2b.drawio.pdf
+++ b/doc/talks/2023-01-18-tocatta/assets/garage2b.drawio.pdf
--- a/doc/talks/2023-01-18-tocatta/assets/garage_tables.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/garage_tables.svg
@ -0,0 +1,537 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<svg
+   width="850"
+   height="480"
+   viewBox="0 0 224.89584 127"
+   version="1.1"
+   id="svg8"
+   inkscape:version="1.2 (dc2aedaf03, 2022-05-15)"
+   sodipodi:docname="garage_tables.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg"
+   xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#"
+   xmlns:cc="http://creativecommons.org/ns#"
+   xmlns:dc="http://purl.org/dc/elements/1.1/">
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="marker1262"
+       refX="0"
+       refY="0"
+       orient="auto"
+       inkscape:stockid="Arrow1Mend"
+       inkscape:isstock="true">
+      <path
+         transform="matrix(-0.4,0,0,-0.4,-4,0)"
+         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1"
+         d="M 0,0 5,-5 -12.5,0 5,5 Z"
+         id="path1260" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow1Mend"
+       refX="0"
+       refY="0"
+       orient="auto"
+       inkscape:stockid="Arrow1Mend"
+       inkscape:isstock="true"
+       inkscape:collect="always">
+      <path
+         transform="matrix(-0.4,0,0,-0.4,-4,0)"
+         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1"
+         d="M 0,0 5,-5 -12.5,0 5,5 Z"
+         id="path965" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow1Lend"
+       refX="0"
+       refY="0"
+       orient="auto"
+       inkscape:stockid="Arrow1Lend"
+       inkscape:isstock="true">
+      <path
+         transform="matrix(-0.8,0,0,-0.8,-10,0)"
+         style="fill:#000000;fill-opacity:1;fill-rule:evenodd;stroke:#000000;stroke-width:1pt;stroke-opacity:1"
+         d="M 0,0 5,-5 -12.5,0 5,5 Z"
+         id="path959" />
+    </marker>
+  </defs>
+  <sodipodi:namedview
+     id="base"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:pageopacity="0.0"
+     inkscape:pageshadow="2"
+     inkscape:zoom="0.98994949"
+     inkscape:cx="429.31483"
+     inkscape:cy="289.40871"
+     inkscape:document-units="mm"
+     inkscape:current-layer="layer1"
+     inkscape:document-rotation="0"
+     showgrid="false"
+     units="px"
+     inkscape:window-width="1678"
+     inkscape:window-height="993"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:showpageshadow="2"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1" />
+  <metadata
+     id="metadata5">
+    <rdf:RDF>
+      <cc:Work
+         rdf:about="">
+        <dc:format>image/svg+xml</dc:format>
+        <dc:type
+           rdf:resource="http://purl.org/dc/dcmitype/StillImage" />
+        <dc:title />
+      </cc:Work>
+    </rdf:RDF>
+  </metadata>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1">
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="39.570904"
+       y="38.452755"
+       id="text2025"><tspan
+         sodipodi:role="line"
+         id="tspan2023"
+         x="39.570904"
+         y="38.452755"
+         style="font-size:5.64444px;stroke-width:0.264583" /></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:10.5833px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="101.95796"
+       y="92.835831"
+       id="text2139"><tspan
+         sodipodi:role="line"
+         id="tspan2137"
+         x="101.95796"
+         y="92.835831"
+         style="stroke-width:0.264583"> </tspan></text>
+    <g
+       id="g2316"
+       transform="translate(-11.455511,1.5722486)">
+      <g
+         id="g2277">
+        <rect
+           style="fill:none;stroke:#000000;stroke-width:0.8;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+           id="rect833"
+           width="47.419891"
+           height="95.353409"
+           x="18.534418"
+           y="24.42766" />
+        <rect
+           style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+           id="rect833-3"
+           width="47.419891"
+           height="86.973076"
+           x="18.534418"
+           y="32.807987" />
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="32.250839"
+           y="29.894743"
+           id="text852"><tspan
+             sodipodi:role="line"
+             id="tspan850"
+             x="32.250839"
+             y="29.894743"
+             style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Object</tspan></text>
+      </g>
+      <g
+         id="g2066"
+         transform="translate(-2.1807817,-3.0621439)">
+        <g
+           id="g1969"
+           transform="matrix(0.12763631,0,0,0.12763631,0.7215051,24.717273)"
+           style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-opacity:1">
+          <path
+             style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.264583;stroke-opacity:1"
+             d="m 203.71837,154.80038 c -1.11451,3.75057 -2.45288,5.84095 -5.11132,7.98327 -2.2735,1.83211 -4.66721,2.65982 -8.09339,2.79857 -2.59227,0.10498 -2.92868,0.0577 -5.02863,-0.70611 -3.99215,-1.45212 -7.1627,-4.65496 -8.48408,-8.57046 -1.28374,-3.80398 -0.61478,-8.68216 1.64793,-12.01698 0.87317,-1.28689 3.15089,-3.48326 4.18771,-4.03815 l 0.53332,-28.51234 5.78454,-5.09197 6.95158,6.16704 -3.21112,3.49026 3.17616,3.45499 -3.17616,3.40822 2.98973,3.28645 -3.24843,3.3829 4.49203,4.58395 0.0516,5.69106 c 1.06874,0.64848 3.81974,3.24046 4.69548,4.56257 0.452,0.68241 1.06834,2.0197 1.36962,2.97176 0.62932,1.98864 0.88051,5.785 0.47342,7.15497 z m -10.0406,2.32604 c -0.88184,-3.17515 -4.92402,-3.78864 -6.75297,-1.02492 -0.58328,0.8814 -0.6898,1.28852 -0.58362,2.23056 0.26492,2.35041 2.45434,3.95262 4.60856,3.37255 1.19644,-0.32217 2.39435,-1.44872 2.72875,-2.56621 0.30682,-1.02529 0.30686,-0.9045 -7.9e-4,-2.01198 z"
+             id="path1971"
+             sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
+        </g>
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="28.809687"
+           y="44.070885"
+           id="text852-9"><tspan
+             sodipodi:role="line"
+             id="tspan850-4"
+             x="28.809687"
+             y="44.070885"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">bucket </tspan></text>
+      </g>
+      <g
+         id="g2066-7"
+         transform="translate(-2.1807817,6.2627616)">
+        <g
+           id="g1969-8"
+           transform="matrix(0.12763631,0,0,0.12763631,0.7215051,24.717273)"
+           style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-opacity:1">
+          <path
+             style="fill:#4040ff;fill-opacity:1;stroke:none;stroke-width:0.264583;stroke-opacity:1"
