HipSpec : Automating Inductive Proofs of Program Properties

Claessen, Koen; Johansson, Moa; Rosén, Dan; Smallbone, Nick

doi:10.29007/3qwr

Cited by 14 publications

(9 citation statements)

References 14 publications

(15 reference statements)

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“…Complex programs might require recursive auxiliary functions. Discovering specifications for such functions automatically is a difficult task, akin to lemma discovery in theorem proving [7,16,25], which largely remains an open problem. SYNQUID expects users to provide the high-level insight about a complex algorithm in the form of auxiliary function signatures.…”

Section: Overviewmentioning

confidence: 99%

Program synthesis from polymorphic refinement types

Polikarpova

Kuraj

Solar-Lezama

2016

Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation

168

152

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We present a method for synthesizing recursive functions that provably satisfy a given specification in the form of a polymorphic refinement type. We observe that such specifications are particularly suitable for program synthesis for two reasons. First, they offer a unique combination of expressive power and decidability, which enables automatic verification-and hence synthesis-of nontrivial programs. Second, a type-based specification for a program can often be effectively decomposed into independent specifications for its components, causing the synthesizer to consider fewer component combinations and leading to a combinatorial reduction in the size of the search space. At the core of our synthesis procedure is a new algorithm for refinement type checking, which supports specification decomposition. We have evaluated our prototype implementation on a large set of synthesis problems and found that it exceeds the state of the art in terms of both scalability and usability. The tool was able to synthesize more complex programs than those reported in prior work (several sorting algorithms and operations on balanced search trees), as well as most of the benchmarks tackled by existing synthesizers, often starting from a more concise and intuitive user input.

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Section: Overviewmentioning

confidence: 99%

Program synthesis from polymorphic refinement types

Polikarpova

Kuraj

Solar-Lezama

2016

Proceedings of the 37th ACM SIGPLAN Conference on Programming Language Design and Implementation

168

152

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“…We also present some techniques for generating inductive subgoals during the proof search, based on Aubin's work [21]; other generalization heuristics, including the ones that rely on theory exploration [31], are compatible with our approach. User-provided lemmas can also be tried and used during proof search, without compromising soundness if they are actually invalid.…”

Section: Resultsmentioning

confidence: 99%

“…In this section, we examine several ways of guessing new inductive goals that are likely to help existing proof attempts progress. There is a large amount of literature dedicated to lemma guessing, either by generalizing a subgoal [9,15,20,21] or by exploring an equational theory systematically to find formulas that seem to hold based on testing [12,31]. In this paper we present simple, relatively straightforward techniques that already yield good results; more sophisticated heuristics can be added on top.…”

Section: Finding Subgoals and Lemmas By Generalizationmentioning

confidence: 99%

“…In Figure 4, we compare Zipperposition with two variations of CVC4 3 on TIP benchmarks. 4 The first one, CVC4, corresponds to cvc4 −−lang smt −−quant−ind to perform goal-directed induction [12]; the second one, CVC4-gen, has the additional flag −−conjecture−gen to generate lemmas by theory exploration, like Hipspec [31]. We use https://github.com/tip-org/tools/ to convert TIP problems into SMT-LIB by removing pattern matching (which is not supported by CVC4).…”

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confidence: 99%

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Superposition with Structural Induction

Cruanes

2017

Frontiers of Combining Systems

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Superposition-based provers have been successfully used to discharge proof obligations stemming from proof assistants. However, many such obligations require induction to be proved. We present a new extension of typed superposition that can perform structural induction. Several inductive goals can be attempted within a single saturation loop, by leveraging AVATAR [1]. Lemmas obtained by generalization or theory exploration can be introduced during search, used, and proved, all in the same search space. We describe an implementation and present some promising results.

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“…The HipSpec system [7] automatically derives and proves properties about functional programs. HipSpec rst uses QuickSpec to discover conjectures to prove.…”

Section: Related Workmentioning

confidence: 99%

Speculate: discovering conditional equations and inequalities about black-box functions by reasoning from test results

BraquehaisRudy

RuncimanColin

2017

SIGPLAN Not.

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This paper presents Speculate, a tool that automatically conjectures laws involving conditional equations and inequalities about Haskell functions. Speculate enumerates expressions involving a given collection of Haskell functions, testing to separate those expressions into apparent equivalence classes. Expressions in the same equivalence class are used to conjecture equations. Representative expressions of di erent equivalence classes are used to conjecture conditional equations and inequalities. Speculate uses lightweight equational reasoning based on term rewriting to discard redundant laws and to avoid needless testing. Several applications demonstrate the e ectiveness of Speculate.CCS Concepts •Software and its engineering →Software testing and debugging; •Theory of computation →Program speci cations;

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HipSpec : Automating Inductive Proofs of Program Properties

Cited by 14 publications

References 14 publications

Program synthesis from polymorphic refinement types

Program synthesis from polymorphic refinement types

Superposition with Structural Induction

Speculate: discovering conditional equations and inequalities about black-box functions by reasoning from test results

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