term-rewriting-rs

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

Usage

To include as a dependency:

toml [dependencies] term-rewriting = "0.1"

To actually make use of the library:

```rust extern crate termrewriting; use termrewriting::{Signature, Term, parsetrs, parseterm};

fn main() { // We can parse a string representation of SK combinatory logic, let mut sig = Signature::default(); let skrules = "S x y_ z_ = (x_ z) (y z); K x y_ = x;"; let trs = parsetrs(&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-rs provides a way to describe arbitrary first-order TRSs (i.e. no λ-binding in rules).

Further Reading