ACD Term Rewriting

TL;DR

ACDTR is a novel logical formula rewriting language that extends AC term rewriting with conjunction distribution, enabling highly expressive and targeted rewriting rules through conjunctive contexts, with a formal semantics and prototype implementation.

Contribution

Introduces ACDTR, a new rewriting language combining AC term rewriting with conjunction distribution and conjunctive contexts, extending logic programming capabilities.

Findings

Defined the formal semantics of ACDTR

Developed a prototype implementation of ACDTR

Demonstrated the expressive power of ACDTR in logical formula rewriting

Abstract

We introduce Associative Commutative Distributive Term Rewriting (ACDTR), a rewriting language for rewriting logical formulae. ACDTR extends AC term rewriting by adding distribution of conjunction over other operators. Conjunction is vital for expressive term rewriting systems since it allows us to require that multiple conditions hold for a term rewriting rule to be used. ACDTR uses the notion of a "conjunctive context", which is the conjunction of constraints that must hold in the context of a term, to enable the programmer to write very expressive and targeted rewriting rules. ACDTR can be seen as a general logic programming language that extends Constraint Handling Rules and AC term rewriting. In this paper we define the semantics of ACDTR and describe our prototype implementation.