A Step-Indexing Approach to Partial Functions

TL;DR

This paper introduces an ACL2 package that uses step-indexing to define and efficiently execute partial recursive functions within ACL2, overcoming limitations of existing methods.

Contribution

It presents a novel step-indexing approach for partial functions in ACL2, enabling first-order logic definitions and efficient execution without inductive definitions.

Findings

Supports efficient execution of partial recursive functions in ACL2

Uses step-indexing to enable first-order logic definitions

Leverages ACL2's guard feature for performance improvements

Abstract

We describe an ACL2 package for defining partial recursive functions that also supports efficient execution. While packages for defining partial recursive functions already exist for other theorem provers, they often require inductive definitions or recursion operators which are not available in ACL2 and they provide little, if any, support for executing the resulting definitions. We use step-indexing as the underlying implementation technology, enabling the definitions to be carried out in first order logic. We also show how recent enhancements to ACL2's guard feature can be used to enable the efficient execution of partial recursive functions.