+             d="m 203.71837,154.80038 c -1.11451,3.75057 -2.45288,5.84095 -5.11132,7.98327 -2.2735,1.83211 -4.66721,2.65982 -8.09339,2.79857 -2.59227,0.10498 -2.92868,0.0577 -5.02863,-0.70611 -3.99215,-1.45212 -7.1627,-4.65496 -8.48408,-8.57046 -1.28374,-3.80398 -0.61478,-8.68216 1.64793,-12.01698 0.87317,-1.28689 3.15089,-3.48326 4.18771,-4.03815 l 0.53332,-28.51234 5.78454,-5.09197 6.95158,6.16704 -3.21112,3.49026 3.17616,3.45499 -3.17616,3.40822 2.98973,3.28645 -3.24843,3.3829 4.49203,4.58395 0.0516,5.69106 c 1.06874,0.64848 3.81974,3.24046 4.69548,4.56257 0.452,0.68241 1.06834,2.0197 1.36962,2.97176 0.62932,1.98864 0.88051,5.785 0.47342,7.15497 z m -10.0406,2.32604 c -0.88184,-3.17515 -4.92402,-3.78864 -6.75297,-1.02492 -0.58328,0.8814 -0.6898,1.28852 -0.58362,2.23056 0.26492,2.35041 2.45434,3.95262 4.60856,3.37255 1.19644,-0.32217 2.39435,-1.44872 2.72875,-2.56621 0.30682,-1.02529 0.30686,-0.9045 -7.9e-4,-2.01198 z"
+             id="path1971-4"
+             sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
+        </g>
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="28.809687"
+           y="44.070885"
+           id="text852-9-5"><tspan
+             sodipodi:role="line"
+             id="tspan850-4-0"
+             x="28.809687"
+             y="44.070885"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">file path </tspan></text>
+        <path
+           style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
+           d="m 174.20027,104.45585 c -0.14225,0.47871 -0.31308,0.74552 -0.65239,1.01896 -0.29018,0.23384 -0.5957,0.33949 -1.03301,0.3572 -0.33087,0.0134 -0.37381,0.007 -0.64184,-0.0901 -0.50954,-0.18534 -0.91422,-0.59414 -1.08287,-1.0939 -0.16385,-0.48552 -0.0785,-1.10816 0.21033,-1.5338 0.11145,-0.16426 0.40217,-0.44459 0.53451,-0.51542 l 0.0681,-3.639207 0.73832,-0.64992 0.88727,0.787138 -0.40986,0.445484 0.4054,0.440982 -0.4054,0.435013 0.3816,0.41947 -0.41461,0.43178 0.57334,0.58508 0.007,0.72639 c 0.13641,0.0828 0.48753,0.4136 0.59931,0.58235 0.0577,0.0871 0.13636,0.25778 0.17481,0.3793 0.0803,0.25382 0.11239,0.73838 0.0604,0.91323 z m -1.28154,0.29689 c -0.11256,-0.40526 -0.62849,-0.48357 -0.86193,-0.13082 -0.0745,0.1125 -0.088,0.16447 -0.0745,0.2847 0.0338,0.3 0.31326,0.5045 0.58822,0.43046 0.15271,-0.0411 0.30561,-0.1849 0.34829,-0.32754 0.0392,-0.13086 0.0392,-0.11544 -1e-4,-0.2568 z"
+           id="path1971-3"
+           sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="177.8474"
+           y="104.05132"
+           id="text852-9-6"><tspan
+             sodipodi:role="line"
+             id="tspan850-4-7"
+             x="177.8474"
+             y="104.05132"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">= partition key </tspan></text>
+        <path
+           style="fill:#4040ff;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
+           d="m 174.20027,113.78076 c -0.14225,0.47871 -0.31308,0.74552 -0.65239,1.01895 -0.29018,0.23385 -0.5957,0.33949 -1.03301,0.3572 -0.33087,0.0134 -0.37381,0.007 -0.64184,-0.0901 -0.50954,-0.18534 -0.91422,-0.59414 -1.08287,-1.0939 -0.16385,-0.48553 -0.0785,-1.10816 0.21033,-1.53381 0.11145,-0.16425 0.40217,-0.44459 0.53451,-0.51541 l 0.0681,-3.63921 0.73832,-0.64992 0.88727,0.78714 -0.40986,0.44548 0.4054,0.44098 -0.4054,0.43502 0.3816,0.41947 -0.41461,0.43178 0.57334,0.58508 0.007,0.72638 c 0.13641,0.0828 0.48753,0.4136 0.59931,0.58235 0.0577,0.0871 0.13636,0.25779 0.17481,0.37931 0.0803,0.25382 0.11239,0.73837 0.0604,0.91323 z m -1.28154,0.29689 c -0.11256,-0.40527 -0.62849,-0.48357 -0.86193,-0.13082 -0.0745,0.1125 -0.088,0.16446 -0.0745,0.2847 0.0338,0.3 0.31326,0.5045 0.58822,0.43046 0.15271,-0.0411 0.30561,-0.18491 0.34829,-0.32754 0.0392,-0.13087 0.0392,-0.11545 -1e-4,-0.2568 z"
+           id="path1971-4-5"
+           sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="177.8474"
+           y="113.37622"
+           id="text852-9-5-3"><tspan
+             sodipodi:role="line"
+             id="tspan850-4-0-5"
+             x="177.8474"
+             y="113.37622"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">= sort key </tspan></text>
+      </g>
+      <g
+         id="g2161"
+         transform="translate(-62.264403,-59.333115)">
+        <g
+           id="g2271"
+           transform="translate(0,67.042823)">
+          <rect
+             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+             id="rect833-6"
+             width="39.008453"
+             height="16.775949"
+             x="84.896881"
+             y="90.266838" />
+          <rect
+             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+             id="rect833-3-1"
+             width="39.008453"
+             height="8.673645"
+             x="84.896881"
+             y="98.369141" />
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+             x="89.826942"
+             y="96.212921"
+             id="text852-0"><tspan
+               sodipodi:role="line"
+               id="tspan850-6"
+               x="89.826942"
+               y="96.212921"
+               style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Version 1</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+             x="89.826942"
+             y="104.71013"
+             id="text852-0-3"><tspan
+               sodipodi:role="line"
+               id="tspan850-6-2"
+               x="89.826942"
+               y="104.71013"
+               style="font-style:italic;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#4d4d4d;stroke-width:0.264583">deleted</tspan></text>
+        </g>
+      </g>
+      <g
+         id="g2263"
+         transform="translate(0,-22.791204)">
+        <g
+           id="g2161-1"
+           transform="translate(-62.264403,-10.910843)">
+          <rect
+             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+             id="rect833-6-5"
+             width="39.008453"
+             height="36.749603"
+             x="84.896881"
+             y="90.266838" />
+          <rect
+             style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+             id="rect833-3-1-5"
+             width="39.008453"
+             height="28.647301"
+             x="84.896881"
+             y="98.369141" />
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+             x="89.826942"
+             y="96.212921"
+             id="text852-0-4"><tspan
+               sodipodi:role="line"
+               id="tspan850-6-7"
+               x="89.826942"
+               y="96.212921"
+               style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Version 2</tspan></text>
+          <text
+             xml:space="preserve"
+             style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+             x="89.826942"
+             y="104.71013"
+             id="text852-0-3-6"><tspan
+               sodipodi:role="line"
+               id="tspan850-6-2-5"
+               x="89.826942"
+               y="104.71013"
