diff --git a/rust/src/gg.rs b/rust/src/gg.rs
index 110e124..320bf6f 100644
--- a/rust/src/gg.rs
+++ b/rust/src/gg.rs
@@ -1,12 +1,17 @@
-use std::hash::Hash;
+use std::hash::{Hash, Hasher};
 use im_rc::{HashSet};
 
-pub mod lexer;
+mod lexer;
+mod decoder;
 
-#[derive(Clone, Eq, Hash, PartialEq)]
+pub use decoder::Decoder;
+
+#[derive(Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
+#[cfg_attr(test, derive(Debug))]
 pub struct OpenEdge(Value, Value); // edge, src
 
-#[derive(Clone, Eq, Hash, PartialEq)]
+#[derive(Clone, Hash, PartialEq, Eq, PartialOrd, Ord)]
+#[cfg_attr(test, derive(Debug))]
 pub enum Value{
     Name(String),
     Number(i64),
@@ -14,13 +19,10 @@ pub enum Value{
     Graph(Graph),
 }
 
-#[derive(Clone, Eq, Hash, PartialEq)]
-struct Edge<V> {
-    dst_val: V,
-    src_val: V,
-}
+pub const ZERO_TUPLE: Value = Value::Tuple(vec![]);
 
-#[derive(Clone, Eq, Hash, PartialEq)]
+#[derive(Clone, PartialEq, Eq, PartialOrd, Ord)]
+#[cfg_attr(test, derive(Debug))]
 pub struct Graph {
     edges: HashSet<(Value, OpenEdge)>, // dst, src
 }
@@ -31,9 +33,58 @@ impl Graph {
         Graph{edges: HashSet::new()}
     }
 
