Partial Evaluation of Order-sorted Equational Programs modulo Axioms

TL;DR

This paper explores partial evaluation techniques for expressive rule-based languages like Maude, focusing on handling rich types and rewriting modulo axioms, and demonstrates significant optimization benefits.

Contribution

It introduces a novel partial evaluation scheme for order-sorted equational programs with axioms, using automatic unfolding and equational generalization.

Findings

Achieved significant speed-ups in program execution.

Extended partial evaluation methods to complex rule-based languages.

Demonstrated practical effectiveness on multiple examples.

Abstract

Partial evaluation (PE) is a powerful and general program optimization technique with many successful applications. However, it has never been investigated in the context of expressive rule-based languages like Maude, CafeOBJ, OBJ, ASF+SDF, and ELAN, which support: 1) rich type structures with sorts, subsorts and overloading; 2) equational rewriting modulo axioms such as commutativity, associativity-commutativity, and associativity-commutativity-identity. In this extended abstract, we illustrate the key concepts by showing how they apply to partial evaluation of expressive rule-based programs written in Maude. Our partial evaluation scheme is based on an automatic unfolding algorithm that computes term variants and relies on equational least general generalization for ensuring global termination. We demonstrate the use of the resulting partial evaluator for program optimization on several examples where it shows significant speed-ups.