+               style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">id</tspan></text>
+        </g>
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="27.56254"
+           y="100.34132"
+           id="text852-0-3-6-6"><tspan
+             sodipodi:role="line"
+             id="tspan850-6-2-5-9"
+             x="27.56254"
+             y="100.34132"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">size</tspan></text>
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="27.56254"
+           y="106.90263"
+           id="text852-0-3-6-6-3"><tspan
+             sodipodi:role="line"
+             id="tspan850-6-2-5-9-7"
+             x="27.56254"
+             y="106.90263"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">MIME type</tspan></text>
+        <text
+           xml:space="preserve"
+           style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+           x="27.56254"
+           y="111.92816"
+           id="text852-0-3-6-6-3-4"><tspan
+             sodipodi:role="line"
+             id="tspan850-6-2-5-9-7-5"
+             x="27.56254"
+             y="111.92816"
+             style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';fill:#000000;stroke-width:0.264583">...</tspan></text>
+      </g>
+    </g>
+    <g
+       id="g898"
+       transform="translate(-6.2484318,29.95006)">
+      <rect
+         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+         id="rect833-7"
+         width="47.419891"
+         height="44.007515"
+         x="95.443573"
+         y="24.42766" />
+      <rect
+         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+         id="rect833-3-4"
+         width="47.419891"
+         height="35.627186"
+         x="95.443573"
+         y="32.807987" />
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="107.46638"
+         y="29.894743"
+         id="text852-4"><tspan
+           sodipodi:role="line"
+           id="tspan850-3"
+           x="107.46638"
+           y="29.894743"
+           style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Version</tspan></text>
+      <path
+         style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
+         d="m 102.90563,41.413279 c -0.14226,0.478709 -0.31308,0.745518 -0.65239,1.018956 -0.29019,0.233843 -0.59571,0.339489 -1.03301,0.357199 -0.33087,0.0134 -0.37381,0.0074 -0.64184,-0.09013 -0.50954,-0.185343 -0.914221,-0.594142 -1.082877,-1.093901 -0.163852,-0.485526 -0.07847,-1.108159 0.210335,-1.533803 0.111448,-0.164254 0.402172,-0.444591 0.534502,-0.515415 l 0.0681,-3.63921 0.73832,-0.64992 0.88727,0.787138 -0.40985,0.445484 0.40539,0.440982 -0.40539,0.435013 0.3816,0.41947 -0.41462,0.431781 0.57335,0.585078 0.007,0.726386 c 0.13641,0.08277 0.48753,0.413601 0.59931,0.58235 0.0577,0.0871 0.13636,0.257787 0.17481,0.379304 0.0803,0.253823 0.11239,0.738377 0.0604,0.913234 z m -1.28155,0.296888 c -0.11255,-0.405265 -0.62848,-0.483569 -0.86192,-0.130817 -0.0744,0.112498 -0.088,0.164461 -0.0745,0.2847 0.0338,0.299998 0.31326,0.504498 0.58822,0.43046 0.15271,-0.04112 0.3056,-0.184909 0.34828,-0.327542 0.0392,-0.130864 0.0392,-0.115447 -1e-4,-0.256801 z"
+         id="path1971-0"
+         sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="104.99195"
+         y="41.008743"
+         id="text852-9-7"><tspan
+           sodipodi:role="line"
+           id="tspan850-4-8"
+           x="104.99195"
+           y="41.008743"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">id </tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="104.99195"
+         y="49.168018"
+         id="text852-9-7-6"><tspan
+           sodipodi:role="line"
+           id="tspan850-4-8-8"
+           x="104.99195"
+           y="49.168018"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">h(block 1)</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="104.99195"
+         y="56.583336"
+         id="text852-9-7-6-8"><tspan
+           sodipodi:role="line"
+           id="tspan850-4-8-8-4"
+           x="104.99195"
+           y="56.583336"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">h(block 2)</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="104.99195"
+         y="64.265732"
+         id="text852-9-7-6-3"><tspan
+           sodipodi:role="line"
+           id="tspan850-4-8-8-1"
+           x="104.99195"
+           y="64.265732"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">...</tspan></text>
+    </g>
+    <g
+       id="g898-3"
+       transform="translate(75.777779,38.888663)">
+      <rect
+         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+         id="rect833-7-6"
+         width="47.419891"
+         height="29.989157"
+         x="95.443573"
+         y="24.42766" />
+      <rect
+         style="fill:none;stroke:#000000;stroke-width:0.799999;stroke-miterlimit:4;stroke-dasharray:none;stroke-dashoffset:0;stroke-opacity:1"
+         id="rect833-3-4-7"
+         width="47.419891"
+         height="21.608831"
+         x="95.443573"
+         y="32.807987" />
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="102.11134"
+         y="29.894743"
+         id="text852-4-5"><tspan
+           sodipodi:role="line"
+           id="tspan850-3-3"
+           x="102.11134"
+           y="29.894743"
+           style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Data block</tspan></text>
+      <path
+         style="fill:#ff6600;fill-opacity:1;stroke:none;stroke-width:0.0337704;stroke-opacity:1"
+         d="m 102.90563,41.413279 c -0.14226,0.478709 -0.31308,0.745518 -0.65239,1.018956 -0.29019,0.233843 -0.59571,0.339489 -1.03301,0.357199 -0.33087,0.0134 -0.37381,0.0074 -0.64184,-0.09013 -0.50954,-0.185343 -0.914221,-0.594142 -1.082877,-1.093901 -0.163852,-0.485526 -0.07847,-1.108159 0.210335,-1.533803 0.111448,-0.164254 0.402172,-0.444591 0.534502,-0.515415 l 0.0681,-3.63921 0.73832,-0.64992 0.88727,0.787138 -0.40985,0.445484 0.40539,0.440982 -0.40539,0.435013 0.3816,0.41947 -0.41462,0.431781 0.57335,0.585078 0.007,0.726386 c 0.13641,0.08277 0.48753,0.413601 0.59931,0.58235 0.0577,0.0871 0.13636,0.257787 0.17481,0.379304 0.0803,0.253823 0.11239,0.738377 0.0604,0.913234 z m -1.28155,0.296888 c -0.11255,-0.405265 -0.62848,-0.483569 -0.86192,-0.130817 -0.0744,0.112498 -0.088,0.164461 -0.0745,0.2847 0.0338,0.299998 0.31326,0.504498 0.58822,0.43046 0.15271,-0.04112 0.3056,-0.184909 0.34828,-0.327542 0.0392,-0.130864 0.0392,-0.115447 -1e-4,-0.256801 z"
+         id="path1971-0-5"
+         sodipodi:nodetypes="ssscsscccccccccccssscsssscc" />
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="104.99195"
+         y="41.008743"
+         id="text852-9-7-62"><tspan
+           sodipodi:role="line"
+           id="tspan850-4-8-9"
+           x="104.99195"
+           y="41.008743"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">hash </tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+         x="104.99195"