-    pub fn with(&self, dst_val: Value, src_edge: OpenEdge) -> Self {
+    pub fn with(&self, dst_val: Value, edge_val: Value, src_val: Value) -> Self {
         Graph{
-            edges: self.edges.update((dst_val, src_edge)),
+            edges: self.edges.update((dst_val, OpenEdge(edge_val, src_val))),
         }
     }
 }
+
+// The implementation of hash for im_rc::HashSet does not sort the entries.
+impl Hash for Graph {
+    fn hash<H: Hasher>(&self, state: &mut H) {
+        let mut edges = Vec::from_iter(&self.edges);
+        edges.sort();
+        edges.iter().for_each(|edge| edge.hash(state));
+    }
+}
+
+#[cfg(test)]
+mod tests {
+
+    use super::*;
+
+    fn number(i: i64) -> Value {
+        Value::Number(i)
+    }
+
+    #[test]
+    fn equality() {
+
+        let g1 = Graph::new()
+            .with(number(0), number(1), number(2))
+            .with(number(3), number(4), number(5));
+
+        let g2 = Graph::new()
+            .with(number(3), number(4), number(5))
+            .with(number(0), number(1), number(2));
+
+        assert_eq!(g1, g2);
+    }
+
+    #[test]
+    fn deep_equality() {
+
+        let g1 = Graph::new().with(number(-2), ZERO_TUPLE, Value::Graph(Graph::new()
+            .with(number(0), number(1), number(2))
+            .with(number(3), number(4), number(5)),
+        ));
+
+        let g2 = Graph::new().with(number(-2), ZERO_TUPLE, Value::Graph(Graph::new()
+            .with(number(3), number(4), number(5))
+            .with(number(0), number(1), number(2)),
+        ));
+
+        assert_eq!(g1, g2);
+    }
+}
diff --git a/rust/src/gg/decoder.rs b/rust/src/gg/decoder.rs
new file mode 100644
index 0000000..173fda7
--- /dev/null
+++ b/rust/src/gg/decoder.rs
@@ -0,0 +1,380 @@
+use std::io::{self, Read};
+
+use super::{Graph, Value, OpenEdge, ZERO_TUPLE};
+use super::lexer::{self, Lexer, Token, TokenKind, Location};
+
+// In order to make sense of this file, check out the accompanying gg.bnf, which describes the
+// grammar in BNF notation. Each method in the Decoder maps more or less exactly to a state within
+// the BNF.
+
+#[cfg_attr(test, derive(Debug))]
+pub enum Error {
+    Decoding(String, Location),
+    IO(io::Error),
+}
+
+impl From<lexer::Error> for Error {
+    fn from(e: lexer::Error) -> Self {
+        match e {
+            lexer::Error::Tokenizing(s, loc) => Error::Decoding(s, loc),
+            lexer::Error::IO(e) => Error::IO(e)
+        }
+    }
+}
+
+static OUTER_GRAPH_TERM: Token = Token{
+    kind: TokenKind::End,
+    value: String::new(),
+};
+
+pub struct Decoder<R: Read> {
+    lexer: Lexer<R>,
+}
+
+impl<R: Read> Decoder<R> {
+
+    pub fn new(r: R) -> Decoder<R> {
+        Decoder{
+            lexer: Lexer::new(r),
+        }
+    }
+
+    pub fn decode_undelimited(&mut self) -> Result<Graph, Error> {
+        self.outer_graph(Graph::new())
+    }
+
+    fn exp_punct(&mut self, v: &'static str) -> Result<(), Error> {
+
+        match self.lexer.next()? {
+            (Token{kind: TokenKind::Punctuation, value: v2}, _) if v == v2 => Ok(()),
+            (tok, loc) => Err(Error::Decoding(
+                format!("expected '{}', found: {}", v, tok),
+                loc,
+            )),
+        }
+    }
+
+    fn generic_graph(&mut self, term_tok: &Token, g: Graph) -> Result<Graph, Error> {
+
+        match self.lexer.next()? {
+
+            (tok, _) if tok == *term_tok => Ok(g),
+
+            (Token{kind: TokenKind::Name, value: name}, _) => {
+                self.exp_punct("=")?;
+                let open_edge = self.generic_graph_tail(term_tok, ZERO_TUPLE)?;
+                self.generic_graph(term_tok, g.with(
+                    Value::Name(name),
+                    open_edge.0,
+                    open_edge.1,
+                ))
+            }
+
+            (tok, loc) => Err(Error::Decoding(
+                format!("expected name or {}, found: {}", term_tok, tok),
+                loc,
+            )),
+        }
+    }
+
+    fn generic_graph_tail(&mut self, term_tok: &Token, edge_val: Value) -> Result<OpenEdge, Error> {
+
+        let val = self.value()?;
+
+        match self.lexer.next()? {
+
+            (Token{kind: TokenKind::Punctuation, value: v}, _) if v == ";" =>
+                Ok(OpenEdge(edge_val, val)),
+
+            (Token{kind: TokenKind::Punctuation, value: v}, _) if v == "<" =>
+
+                if edge_val == ZERO_TUPLE {
+                    self.generic_graph_tail(term_tok, val)
+                } else {
+                    Ok(OpenEdge(edge_val, Value::Tuple(vec![
+                        self.generic_graph_tail(term_tok, val)?,
+                    ])))
+                },
+
+            (tok, loc) => {
