Formalizing Rewriting Induction on Isabelle/HOL

Abstract

Equations that hold on some data structures such as natural numbers or lists are called inductive theorems in equational logic. Rewriting induction is a method based on term rewriting systems developed for proving inductive theorems. Interactive theorem provers are software tools that can be used to prove mathematical theorems interactively; by mechanically applying logical inference rules, the correctness of input proofs is checked. Such activity of giving machine-checked proofs is called “formalization.” By formalizing paper proofs, it is possible to ascertain whether the proof is really correct (on the logic in consideration). Many theorems on term rewriting systems have been formalized using the interactive theorem prover Isabelle/HOL; an Isabelle/HOL library containing theorems of term rewriting systems is known as the Isabelle/HOL Formalization of Rewriting (IsaFoR). Rewriting induction, however, had not been formalized in IsaFoR. In this paper, we report a formalization of rewriting induction given in (Aoto & Toyama, 2016) in Isabelle/HOL.