Crate term_rewriting

A Rust library for representing, parsing, and computing with first-order term rewriting systems.

Example

use term_rewriting::{Signature, Term, parse_trs, parse_term};

// We can parse a string representation of SK combinatory logic,
let mut sig = Signature::default();
let sk_rules = "S x_ y_ z_ = (x_ z_) (y_ z_); K x_ y_ = x_;";
let trs = parse_trs(&mut sig, sk_rules).expect("parsed TRS");

// and we can also parse an arbitrary term.
let mut sig = Signature::default();
let term = "S K K (K S K)";
let parsed_term = parse_term(&mut sig, term).expect("parsed term");

// These can also be constructed by hand.
let mut sig = Signature::default();
let app = sig.new_op(2, Some(".".to_string()));
let s = sig.new_op(0, Some("S".to_string()));
let k = sig.new_op(0, Some("K".to_string()));

let constructed_term = Term::Application {
    op: app,
    args: vec![
        Term::Application {
            op: app,
            args: vec![
                Term::Application {
                    op: app,
                    args: vec![
                        Term::Application { op: s, args: vec![] },
                        Term::Application { op: k, args: vec![] },
                    ]
                },
                Term::Application { op: k, args: vec![] }
            ]
        },
        Term::Application {
            op: app,
            args: vec![
                Term::Application {
                    op: app,
                    args: vec![
                        Term::Application { op: k, args: vec![] },
                        Term::Application { op: s, args: vec![] },
                    ]
                },
                Term::Application { op: k, args: vec![] }
            ]
        }
    ]
};

// This is the same output the parser produces.
assert_eq!(parsed_term, constructed_term);

Term Rewriting Systems

Term Rewriting Systems (TRS) are a simple formalism from theoretical computer science used to model the behavior and evolution of tree-based structures like natural langauge parse trees or abstract syntax trees.

A TRS is defined as a pair (S, R). S is a set of symbols called the signature and together with a disjoint and countably infinite set of variables, defines the set of all possible trees, or terms, which the system can consider. R is a set of rewrite rules. A rewrite rule is an equation, s = t, and is interpreted as follows: any term matching the pattern described by s can be rewritten according to the pattern described by t. Together S and R define a TRS that describes a system of computation, which can be considered as a sort of programming language. term_rewriting provides a way to describe arbitrary first-order TRSs (i.e. no lambda-binding in rules).

Further Reading

• Baader & Nipkow (1999). Term rewriting and all that. Cambridge University Press.
• Bezem, Klop, & de Vrijer (Eds.) (2003). Term Rewriting Systems. Cambridge University Press.
• Rewriting. (2017). Wikipedia.

Structs

Operator	A symbol with fixed arity. Only carries meaning alongside a Signature.
Rule	A rewrite rule equating a left-hand-side Term with one or more right-hand-side Terms.
Signature	Records a universe of symbols.
SignatureChange	Allows terms/rules/TRSs to be reified for use with another signature. See Signature::merge.
TRS	A first-order term rewriting system.
Variable	A symbol for an unspecified term. Only carries meaning alongside a Signature.

Enums

Atom
Context	A first-order context: a Term that may have Holes.
MergeStrategy	Specifies how to merge two signatures. See Signature::merge.
ParseError
Term	A first-order term: either a Variable or an application of an Operator.

Functions

parse	Parse a string as a TRS and a list of Terms.
parse_term	Similar to parse, but produces only a Term.
parse_trs	Similar to parse, but produces only a TRS.

Type Definitions

Place

Represents a place in a Term.