Abstract
We propose a framework for synthesizing inductive invariants for incomplete verification engines, which soundly reduce logical problems in undecidable theories to decidable theories. Our framework is based on the counterexample guided inductive synthesis principle and allows verification engines to communicate non-provability information to guide invariant synthesis. We show precisely how the verification engine can compute such non-provability information and how to build effective learning algorithms when invariants are expressed as Boolean combinations of a fixed set of predicates. Moreover, we evaluate our framework in two verification settings, one in which verification engines need to handle quantified formulas and one in which verification engines have to reason about heap properties expressed in an expressive but undecidable separation logic. Our experiments show that our invariant synthesis framework based on non-provability information can both effectively synthesize inductive invariants and adequately strengthen contracts across a large suite of programs. This work is an extended version of a conference paper titled “Invariant Synthesis for Incomplete Verification Engines”.
Highlights
The paradigm of deductive verification [24,32] combines manual annotations and semiautomated theorem proving to prove programs correct
We show how the formula-driven problem of learning expressions from conjunctive/disjunctive non-provability information (CD-non-provability information (NPI)) constraints can be reduced to the data-driven ICE model
We investigate data-driven invariant synthesis for incomplete verification engines and show that the problem can be reduced to ICE learning if the learning algorithm learns from non-provability information and produces hypotheses in a class that is restricted to positive Boolean formulas over a fixed set of predicates
Summary
The paradigm of deductive verification [24,32] combines manual annotations and semiautomated theorem proving to prove programs correct. In this situation, automated verification engines commonly use a variety of bounded quantifier instantiation techniques (such as E-matching, triggers, and modelbased quantifier instantiation) to replace universal quantification by conjunctions over a specific set of terms This soundly reduces satisfiability checking of the negated verification conditions to a decidable theory. Based on such techniques, we implement our framework and we show that it is able to effectively generate invariants that prove a challenging suite of programs correct against universally quantified specifications. To the best of our knowledge, our framework is the first to systematically address the problem of invariant synthesis for incomplete verification engines that work by soundly reducing undecidable logics to decidable ones. This work presents a second case study, namely the implementation of our framework for verifying programs against specifications with universal quantification as well as an empirical evaluation for this setting (Sect. 4), which was not contained in the conference paper
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