+         y="49.168018"
+         id="text852-9-7-6-1"><tspan
+           sodipodi:role="line"
+           id="tspan850-4-8-8-2"
+           x="104.99195"
+           y="49.168018"
+           style="font-style:normal;font-variant:normal;font-weight:normal;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">data</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow1Mend)"
+       d="M 42.105292,69.455903 89.563703,69.317144"
+       id="path954"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:1;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#marker1262)"
+       d="m 134.32612,77.363197 38.12618,0.260865"
+       id="path1258"
+       sodipodi:nodetypes="cc" />
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="8.6727352"
+       y="16.687063"
+       id="text852-3"><tspan
+         sodipodi:role="line"
+         id="tspan850-67"
+         x="8.6727352"
+         y="16.687063"
+         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Objects table </tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="89.190445"
+       y="16.687063"
+       id="text852-3-5"><tspan
+         sodipodi:role="line"
+         id="tspan850-67-3"
+         x="89.190445"
+         y="16.687063"
+         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Versions table </tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-style:normal;font-weight:normal;font-size:5.64444px;line-height:1.25;font-family:sans-serif;fill:#000000;fill-opacity:1;stroke:none;stroke-width:0.264583"
+       x="174.55702"
+       y="16.687063"
+       id="text852-3-56"><tspan
+         sodipodi:role="line"
+         id="tspan850-67-2"
+         x="174.55702"
+         y="16.687063"
+         style="font-style:normal;font-variant:normal;font-weight:bold;font-stretch:normal;font-size:5.64444px;font-family:'Liberation Mono';-inkscape-font-specification:'Liberation Mono Bold';stroke-width:0.264583">Blocks table</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/inframap.jpg
+++ b/doc/talks/2023-01-18-tocatta/assets/inframap.jpg
--- a/doc/talks/2023-01-18-tocatta/assets/lattice1.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice1.svg
@ -0,0 +1,433 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice1.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="445.81962"
+     inkscape:cy="222.66987"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice2.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice2.svg
@ -0,0 +1,514 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice2.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="384.39345"
+     inkscape:cy="227.46879"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="139.48744"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="131.61919"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice3.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice3.svg
@ -0,0 +1,515 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice3.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="324.06479"
+     inkscape:cy="168.98876"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="139.48744"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="119.58919"
+       cy="67.645035"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice4.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice4.svg
@ -0,0 +1,525 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice4.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="0.73673541"
+     inkscape:cx="287.07728"
+     inkscape:cy="294.54265"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="126.08154"
+       cy="67.968384"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="119.58919"
+       cy="67.645035"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="52.022549"
+       id="text4280"><tspan
+         sodipodi:role="line"
+         id="tspan4278"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="52.022549">return OK</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice5.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice5.svg
@ -0,0 +1,536 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice5.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="276.89766"
+     inkscape:cy="254.34273"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="126.08154"
+       cy="67.968384"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="119.58919"
+       cy="67.645035"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.261436"
+       id="text3707-1"><tspan
+         sodipodi:role="line"
+         id="tspan3705-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.261436">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="52.022549"
+       id="text4280"><tspan
+         sodipodi:role="line"
+         id="tspan4278"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="52.022549">return OK</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice6.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice6.svg
@ -0,0 +1,553 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice6.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="277.85744"
+     inkscape:cy="254.34273"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="126.08154"
+       cy="67.968384"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="119.58919"
+       cy="67.645035"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.261436"
+       id="text3707-1"><tspan
+         sodipodi:role="line"
+         id="tspan3705-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.261436">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-4"
+       cx="18.004833"
+       cy="70.942116"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="73.643356"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-65"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="73.643356">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="52.022549"
+       id="text4280"><tspan
+         sodipodi:role="line"
+         id="tspan4278"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="52.022549">return OK</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice7.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice7.svg
@ -0,0 +1,581 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice7.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="276.89766"
+     inkscape:cy="254.34273"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="126.08154"
+       cy="67.968384"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="119.58919"
+       cy="67.645035"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.261436"
+       id="text3707-1"><tspan
+         sodipodi:role="line"
+         id="tspan3705-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.261436">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-4"
+       cx="18.004833"
