Templates in Rewriting Induction

TL;DR

This paper introduces a template-based approach to improve lemma generation in Rewriting Induction, enabling the proof of program equivalences involving complex calculations and constraints.

Contribution

It presents a novel integration of templates into Bounded Rewriting Induction to enhance automatic lemma generation for higher-order LCSTRSs.

Findings

Enables proving equivalences previously out of reach

Improves lemma generation in higher-order RI

Leverages typical programming constructs as templates

Abstract

Rewriting Induction (RI) is a formal system in term rewriting to establish program equivalence. The recently defined Bounded RI for higher-order Logically Constrained Term Rewriting Systems (LCSTRSs) yields a convenient proof system for analyzing real programming code. A practical challenge in RI is the automatic generation of induction hypotheses, called lemmas. While various lemma generation techniques exist for plain term rewriting, there are much fewer that consider the intricacies brought on by calculations or constraints. Taking advantage of recent developments in higher-order RI, we here present a new approach based on templates, which operates by recognising typical programming constructs as instances of higher-order functions. While templates have been used as a stand-alone method to justify the correctness of program transformations, we here consider their integration in Bounded RI to obtain a complementary lemma generation heuristic. This allows us to prove equivalences that were previously out of reach.