Mathematical Induction in Otter-Lambda

Otter-lambda is Otter modified by adding code to implement an algorithm for lambda unification. Otter is a resolution-based, clause-language first-order prover that accumulates deduced clauses and uses strategies to control the deduction and retention of clauses. This is the first time that such a first-order prover has been combined in one program with a unification algorithm capable of instantiating variables to lambda terms to assist in the deductions. The resulting prover has all the advantages of the proof-search algorithm of Otter (speed, variety of inference rules, excellent handling of equality) and also the power of lambda unification. We illustrate how these capabilities work well together by using Otterlambda to find proofs by mathematical induction. Lambda unification instantiates the induction schema to find a useful instance of induction, and then Otter's first-order reasoning can be used to carry out the base case and induction step. If necessary, induction can be ...

• Type: Journal
• Year: 2006
• Where: JAR
• Authors: Michael Beeson
• Keywords: First-order Prover, JAR 2006, Lambda Unification, Prover