+       cy="70.942116"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="73.643356"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-65"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="73.643356">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="52.022549"
+       id="text4280"><tspan
+         sodipodi:role="line"
+         id="tspan4278"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="52.022549">return OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="92.005798"
+       id="text4280-3"><tspan
+         sodipodi:role="line"
+         id="tspan4278-7"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-5"
+       cx="18.004833"
+       cy="81.007744"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="83.577797"
+       id="text3750-0-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-9"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="83.577797">$\to \{a\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/lattice8.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/lattice8.svg
@ -0,0 +1,581 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="400"
+   viewBox="0 0 264.58333 105.83333"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="lattice8.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="399.39712"
+     inkscape:cy="248.39311"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:1;stop-color:#000000"
+       id="rect288"
+       width="209.84705"
+       height="104.42732"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="stroke-width:0.264583;fill:#000000"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="stroke-width:0.264583;fill:#000000"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="stroke-width:0.264583;fill:#000000"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;stroke-width:0.264583;fill:#000000"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="stroke-width:0.264583;fill:#000000"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="132.33408"
+       cy="68.007973"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="126.08154"
+       cy="67.968384"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="119.58919"
+       cy="67.645035"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583;fill:#000000"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="stroke-width:0.264583;fill:#000000"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.261436"
+       id="text3707-1"><tspan
+         sodipodi:role="line"
+         id="tspan3705-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.261436">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-4"
+       cx="18.004833"
+       cy="70.942116"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="73.643356"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-65"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="73.643356">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="52.022549"
+       id="text4280"><tspan
+         sodipodi:role="line"
+         id="tspan4278"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="52.022549">return OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="14.395845"
+       y="92.005798"
+       id="text4280-3"><tspan
+         sodipodi:role="line"
+         id="tspan4278-7"
+         style="fill:#000000;stroke-width:0.264583"
+         x="14.395845"
+         y="92.005798">return $\{\}\sqcup\{a\}=\{a\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-5"
+       cx="18.004833"
+       cy="81.007744"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="83.577797"
+       id="text3750-0-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-9"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="83.577797">$\to \{a\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_1.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_1.svg
@ -0,0 +1,576 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_1.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="469.81422"
+     inkscape:cy="257.22209"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="141.05479"
+       cy="95.316383"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="134.56244"
+       cy="94.993034"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_10.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_10.svg
@ -0,0 +1,715 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_10.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="664.65036"
+     inkscape:cy="366.63745"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0"
+       cx="67.201363"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="127.6125"
+       id="text3750-9"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="127.6125">$\to \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="62.764446"
+       y="146.3129"
+       id="text4280-6"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="62.764446"
+         y="146.3129"
+         id="tspan2630">return $\{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7"
+       cx="67.201363"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="136.59073"
+       id="text3750-3-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="136.59073">$\to \{\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0-6"
+       cx="174.36296"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="179.81555"
+       y="127.6125"
+       id="text3750-9-1"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3-8"
+         style="fill:#000000;stroke-width:0.264583"
+         x="179.81555"
+         y="127.6125">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="162.7999"
+       y="118.94403"
+       id="text3707-5-3-7"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="162.7999"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
+       x="134.97845"
+       y="132.58472"
+       id="text3899"><tspan
+         sodipodi:role="line"
+         id="tspan3897"
+         style="stroke-width:0.264583"
+         x="134.97845"
+         y="132.58472">;</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="169.92604"
+       y="146.3129"
+       id="text4280-6-7"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="169.92604"
+         y="146.3129"
+         id="tspan2630-9">return $\{b\}$</tspan></text>
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7-2"
+       cx="174.36296"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="179.81555"
+       y="136.59073"
+       id="text3750-3-6-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="179.81555"
+         y="136.59073">$\to \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:end;text-anchor:end;fill:#ff0000;stroke-width:0.264583"
+       x="259.75"
+       y="135.53111"
+       id="text9043"><tspan
+         sodipodi:role="line"
+         id="tspan9041"
+         style="fill:#ff0000;stroke-width:0.264583"
+         x="259.75"
+         y="135.53111">${\Large\textbf{??!}}$~~~~~</tspan><tspan
