The Axiom Profiler: Understanding and Debugging SMT Quantifier Instantiations

Abstract

SMT solvers typically reason about universal quantifiers via E-matching: syntactic matching patterns for each quantifier prescribe shapes of ground terms whose presence in the SMT run will trigger quantifier instantiations. The effectiveness and performance of the SMT solver depend crucially on well-chosen patterns. Overly restrictive patterns cause relevant quantifier instantiations to be missed, while overly permissive patterns can cause performance degradation including non-termination if the solver gets stuck in a matching loop. Understanding and debugging such instantiation problems is an overwhelming task, due to the typically large number of quantifier instantiations and their non-trivial interactions with each other and other solver aspects. In this paper, we present the Axiom Profiler, a tool that enables users to analyse instantiation problems effectively, by filtering and visualising rich logging information from SMT runs. Our tool implements novel techniques for automatically detecting matching loops and explaining why they repeat indefinitely. We evaluated the tool on the full test suites of five existing program verifiers, where it discovered and explained multiple previously-unknown matching loops.