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Modular verification tools allow programmers to compositionally specify and prove function specifications. When using a modular verifier, proving a specification about a functionfrequires additional specifications for the functions called byf. With existing state of the art tools, programmers must manually write the specifications for callee functions. We present a counterexample guided algorithm to automatically infer these specifications. The algorithm is parameterized over a verifier, counterexample generator, and constraint guided synthesizer. We show that if each of these three components is sound and complete over a finite set of possible specifications, our algorithm is sound and complete as well. Additionally, we introducesize-boundedsynthesis functions, which extends our completeness result to an infinite set of possible specifications. In particular, we describe a size-bounded synthesis function for linear integer arithmetic constraints. We conclude with an evaluation demonstrating our technique on a variety of benchmarks. When using a modular verifier, proving a specification about a functionfrequires additional specifications for the functions called byf. With existing state of the art tools, programmers must manually write the specifications for callee functions. We present a counterexample guided algorithm to automatically infer these specifications. The algorithm is parameterized over a verifier, counterexample generator, and constraint guided synthesizer. We show that if each of these three components is sound and complete over a finite set of possible specifications, our algorithm is sound and complete as well. Additionally, we introducesize-boundedsynthesis functions, which extends our completeness result to an infinite set of possible specifications. In particular, we describe a size-bounded synthesis function for linear integer arithmetic constraints. We conclude with an evaluation demonstrating our technique on a variety of benchmarks. 

Abstract Program equivalence checking is the task of confirming that two programs have the same behavior on corresponding inputs. We develop a calculus based on symbolic execution and coinduction to check the equivalence of programs in a non-strict functional language. Additionally, we show that our calculus can be used to derive counterexamples for pairs of inequivalent programs, including counterexamples that arise from non-termination. We describe a fully automated approach for finding both equivalence proofs and counterexamples. Our implementation,nebula, proves equivalences of programs written in Haskell. We demonstratenebula’s practical effectiveness at both proving equivalence and producing counterexamples automatically by applyingnebulato existing benchmark properties. 

Program equivalence checking is the task of confirming that two programs have the same behavior on corresponding inputs. We develop a calculus based on symbolic execution and coinduction to check the equivalence of programs in a non-strict functional language. Additionally, we show that our calculus can be used to derive counterexamples for pairs of inequivalent programs, including counterexamples that arise from non-termination. We describe a fully automated approach for finding both equivalence proofs and counterexamples. Our implementation, Nebula, proves equivalences of programs written in Haskell. We demonstrate Nebula's practical effectiveness at both proving equivalence and producing counterexamples automatically by applying Nebula to existing benchmark properties. 

Programming-by-example (PBE) is a synthesis paradigm that allows users to generate functions by simply providing input-output examples. While a promising interaction paradigm, synthesis is still too slow for realtime interaction and more widespread adoption. Existing approaches to PBE synthesis have used automated reasoning tools, such as SMT solvers, as well as works applying machine learning techniques. At its core, the automated reasoning approach relies on highly domain specific knowledge of programming languages. On the other hand, the machine learning approaches utilize the fact that when working with program code, it is possible to generate arbitrarily large training datasets. In this work, we propose a system for using machine learning in tandem with automated reasoning techniques to solve Syntax Guided Synthesis (SyGuS) style PBE problems. By preprocessing SyGuS PBE problems with a neural network, we can use a data driven approach to reduce the size of the search space, then allow automated reasoning-based solvers to more quickly find a solution analytically. Our system is able to run atop existing SyGuS PBE synthesis tools, decreasing the runtime of the winner of the 2019 SyGuS Competition for the PBE Strings track by 47.65% to outperform all of the competing tools.