+         sodipodi:role="line"
+         style="fill:#ff0000;stroke-width:0.264583"
+         x="259.75"
+         y="146.11446"
+         id="tspan9372">$\{a\} \not\sqsubseteq \{b\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_2.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_2.svg
@ -0,0 +1,576 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_2.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="586.70996"
+     inkscape:cy="321.01077"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="141.05479"
+       cy="95.316383"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_3.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_3.svg
@ -0,0 +1,576 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_3.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="2.0838024"
+     inkscape:cx="465.25525"
+     inkscape:cy="269.21938"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_4.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_4.svg
@ -0,0 +1,587 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_4.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="505.32622"
+     inkscape:cy="316.72869"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_5.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_5.svg
@ -0,0 +1,604 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_5.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="408.21983"
+     inkscape:cy="319.65343"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0"
+       cx="67.201363"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="127.6125"
+       id="text3750-9"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="127.6125">$\to \{a\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_6.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_6.svg
@ -0,0 +1,632 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_6.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="408.21983"
+     inkscape:cy="319.65343"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0"
+       cx="67.201363"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="127.6125"
+       id="text3750-9"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="127.6125">$\to \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="62.764446"
+       y="146.3129"
+       id="text4280-6"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="62.764446"
+         y="146.3129"
+         id="tspan2630">return $\{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7"
+       cx="67.201363"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="136.59073"
+       id="text3750-3-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="136.59073">$\to \{\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_7.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_7.svg
@ -0,0 +1,654 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_7.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="553.45515"
+     inkscape:cy="346.80022"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0"
+       cx="67.201363"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="127.6125"
+       id="text3750-9"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="127.6125">$\to \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="62.764446"
+       y="146.3129"
+       id="text4280-6"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="62.764446"
+         y="146.3129"
+         id="tspan2630">return $\{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7"
+       cx="67.201363"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="136.59073"
+       id="text3750-3-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="136.59073">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="162.7999"
+       y="118.94403"
+       id="text3707-5-3-7"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="162.7999"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
+       x="134.97845"
+       y="132.58472"
+       id="text3899"><tspan
+         sodipodi:role="line"
+         id="tspan3897"
+         style="stroke-width:0.264583"
+         x="134.97845"
+         y="132.58472">;</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_8.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_8.svg
@ -0,0 +1,671 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_8.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.4734708"
+     inkscape:cx="448.94001"
+     inkscape:cy="322.36811"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0"
+       cx="67.201363"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="127.6125"
+       id="text3750-9"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="127.6125">$\to \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="62.764446"
+       y="146.3129"
+       id="text4280-6"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="62.764446"
+         y="146.3129"
+         id="tspan2630">return $\{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7"
+       cx="67.201363"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="136.59073"
+       id="text3750-3-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="136.59073">$\to \{\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0-6"
+       cx="174.36296"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="179.81555"
+       y="127.6125"
+       id="text3750-9-1"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3-8"
+         style="fill:#000000;stroke-width:0.264583"
+         x="179.81555"
+         y="127.6125">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="162.7999"
+       y="118.94403"
+       id="text3707-5-3-7"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="162.7999"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
+       x="134.97845"
+       y="132.58472"
+       id="text3899"><tspan
+         sodipodi:role="line"
+         id="tspan3897"
+         style="stroke-width:0.264583"
+         x="134.97845"
+         y="132.58472">;</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/latticeB_9.svg
+++ b/doc/talks/2023-01-18-tocatta/assets/latticeB_9.svg
@ -0,0 +1,699 @@
+<?xml version="1.0" encoding="UTF-8" standalone="no"?>
+<!-- Created with Inkscape (http://www.inkscape.org/) -->
+
+<svg
+   width="1000"
+   height="600"
+   viewBox="0 0 264.58333 158.75"
+   version="1.1"
+   id="svg5"
+   inkscape:version="1.2.2 (b0a8486541, 2022-12-01)"
+   sodipodi:docname="latticeB_9.svg"
+   xmlns:inkscape="http://www.inkscape.org/namespaces/inkscape"
+   xmlns:sodipodi="http://sodipodi.sourceforge.net/DTD/sodipodi-0.dtd"
+   xmlns="http://www.w3.org/2000/svg"
+   xmlns:svg="http://www.w3.org/2000/svg">
+  <sodipodi:namedview
+     id="namedview7"
+     pagecolor="#ffffff"
+     bordercolor="#666666"
+     borderopacity="1.0"
+     inkscape:showpageshadow="2"
+     inkscape:pageopacity="0.0"
