ginger/graph/graph.go

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// Package graph implements a generic directed graph type, with support for
// tuple vertices in addition to traditional "value" vertices.
package graph
import (
"fmt"
"strings"
)
// Value is any value which can be stored within a Graph. Values should be
// considered immutable, ie once used with the graph package their internal
// value does not change.
type Value interface {
Equal(Value) bool
String() string
}
// OpenEdge consists of the edge value (E) and source vertex value (V) of an
// edge in a Graph. When passed into the AddValueIn method a full edge is
// created. An OpenEdge can also be sourced from a tuple vertex, whose value is
// an ordered set of OpenEdges of this same type.
type OpenEdge[E, V Value] struct {
val *V
tup []*OpenEdge[E, V]
edgeVal E
}
func (oe *OpenEdge[E, V]) equal(oe2 *OpenEdge[E, V]) bool {
if !oe.edgeVal.Equal(oe2.edgeVal) {
return false
}
if oe.val != nil {
return oe2.val != nil && (*oe.val).Equal(*oe2.val)
}
if len(oe.tup) != len(oe2.tup) {
return false
}
for i := range oe.tup {
if !oe.tup[i].equal(oe2.tup[i]) {
return false
}
}
return true
}
func (oe *OpenEdge[E, V]) String() string {
vertexType := "tup"
var fromStr string
if oe.val != nil {
vertexType = "val"
fromStr = (*oe.val).String()
} else {
strs := make([]string, len(oe.tup))
for i := range oe.tup {
strs[i] = oe.tup[i].String()
}
fromStr = fmt.Sprintf("[%s]", strings.Join(strs, ", "))
}
return fmt.Sprintf("%s(%s, %s)", vertexType, fromStr, oe.edgeVal.String())
}
// WithEdgeValue returns a copy of the OpenEdge with the given Value replacing
// the previous edge value.
//
// NOTE I _think_ this can be factored out once Graph is genericized.
func (oe *OpenEdge[E, V]) WithEdgeValue(val E) *OpenEdge[E, V] {
oeCp := *oe
oeCp.edgeVal = val
return &oeCp
}
// EdgeValue returns the Value which lies on the edge itself.
func (oe OpenEdge[E, V]) EdgeValue() E {
return oe.edgeVal
}
// FromValue returns the Value from which the OpenEdge was created via ValueOut,
// or false if it wasn't created via ValueOut.
func (oe OpenEdge[E, V]) FromValue() (V, bool) {
if oe.val == nil {
var zero V
return zero, false
}
return *oe.val, true
}
// FromTuple returns the tuple of OpenEdges from which the OpenEdge was created
// via TupleOut, or false if it wasn't created via TupleOut.
func (oe OpenEdge[E, V]) FromTuple() ([]*OpenEdge[E, V], bool) {
if oe.val != nil {
return nil, false
}
return oe.tup, true
}
// ValueOut creates a OpenEdge which, when used to construct a Graph, represents
// an edge (with edgeVal attached to it) coming from the vertex containing val.
func ValueOut[E, V Value](edgeVal E, val V) *OpenEdge[E, V] {
return &OpenEdge[E, V]{
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val: &val,
edgeVal: edgeVal,
}
}
// TupleOut creates an OpenEdge which, when used to construct a Graph,
// represents an edge (with edgeVal attached to it) coming from the vertex
// comprised of the given ordered-set of input edges.
func TupleOut[E, V Value](edgeVal E, ins ...*OpenEdge[E, V]) *OpenEdge[E, V] {
if len(ins) == 1 {
var (
zero V
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in = ins[0]
)
if edgeVal.Equal(zero) {
return in
}
if in.edgeVal.Equal(zero) {
return in.WithEdgeValue(edgeVal)
}
}
return &OpenEdge[E, V]{
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tup: ins,
edgeVal: edgeVal,
}
}
type graphValueIn[E, V Value] struct {
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val V
edge *OpenEdge[E, V]
}
func (valIn graphValueIn[E, V]) equal(valIn2 graphValueIn[E, V]) bool {
return valIn.val.Equal(valIn2.val) && valIn.edge.equal(valIn2.edge)
}
// Graph is an immutable container of a set of vertices. The Graph keeps track
// of all Values which terminate an OpenEdge. E indicates the type of edge
// values, while V indicates the type of vertex values.
//
// NOTE The current implementation of Graph is incredibly inefficient, there's
// lots of O(N) operations, unnecessary copying on changes, and duplicate data
// in memory.
type Graph[E, V Value] struct {
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edges []*OpenEdge[E, V]
valIns []graphValueIn[E, V]
}
func (g *Graph[E, V]) cp() *Graph[E, V] {
cp := &Graph[E, V]{
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edges: make([]*OpenEdge[E, V], len(g.edges)),
valIns: make([]graphValueIn[E, V], len(g.valIns)),
}
copy(cp.edges, g.edges)
copy(cp.valIns, g.valIns)
return cp
}
func (g *Graph[E, V]) String() string {
var strs []string
for _, valIn := range g.valIns {
strs = append(
strs,
fmt.Sprintf("valIn(%s, %s)", valIn.edge.String(), valIn.val.String()),
)
}
return fmt.Sprintf("graph(%s)", strings.Join(strs, ", "))
}
// NOTE this method is used more for its functionality than for any performance
// reasons... it's incredibly inefficient in how it deduplicates edges, but by
// doing the deduplication we enable the graph map operation to work correctly.
func (g *Graph[E, V]) dedupeEdge(edge *OpenEdge[E, V]) *OpenEdge[E, V] {
// check if there's an existing edge which is fully equivalent in the graph
// already, and if so return that.
for i := range g.edges {
if g.edges[i].equal(edge) {
return g.edges[i]
}
}
// if this edge is a value edge then there's nothing else to do, return it.
if _, ok := edge.FromValue(); ok {
return edge
}
// this edge is a tuple edge, it's possible that one of its sub-edges is
// already in the graph. dedupe each sub-edge individually.
tupEdges := make([]*OpenEdge[E, V], len(edge.tup))
for i := range edge.tup {
tupEdges[i] = g.dedupeEdge(edge.tup[i])
}
return TupleOut(edge.EdgeValue(), tupEdges...)
