Theory Exploration Powered by Deductive Synthesis

Abstract

This paper presents a symbolic method for automatic theorem generation based on deductive inference. Many software verification and reasoning tasks require proving complex logical properties; coping with this complexity is generally done by declaring and proving relevant sub-properties. This gives rise to the challenge of discovering useful sub-properties that can assist the automated proof process. This is known as the theory exploration problem, and so far, predominant solutions that emerged rely on evaluation using concrete values. This limits the applicability of these theory exploration techniques to complex programs and properties. In this work, we introduce a new symbolic technique for theory exploration, capable of (offline) generation of a library of lemmas from a base set of inductive data types and recursive definitions. Our approach introduces a new method for using abstraction to overcome the above limitations, combining it with deductive synthesis to reason about abstract values. Our implementation has shown to find more lemmas than prior art, avoiding redundant lemmas (in terms of provability), while being faster in most cases. This new abstraction-based theory exploration method is a step toward applying theory exploration to software verification and synthesis.