+                self.lexer.push_next(tok, loc);
+                Ok(OpenEdge(edge_val, val))
+            },
+        }
+    }
+
+    fn outer_graph(&mut self, g: Graph) -> Result<Graph, Error> {
+        self.generic_graph(&OUTER_GRAPH_TERM, g)
+    }
+
+    fn graph(&mut self, g: Graph) -> Result<Graph, Error> {
+
+        let term_tok = Token{
+            kind: TokenKind::Punctuation,
+            value: String::from("}"),
+        };
+
+        self.generic_graph(&term_tok, g)
+    }
+
+    fn tuple(&mut self, tuple_vec: &mut Vec<OpenEdge>) -> Result<(), Error> {
+
+        loop {
+            match self.lexer.next()? {
+
+                (Token{kind: TokenKind::Punctuation, value: v}, _) if v == ")" =>
+                    return Ok(()),
+
+                (tok, loc) => {
+                    self.lexer.push_next(tok, loc);
+                    tuple_vec.push(self.tuple_tail(ZERO_TUPLE)?);
+                },
+            }
+        }
+    }
+
+    fn tuple_tail(&mut self, edge_val: Value) -> Result<OpenEdge, Error> {
+
+        let val = self.value()?;
+
+        match self.lexer.next()? {
+
+            (Token{kind: TokenKind::Punctuation, value: v}, _) if v == "," =>
+                Ok(OpenEdge(edge_val, val)),
+
+            (Token{kind: TokenKind::Punctuation, value: v}, _) if v == "<" =>
+
+                if edge_val == ZERO_TUPLE {
+                    self.tuple_tail(val)
+                } else {
+                    Ok(OpenEdge(edge_val, Value::Tuple(vec![
+                        self.tuple_tail(val)?,
+                    ])))
+                },
+
+            (tok, loc) => {
+                self.lexer.push_next(tok, loc);
+                Ok(OpenEdge(edge_val, val))
+            },
+
+        }
+    }
+
+    fn value(&mut self) -> Result<Value, Error> {
+
+        match self.lexer.next()? {
+
+            (Token{kind: TokenKind::Name, value: v}, _) =>
+                Ok(Value::Name(v)),
+
+            (Token{kind: TokenKind::Number, value: v}, loc) =>
+                match v.parse::<i64>() {
+                    Ok(n) => Ok(Value::Number(n)),
+                    Err(e) => Err(Error::Decoding(
+                        format!("parsing {:#?} as integer: {}", v, e),
+                        loc,
+                    )),
+                },
+
+            (Token{kind: TokenKind::Punctuation, value: v}, _) if v == "(" => {
+                let mut vec = Vec::new();
+                self.tuple(&mut vec)?;
+                Ok(Value::Tuple(vec))
+            },
+
+            (Token{kind: TokenKind::Punctuation, value: v}, _) if v == "{" =>
+                Ok(Value::Graph(self.graph(Graph::new())?)),
+
+            (tok, loc) => Err(Error::Decoding(
+                format!("expected name, number, '(', or '{{', found: {}", tok),
+                loc,
+            )),
+        }
+    }
+}
+
+#[cfg(test)]
+mod tests {
+
+    use super::*;
+
+    #[test]
+    fn decoder() {
+
+        fn name(s: &'static str) -> Value {
+            Value::Name(s.to_string())
+        }
+
+        fn number(i: i64) -> Value {
+            Value::Number(i)
+        }
+
+        struct Test {
+            input: &'static str,
+            exp: Graph,
+        }
+
+        let tests = vec!{
+            Test{
+                input: "",
+                exp: Graph::new(),
+            },
+            Test{
+                input: "out = 1",
+                exp: Graph::new().
+                        with(name("out"), ZERO_TUPLE, number(1)),
+            },
+            Test{
+                input: "out = 1;",
+                exp: Graph::new().
+                        with(name("out"), ZERO_TUPLE, number(1)),
+            },
+            Test{
+                input: "out = incr < 1",
+                exp: Graph::new().
+                        with(name("out"), name("incr"), number(1)),
+            },
+            Test{
+                input: "out = incr < 1;",
+                exp: Graph::new().
+                        with(name("out"), name("incr"), number(1)),
+            },
+            Test{
+                input: "out = a < b < 1",
+                exp: Graph::new().with(
+                    name("out"),
+                    name("a"),
+                    Value::Tuple(vec![OpenEdge(name("b"), number(1))]),
+                ),
+            },
+            Test{
+                input: "out = a < b < 1;",
+                exp: Graph::new().with(
+                    name("out"),
+                    name("a"),
+                    Value::Tuple(vec![OpenEdge(name("b"), number(1))]),
+                ),
+            },
+            Test{
+                input: "out = a < b < (1, c < 2, d < e < 3)",
+                exp: Graph::new().with(
