[−][src]Crate term_rewriting

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

Usage

[dependencies]
term_rewriting = "0.7"

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 s = sig.new_op(0, Some("S".to_string()));
let k = sig.new_op(0, Some("K".to_string()));
let app = sig.new_op(2, Some(".".to_string()));

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

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

TRS syntax

Several functions are available which parse TRS-related data structures according to the following grammar (defined in augmented Backus-Naur form):

parse: a TRS and list of Terms (program)
parse_trs: a TRS (trs)
parse_term: a Term (top-level-term)
parse_rule: a Rule (rule)
parse_context: a Context (top-level-context)
parse_rulecontext: a RuleContext (rulecontext)

program = *wsp *( *comment statement ";" *comment ) *wsp

statement = rule / top-level-term

rule = top-level-term *wsp "=" *wsp top-level-term
rule /= rule *wsp "|" *wsp top-level-term

top-level-term = term
top-level-term /= top-level-term 1*wsp top-level-term

term = variable
term /= application
term /= "(" *wsp top-level-term *wsp ")"

rulecontext = top-level-term *wsp "=" *wsp top-level-term
rulecontext /= rule *wsp "|" *wsp top-level-term

top-level-context = context
top-level-context /= top-level-context 1*wsp top-level-context

context = variable
context /= application
context /= hole
context /= "(" *wsp top-level-context *wsp ")"

hole = "[!]"

variable = identifier"_"

application = identifier "(" [ term *( 1*wsp term ) ] ")"
application /= identifier
application /= binary-application

; binary application is the '.' operator with arity 2.
binary-application = "(" *wsp term *wsp term *wsp ")"

identifier = 1*( ALPHA / DIGIT )

comment = "#" *any-char-but-newline "\n"

wsp = SP / TAB / CR / LF

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).

Modules

trace

Record sequences of rewrites.

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 `Term`s.
RuleContext	A `Rule` with `Hole`s; a sort of `Rule` template.
Signature	Records a universe of symbols.
SignatureChange	Allows `Term`s/`Rule`s/`TRS`s 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	`Atom`s are the parts of a `TRS` that are not constructed from smaller parts: `Variable`s and `Operator`s.
Context	A first-order `Context`: a `Term` that may have `Hole`s; a sort of `Term` template.
MergeStrategy	Specifies how to merge two signatures. See `Signature::merge`.
ParseError	The error type for parsing operations.
Strategy
TRSError	The error type for `TRS` manipulations.
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 `Term`s.
parse_context	Parse a string as a `Context`.
parse_rule	Parse a string as a `Rule`.
parse_rulecontext	Parse a string as a `RuleContext`.
parse_term	Parse a string as a `Term`.
parse_trs	Parse a string as a `TRS`.

Type Definitions

Place

Represents a place in a Term.