+     inkscape:pagecheckerboard="0"
+     inkscape:deskcolor="#d1d1d1"
+     inkscape:document-units="mm"
+     showgrid="false"
+     inkscape:zoom="1.0419012"
+     inkscape:cx="664.65036"
+     inkscape:cy="366.63745"
+     inkscape:window-width="1920"
+     inkscape:window-height="999"
+     inkscape:window-x="0"
+     inkscape:window-y="0"
+     inkscape:window-maximized="1"
+     inkscape:current-layer="layer2" />
+  <defs
+     id="defs2">
+    <marker
+       style="overflow:visible"
+       id="Arrow2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-2"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-8" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-75-7-1"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-9-3-2" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-93-1-4"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-6-8-7" />
+    </marker>
+    <marker
+       style="overflow:visible"
+       id="Arrow2-9-7-2-8"
+       refX="0"
+       refY="0"
+       orient="auto-start-reverse"
+       inkscape:stockid="Arrow2"
+       markerWidth="7.6999998"
+       markerHeight="5.5999999"
+       viewBox="0 0 7.7 5.6"
+       inkscape:isstock="true"
+       inkscape:collect="always"
+       preserveAspectRatio="xMidYMid">
+      <path
+         transform="scale(0.7)"
+         d="M -2,-4 9,0 -2,4 c 2,-2.33 2,-5.66 0,-8 z"
+         style="fill:context-stroke;fill-rule:evenodd;stroke:none"
+         id="arrow2L-1-0-6-4" />
+    </marker>
+  </defs>
+  <g
+     inkscape:label="Layer 1"
+     inkscape:groupmode="layer"
+     id="layer1"
+     sodipodi:insensitive="true">
+    <rect
+       style="fill:#ffffff;stroke:none;stroke-width:0.999998;stop-color:#000000"
+       id="rect288"
+       width="262.58151"
+       height="156.82782"
+       x="0.77790999"
+       y="0.93738818" />
+  </g>
+  <g
+     inkscape:groupmode="layer"
+     id="layer2"
+     inkscape:label="Layer 2">
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="99.307442"
+       id="text951"><tspan
+         sodipodi:role="line"
+         id="tspan949"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="99.307442">$\{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+       x="164.56372"
+       y="13.151893"
+       id="text1005"><tspan
+         sodipodi:role="line"
+         id="tspan1003"
+         style="fill:#000000;stroke-width:0.264583"
+         x="164.56372"
+         y="13.151893">$\{a,b,c\}$</tspan></text>
+    <g
+       id="g1175"
+       transform="translate(51.996784,3.5774043)">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="67.008698"
+         id="text1009"><tspan
+           sodipodi:role="line"
+           id="tspan1007"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="67.008698">$\{a\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="67.017166"
+         id="text1009-3"><tspan
+           sodipodi:role="line"
+           id="tspan1007-6"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="67.017166">$\{b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="67.008698"
+         id="text1009-7"><tspan
+           sodipodi:role="line"
+           id="tspan1007-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="67.008698">$\{c\}$</tspan></text>
+    </g>
+    <g
+       id="g1183"
+       transform="translate(51.996784,1.0317046)"
+       style="fill:#000000">
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="112.90984"
+         y="40.841526"
+         id="text1117"><tspan
+           sodipodi:role="line"
+           id="tspan1115"
+           style="fill:#000000;stroke-width:0.264583"
+           x="112.90984"
+           y="40.841526">$\{a,c\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="49.27084"
+         y="40.841526"
+         id="text1117-3"><tspan
+           sodipodi:role="line"
+           id="tspan1115-5"
+           style="fill:#000000;stroke-width:0.264583"
+           x="49.27084"
+           y="40.841526">$\{a,b\}$</tspan></text>
+      <text
+         xml:space="preserve"
+         style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;text-align:center;text-anchor:middle;fill:#000000;stroke-width:0.264583"
+         x="176.20593"
+         y="40.841526"
+         id="text1117-6"><tspan
+           sodipodi:role="line"
+           id="tspan1115-2"
+           style="fill:#000000;stroke-width:0.264583"
+           x="176.20593"
+           y="40.841526">$\{b,c\}$</tspan></text>
+    </g>
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2)"
+       d="M 153.33622,90.367682 118.34198,73.428915"
+       id="path1300" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9)"
+       d="M 177.46016,90.367682 212.4544,73.428915"
+       id="path1300-2" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93)"
+       d="M 153.33622,61.655656 118.34198,44.716889"
+       id="path1300-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7)"
+       d="M 177.46016,61.655656 212.4544,44.716889"
+       id="path1300-2-6" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1)"
+       d="M 118.34198,61.655656 153.33622,44.716889"
+       id="path1300-0-7" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2)"
+       d="M 212.4544,61.655656 177.46016,44.716889"
+       id="path1300-2-6-9" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-93-1-4)"
+       d="M 118.34198,34.227412 153.33622,17.288645"
+       id="path1300-0-7-5" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-7-2-8)"
+       d="M 212.4544,34.227412 177.46016,17.288645"
+       id="path1300-2-6-9-0" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75)"
+       d="m 228.52843,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-2)"
+       d="m 101.90418,61.091809 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-9"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7)"
+       d="m 165.29305,89.571762 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6"
+       sodipodi:nodetypes="cc" />
+    <path
+       style="fill:none;stroke:#000000;stroke-width:0.5;stroke-linecap:butt;stroke-linejoin:miter;stroke-dasharray:none;stroke-opacity:1;marker-end:url(#Arrow2-9-75-7-1)"
+       d="m 165.29305,32.445235 0.33313,-12.554874 m -0.33313,12.554874 0.33313,-12.554874"
+       id="path1300-2-2-6-9"
+       sodipodi:nodetypes="cc" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663"
+       cx="147.35568"
+       cy="95.24971"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3"
+       cx="176.97627"
+       cy="68.155472"
+       r="2.7302806" />
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1"
+       cx="18.004833"
+       cy="39.402473"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0"
+       cx="18.004833"
+       cy="30.371933"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6"
+       cx="18.004833"
+       cy="21.341394"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="13.702217"