+                    name("out"),
+                    name("a"),
+                    Value::Tuple(vec![
+                        OpenEdge(name("b"), Value::Tuple(vec![
+                            OpenEdge(ZERO_TUPLE, number(1)),
+                            OpenEdge(name("c"), number(2)),
+                            OpenEdge(name("d"), Value::Tuple(vec![
+                                OpenEdge(name("e"), number(3)),
+                            ])),
+                        ])),
+                    ]),
+                ),
+            },
+            Test{
+                input: "out = (c < 2,);",
+                exp: Graph::new().with(
+                    name("out"),
+                    ZERO_TUPLE,
+                    Value::Tuple(vec![
+                        OpenEdge(name("c"), number(2)),
+                    ]),
+                ),
+            },
+            Test{
+                input: "out = (1, c < 2) < 3;",
+                exp: Graph::new().with(
+                    name("out"),
+                    Value::Tuple(vec![
+                        OpenEdge(ZERO_TUPLE, number(1)),
+                        OpenEdge(name("c"), number(2)),
+                    ]),
+                    number(3),
+                ),
+            },
+            Test{
+                input: "out = a < b < (1, c < (d < 2, 3))",
+                exp: Graph::new().with(
+                    name("out"),
+                    name("a"),
+                    Value::Tuple(vec![
+                        OpenEdge(name("b"), Value::Tuple(vec![
+                            OpenEdge(ZERO_TUPLE, number(1)),
+                            OpenEdge(name("c"), Value::Tuple(vec![
+                                OpenEdge(name("d"), number(2)),
+                                OpenEdge(ZERO_TUPLE, number(3)),
+                            ])),
+                        ])),
+                    ]),
+                ),
+            },
+            Test{
+                input: "out = { a = 1; b = 2 < 3; c = 4 < 5 < 6 }",
+                exp: Graph::new().with(
+                    name("out"),
+                    ZERO_TUPLE,
+                    Value::Graph(Graph::new()
+                        .with(name("a"), ZERO_TUPLE, number(1))
+                        .with(name("b"), number(2), number(3))
+                        .with(name("c"), number(4), Value::Tuple(vec![
+                            OpenEdge(number(5), number(6)),
+                        ])),
+                    ),
+                ),
+            },
+            Test{
+                input: "out = { a = 1; };",
+                exp: Graph::new().with(
+                    name("out"),
+                    ZERO_TUPLE,
+                    Value::Graph(Graph::new()
+                        .with(name("a"), ZERO_TUPLE, number(1)),
+                    ),
+                ),
+            },
+            Test{
+                input: "out = { a = 1; } < 2",
+                exp: Graph::new().with(
+                    name("out"),
+                    Value::Graph(Graph::new()
+                        .with(name("a"), ZERO_TUPLE, number(1)),
+                    ),
+                    number(2),
+                ),
+            },
+            Test{
+                input: "out = { a = 1; } < 2; foo = 5 < 6",
+                exp: Graph::new()
+                    .with(
+                        name("out"),
+                        Value::Graph(Graph::new()
+                            .with(name("a"), ZERO_TUPLE, number(1)),
+                        ),
+                        number(2),
+                    )
+                    .with(name("foo"), number(5), number(6)),
+            },
+            Test{
+                input: "out = { a = 1 } < 2; foo = 5 < 6;",
+                exp: Graph::new()
+                    .with(
+                        name("out"),
+                        Value::Graph(Graph::new()
+                            .with(name("a"), ZERO_TUPLE, number(1)),
+                        ),
+                        number(2),
+                    )
+                    .with(name("foo"), number(5), number(6)),
+            },
+        };
+
+        for test in tests {
+            println!("INPUT: {:#?}", test.input);
+
+            let mut d = Decoder::new(test.input.as_bytes());
+            let got = d.decode_undelimited().expect("no errors expected");
+            assert_eq!(test.exp, got);
+        }
+
+    }
+}
diff --git a/rust/src/gg/gg.bnf b/rust/src/gg/gg.bnf
index 3321945..76c3621 100644
--- a/rust/src/gg/gg.bnf
+++ b/rust/src/gg/gg.bnf
@@ -6,22 +6,19 @@
                 | <ascii-number> <number-tail>
 <number-tail> ::= <ascii-number> <number-tail> | ""
 
