Decision Procedures for Proving Inductive Theorems without Induction

Takahito Aoto (1) , Sorin Stratulat (2)

1 RIEC - Research Institute of Electrical Communication [Sendai]
2 LITA - Laboratoire d'Informatique Théorique et Appliquée

Automated inductive reasoning for term rewriting has been extensively studied in the literature. Classes of equations and term rewriting systems (TRSs) with decidable inductive validity have been identified and used to automatize the inductive reasoning. We give procedures for deciding the inductive validity of equations in some standard TRSs on natural numbers and lists. Contrary to previous decidability results, our procedures can automatically decide without involving induction reasoning the inductive validity of arbitrary equations for these TRSs, that is, without imposing any syntactical restrictions on the form of equations. We also report on the complexity of our decision procedures. These decision procedures are implemented in our automated provers for inductive theorems of TRSs and experiments are reported.

Mots clés: Inductive Theorems; Term Rewriting Systems; Decision Procedure; Initial Algebra

Domaines: Calcul formel [cs.SC]

Takahito Aoto, Sorin Stratulat. Decision Procedures for Proving Inductive Theorems without Induction. 16th International Symposium on Principles and Practice of Declarative Programming (PPDP) 2014, Sep 2014, Canterbury, United Kingdom. ⟨10.1145/2643135.2643156⟩. ⟨hal-01098929⟩