Chapter 14 - Inductionless Induction

Abstract

The aim of inductive theorem proving is to prove statements about particular structures, e.g., natural numbers, lists, and arrays. Natural first-order axiomatizations of such familiar objects fail to capture the true statements we want to prove. The inductionless induction approach is the basis of several inductive theorem provers. In general such theorem provers are small: nothing comparable with the Boyer and Moore theorem prover in terms of applications. Probably the most well-known one is part of the RRL system (this system also includes a cover set induction tool which is not a proof by consistency technique). There are some other implementations such as ReDuX1 or UNICOM. However, the main advantage of inductionless induction is the ability to use general purpose first-order theorem provers for inductive theorem proving; there is no real need to develop a dedicated tool. The only requirement is to design dedicated strategies within a first-order theorem prover.