Deductive Synthesis of the Unification Algorithm: The Automation of Introspection

Abstract

We are working to create the first automatic deductive synthesis of a unification algorithm. The program is extracted from a proof of the existence of an output substitution that satisfies a given logical specification. Tests are introduced via case analysis in the proof, and recursion by application of the mathematical induction principle. The automation of the proof is challenging because it combines full quantifier reasoning and induction in a single framework. The program obtained is simpler than those previously constructed manually. Improvements in theorem proving technology lead us to believe that deductive synthesis could become a viable part of software production. Also, we suggest that a theorem prover’s reasoning about itself can be regarded as a form of introspection, which may enable it to improve itself.