A theory for Abstract Reduction Systems (ARS) in the proof assistant PVS (Prototype Verification System) called ars is described. Adequate specifications of basic definitions and notions of the theory of ARSs such as reduction, confluence and normal form are given and well-known results formalized. The formalizations include non trivial results of the theory of ARSs such as the correctness of the principle of Noetherian Induction, Newman’s Lemma and its generalizations, and Commutation Lemmas, among others. Although term rewriting proving technologies have been provided in several specification languages and proof assistants, to our knowledge, before the development presented in this paper there was no complete formalization of an abstract reduction theory in PVS. This makes relevant the presented ars specification as the basis of a PVStheory called trs for the general treatment of Term Rewriting Systems.
Unique normal form property of compatible term rewriting systems: a new proof of Chew's theorem