-<value> ::= <name> | <number> | <tuple> | <graph>
+<value> ::= <name> | <number> | "(" <tuple> | "{" <graph>
 
-<tuple>                 ::= "(" <tuple-edge>
-<tuple-edge>            ::= ")" | <tuple-edge-incomplete>
-<tuple-edge-incomplete> ::= <value> ")"
-                          | <value> "," <tuple-edge>
-                          | <value> "<" <tuple-edge-incomplete>
+<tuple>      ::= ")" | <tuple-tail> <tuple>
+<tuple-tail> ::= <value> ""
+               | <value> ","
+               | <value> "<" <tuple-tail>
 
-<graph>                 ::= "{" <graph-branch>
-<graph-branch>          ::= "}" | <name> "<" <graph-edge-incomplete>
-<graph-edge-incomplete> ::= <value> "}"
-                          | <value> ";" <graph-branch>
-                          | <value> "<" <graph-edge-incomplete>
+<graph>      ::= "}" | <name> "=" <graph-tail> <graph>
+<graph-tail> ::= <value> ""
+               | <value> ";"
+               | <value> "<" <graph-tail>
 
-<outer-graph>                 ::= <outer-graph-branch>
-<outer-graph-branch>          ::= <end> | <name> "<" <outer-graph-edge-incomplete>
-<outer-graph-edge-incomplete> ::= <value> <end>
-                                | <value> ";" <outer-graph-branch>
-                                | <value> "<" <outer-graph-edge-incomplete>
+<outer-graph>      ::= <end> | <name> "=" <outer-graph-tail> <outer-graph>
+<outer-graph-tail> ::= <value> ""
+                     | <value> ";"
+                     | <value> "<" <outer-graph-tail>
diff --git a/rust/src/gg/lexer.rs b/rust/src/gg/lexer.rs
index eb222d6..592020b 100644
--- a/rust/src/gg/lexer.rs
+++ b/rust/src/gg/lexer.rs
@@ -4,7 +4,8 @@ use unicode_categories::UnicodeCategories;
 
 use char_reader::CharReader;
 
-#[derive(Copy, Clone, Debug, PartialEq)]
+#[derive(Copy, Clone, PartialEq)]
+#[cfg_attr(test, derive(Debug))]
 pub struct Location {
     pub row: i64,
     pub col: i64,
@@ -16,9 +17,9 @@ impl fmt::Display for Location {
     }
 }
 
-#[derive(Debug)]
+#[cfg_attr(test, derive(Debug))]
 pub enum Error {
-    Tokenizing(&'static str, Location),
+    Tokenizing(String, Location),
     IO(io::Error),
 }
 
@@ -28,7 +29,8 @@ impl From<io::Error> for Error {
     }
 }
 
-#[derive(Debug, PartialEq)]
+#[derive(PartialEq, Clone)]
+#[cfg_attr(test, derive(Debug))]
 pub enum TokenKind {
     Name,
     Number,
@@ -36,16 +38,28 @@ pub enum TokenKind {
     End,
 }
 
-#[derive(Debug, PartialEq)]
+#[derive(PartialEq, Clone)]
+#[cfg_attr(test, derive(Debug))]
 pub struct Token {
     pub kind: TokenKind,
     pub value: String,
 }
 
+impl fmt::Display for Token {
+    fn fmt(&self, f: &mut fmt::Formatter) -> fmt::Result {
+        match self.kind {
+            TokenKind::Name => write!(f, "{:#?}", self.value),
+            TokenKind::Number => write!(f, "{}", self.value),
+            TokenKind::Punctuation => write!(f, "'{}'", self.value),
+            TokenKind::End => write!(f, "<end>"),
+        }
+    }
+}
+
 pub struct Lexer<R: Read> {
     r: CharReader<BufReader<R>>,
     buf: String,
-
+    next_stack: Vec<(Token, Location)>,
     next_loc: Location,
 }
 
@@ -55,6 +69,7 @@ impl<R: Read> Lexer<R>{
         Lexer{
             r: CharReader::new(BufReader::new(r)),
             buf: String::new(),
+            next_stack: Vec::new(),
             next_loc: Location{
                 row: 0,
                 col: 0,
@@ -131,8 +146,16 @@ impl<R: Read> Lexer<R>{
         c == '-' || ('0' <= c && c <= '9')
     }
 
+    pub fn push_next(&mut self, token: Token, loc: Location) {
+        self.next_stack.push((token, loc))
+    }
+
     pub fn next(&mut self) -> Result<(Token, Location), Error> {
 
+        if let Some(r) = self.next_stack.pop() {
+            return Ok(r);
+        }
+
         loop {
 
             let (c, ok) = self.peek_a_bool()?;
@@ -169,7 +192,10 @@ impl<R: Read> Lexer<R>{
                 self.discard_while(|c| c.is_ascii_whitespace())?;
 
             } else {
-                return Err(Error::Tokenizing("invalid character", self.next_loc));
+                return Err(Error::Tokenizing(
+                    format!("unexpected character: {:#?}", c).to_string(),
+                    self.next_loc,
+                ));
             }
         }
     }
@@ -280,7 +306,7 @@ mod tests {
                 }
             }
 
-            assert_eq!(*res.as_slice(), *test.exp)
+            assert_eq!(*test.exp, *res.as_slice())
         }
     }
 }