Encapsulation for Practical Simplification Procedures

TL;DR

This paper demonstrates how ACL2 encapsulation can be effectively used to verify properties of two different simplification procedures based on term rewriting, ensuring their termination, irreducibility, and soundness.

Contribution

It introduces a method for verifying complex simplification algorithms using ACL2 encapsulation, emphasizing its importance for efficient formal verification.

Findings

Both procedures are proven terminating and sound.

Properties of the rewriting functions are formally established.

Encapsulation facilitates rapid verification of complex algorithms.

Abstract

ACL2 was used to prove properties of two simplification procedures. The procedures differ in complexity but solve the same programming problem that arises in the context of a resolution/paramodulation theorem proving system. Term rewriting is at the core of the two procedures, but details of the rewriting procedure itself are irrelevant. The ACL2 encapsulate construct was used to assert the existence of the rewriting function and to state some of its properties. Termination, irreducibility, and soundness properties were established for each procedure. The availability of the encapsulation mechanism in ACL2 is considered essential to rapid and efficient verification of this kind of algorithm.