}
// ValueIns returns, if any, all OpenEdges which lead to the given Value in the
// Graph (ie, all those added via AddValueIn).
//
// The returned slice should not be modified.
func (g *Graph[E, V]) ValueIns(val Value) []*OpenEdge[E, V] {
var edges []*OpenEdge[E, V]
for _, valIn := range g.valIns {
if valIn.val.Equal(val) {
edges = append(edges, valIn.edge)
}
}
return edges
}
// AddValueIn takes a OpenEdge and connects it to the Value vertex containing
// val, returning the new Graph which reflects that connection.
func (g *Graph[E, V]) AddValueIn(val V, oe *OpenEdge[E, V]) *Graph[E, V] {
valIn := graphValueIn[E, V]{
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val: val,
edge: oe,
}
for i := range g.valIns {
if g.valIns[i].equal(valIn) {
return g
}
}
valIn.edge = g.dedupeEdge(valIn.edge)
g = g.cp()
g.valIns = append(g.valIns, valIn)
return g
}
// Equal returns whether or not the two Graphs are equivalent in value.
func (g *Graph[E, V]) Equal(g2 *Graph[E, V]) bool {
if len(g.valIns) != len(g2.valIns) {
return false
}
outer:
for _, valIn := range g.valIns {
for _, valIn2 := range g2.valIns {
if valIn.equal(valIn2) {
continue outer
}
}
return false
}
return true
}
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func mapReduce[Ea, Va Value, Vb any](
root *OpenEdge[Ea, Va],
mapVal func(Va) (Vb, error),
reduceEdge func(*OpenEdge[Ea, Va], []Vb) (Vb, error),
) (
Vb, error,
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) {
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if valA, ok := root.FromValue(); ok {
valB, err := mapVal(valA)
if err != nil {
var zero Vb
return zero, err
}
return reduceEdge(root, []Vb{valB})
}
tupA, _ := root.FromTuple()
valsB := make([]Vb, len(tupA))
for i := range tupA {
valB, err := mapReduce[Ea, Va, Vb](
tupA[i], mapVal, reduceEdge,
)
if err != nil {
var zero Vb
return zero, err
}
valsB[i] = valB
}
return reduceEdge(root, valsB)
}
type mappedVal[Va Value, Vb any] struct {
valA Va
valB Vb // result
}
type reducedEdge[Ea, Va Value, Vb any] struct {
edgeA *OpenEdge[Ea, Va]
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valB Vb // result
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}
// MapReduce recursively computes a resultant Value of type Vb from an
// OpenEdge[Ea, Va].
//
// Tuple edges which are encountered will have Reduce called on each OpenEdge
// branch of the tuple, to obtain a Vb for each branch. The edge value of the
// tuple edge (Ea) and the just obtained Vbs are then passed to reduceEdge to
// obtain a Vb for that edge.
//
// The values of value edges (Va) which are encountered are mapped to Vb using
// the mapVal function. The edge value of those value edges (Ea) and the just
// obtained Vb value are then passed to reduceEdge to obtain a Vb for that edge.
//
// If either the map or reduce function returns an error then processing is
// immediately cancelled and that error is returned directly.
//
// If a value or edge is connected to multiple times within the root OpenEdge it
// will only be mapped/reduced a single time, and the result of that single
// map/reduction will be passed to each dependant operation.
//
func MapReduce[Ea, Va Value, Vb any](
root *OpenEdge[Ea, Va],
mapVal func(Va) (Vb, error),
reduceEdge func(Ea, []Vb) (Vb, error),
) (
Vb, error,
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) {
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var (
zeroB Vb
// we use these to memoize reductions on values and edges, so a
// reduction is only performed a single time for each value/edge.
//
// NOTE this is not implemented very efficiently.
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mappedVals []mappedVal[Va, Vb]
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reducedEdges []reducedEdge[Ea, Va, Vb]
)
return mapReduce[Ea, Va, Vb](
root,
func(valA Va) (Vb, error) {
for _, mappedVal := range mappedVals {
if mappedVal.valA.Equal(valA) {
return mappedVal.valB, nil
}
}
valB, err := mapVal(valA)
if err != nil {
return zeroB, err
}
mappedVals = append(mappedVals, mappedVal[Va, Vb]{
valA: valA,
valB: valB,
})
return valB, nil
},
func(edgeA *OpenEdge[Ea, Va], valBs []Vb) (Vb, error) {
for _, reducedEdge := range reducedEdges {
if reducedEdge.edgeA.equal(edgeA) {
return reducedEdge.valB, nil
}
}
valB, err := reduceEdge(edgeA.EdgeValue(), valBs)
if err != nil {
return zeroB, err
}
reducedEdges = append(reducedEdges, reducedEdge[Ea, Va, Vb]{
edgeA: edgeA,
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valB: valB,
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})
return valB, nil
},
)
}