+       id="text3707"><tspan
+         sodipodi:role="line"
+         id="tspan3705"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="13.702217">$write(\{a\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="24.042637"
+       id="text3750"><tspan
+         sodipodi:role="line"
+         id="tspan3748"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="24.042637">$\sqsupseteq \{a\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="33.02087"
+       id="text3750-3"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="33.02087">$\not\sqsupseteq \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="41.972523"
+       id="text3750-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="41.972523">$\not\sqsupseteq \{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-1-4"
+       cx="18.004833"
+       cy="90.979645"
+       r="2.7302806" />
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-5"
+       cx="18.004833"
+       cy="81.949104"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-2"
+       cx="18.004833"
+       cy="72.918564"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="6.9525447"
+       y="65.279381"
+       id="text3707-5"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4"
+         style="fill:#000000;stroke-width:0.264583"
+         x="6.9525447"
+         y="65.279381">$write(\{b\})$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="59.340172"
+       y="118.94403"
+       id="text3707-5-3"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6"
+         style="fill:#000000;stroke-width:0.264583"
+         x="59.340172"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="75.619804"
+       id="text3750-7"><tspan
+         sodipodi:role="line"
+         id="tspan3748-4"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="75.619804">$\not\sqsupseteq \{b\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="23.457415"
+       y="84.598038"
+       id="text3750-3-4"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="23.457415"
+         y="84.598038">$\sqsupseteq \{b\} \to$ OK</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#999999;stroke-width:0.264583"
+       x="23.457415"
+       y="93.54969"
+       id="text3750-0-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-6-7"
+         style="fill:#999999;stroke-width:0.264583"
+         x="23.457415"
+         y="93.54969">$\not\sqsupseteq \{b\}$</tspan></text>
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6"
+       cx="118.63729"
+       cy="67.630196"
+       r="2.7302806" />
+    <circle
+       style="fill:#800080;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0"
+       cx="67.201363"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="127.6125"
+       id="text3750-9"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="127.6125">$\to \{a\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="62.764446"
+       y="146.3129"
+       id="text4280-6"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="62.764446"
+         y="146.3129"
+         id="tspan2630">return $\{a\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7"
+       cx="67.201363"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="72.653946"
+       y="136.59073"
+       id="text3750-3-6"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0"
+         style="fill:#000000;stroke-width:0.264583"
+         x="72.653946"
+         y="136.59073">$\to \{\}$</tspan></text>
+    <circle
+       style="fill:#ff0000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-6-6-0-6"
+       cx="174.36296"
+       cy="124.91125"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="179.81555"
+       y="127.6125"
+       id="text3750-9-1"><tspan
+         sodipodi:role="line"
+         id="tspan3748-3-8"
+         style="fill:#000000;stroke-width:0.264583"
+         x="179.81555"
+         y="127.6125">$\to \{\}$</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="162.7999"
+       y="118.94403"
+       id="text3707-5-3-7"><tspan
+         sodipodi:role="line"
+         id="tspan3705-4-6-5"
+         style="fill:#000000;stroke-width:0.264583"
+         x="162.7999"
+         y="118.94403">$read()$:</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;stroke-width:0.264583"
+       x="134.97845"
+       y="132.58472"
+       id="text3899"><tspan
+         sodipodi:role="line"
+         id="tspan3897"
+         style="stroke-width:0.264583"
+         x="134.97845"
+         y="132.58472">;</tspan></text>
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="169.92604"
+       y="146.3129"
+       id="text4280-6-7"><tspan
+         sodipodi:role="line"
+         style="fill:#000000;stroke-width:0.264583"
+         x="169.92604"
+         y="146.3129"
+         id="tspan2630-9">return $\{b\}$</tspan></text>
+    <circle
+       style="fill:#008000;stroke:none;stroke-width:0.499999;stroke-dasharray:none;stop-color:#000000"
+       id="path3663-3-0-7-2"
+       cx="174.36296"
+       cy="133.94179"
+       r="2.7302806" />
+    <text
+       xml:space="preserve"
+       style="font-size:8.46667px;line-height:1.25;font-family:sans-serif;fill:#000000;stroke-width:0.264583"
+       x="179.81555"
+       y="136.59073"
+       id="text3750-3-6-0"><tspan
+         sodipodi:role="line"
+         id="tspan3748-2-0-2"
+         style="fill:#000000;stroke-width:0.264583"
+         x="179.81555"
+         y="136.59073">$\to \{b\}$</tspan></text>
+  </g>
+</svg>
--- a/doc/talks/2023-01-18-tocatta/assets/location-aware.png
+++ b/doc/talks/2023-01-18-tocatta/assets/location-aware.png
--- a/doc/talks/2023-01-18-tocatta/assets/logo_chatons.png
+++ b/doc/talks/2023-01-18-tocatta/assets/logo_chatons.png
--- a/doc/talks/2023-01-18-tocatta/assets/map.png
+++ b/doc/talks/2023-01-18-tocatta/assets/map.png
--- a/doc/talks/2023-01-18-tocatta/assets/minio.png
+++ b/doc/talks/2023-01-18-tocatta/assets/minio.png
--- a/doc/talks/2023-01-18-tocatta/assets/neptune.jpg
+++ b/doc/talks/2023-01-18-tocatta/assets/neptune.jpg
--- a/doc/talks/2023-01-18-tocatta/assets/quentin.jpg
+++ b/doc/talks/2023-01-18-tocatta/assets/quentin.jpg
--- a/doc/talks/2023-01-18-tocatta/assets/rust_logo.png
+++ b/doc/talks/2023-01-18-tocatta/assets/rust_logo.png
--- a/doc/talks/2023-01-18-tocatta/assets/slide1.png
+++ b/doc/talks/2023-01-18-tocatta/assets/slide1.png
--- a/doc/talks/2023-01-18-tocatta/assets/slide2.png
+++ b/doc/talks/2023-01-18-tocatta/assets/slide2.png
--- a/doc/talks/2023-01-18-tocatta/assets/slide3.png
+++ b/doc/talks/2023-01-18-tocatta/assets/slide3.png
--- a/doc/talks/2023-01-18-tocatta/assets/slideB1.png
+++ b/doc/talks/2023-01-18-tocatta/assets/slideB1.png
--- a/doc/talks/2023-01-18-tocatta/assets/slideB2.png
+++ b/doc/talks/2023-01-18-tocatta/assets/slideB2.png
--- a/Show More
+++ b/Show More