Automating Inductive Proofs Using Theory Exploration

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

doi:10.1007/978-3-642-38574-2_27

Cited by 83 publications

(80 citation statements)

References 17 publications

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“…The explore tactic is a simple form of term synthesis at the Dafny level, as used in e.g. HipSpec for Haskell [9]. We plan to implement tactics for richer explorations, supporting more than single statements and conditionals.…”

Section: Related Work Conclusion and Future Workmentioning

confidence: 99%

Mechanised Verification Patterns for Dafny

Grov¹,

Lin²,

Tumas³

2016

FM 2016: Formal Methods

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Abstract. In Dafny, the program text is used to both specify and implement programs in the same language [24]. It then uses a fully automated theorem prover to verify that the implementation satisfies the specification. However, the prover often needs further guidance from the user, and another role of the language is to provide such necessary hints and guidance. In this paper, we present a set of verification patterns to support this process. In previous work, we have developed a tactic language for Dafny, where users can encode their verification patterns and re-apply them for several proof tasks [16]. We extend this language with new features, implement our patterns in this tactic language and show, through experiments, generality of the patterns, and applicability of the tactic language.

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Section: Related Work Conclusion and Future Workmentioning

confidence: 99%

Mechanised Verification Patterns for Dafny

Grov¹,

Lin²,

Tumas³

2016

FM 2016: Formal Methods

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“…It consists of 50 theorems about lists and natural numbers and originates from evaluation of techniques for discovering auxiliary lemmas in the CLAM prover [6]. The original paper did not provide definitions for the functions used in the benchmarks, so the definitions provided here come from the evaluation of the HipSpec system [3]. These proofs are generally a bit harder, and may require additional lemmas to be found and proved (by another induction) or generalisation of the conjecture in order to strengthen the inductive hypothesis.…”

Section: Productive Use Of Failure Benchmarksmentioning

confidence: 99%

“…We have recently seen increased interest in inductive theorem proving, both with specialised provers such as IsaPlanner, Zeno and HipSpec [3,5,13], SMTsolvers such as CVC4 [11], the auto-active prover Dafny [10], recent work on the first-order SPASS prover [14], as well as some support in proof assistants [8,9].…”

Section: Introductionmentioning

confidence: 99%

TIP: Tons of Inductive Problems

Claessen

Johansson

Rosén

et al. 2015

Lecture Notes in Computer Science

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Abstract. This paper describes our collection of benchmarks for inductive theorem provers. The recent spur of interest in automated inductive theorem proving has increased the demands for evaluation and comparison between systems. We expect the benchmark suite to continually grow as more problems are submitted by the community. New challenge problems will promote further development of provers which will greatly benefit both developers and users of inductive theorem provers.

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“…Entailments of this kind are typical of automated theory exploration (see e.g. [16]), where potential lemmas are generated bottom-up from the definitions of the theory and, if proven valid, added to a lemma library. Such approaches rely heavily on relatively cheap methods of filtering out the many invalid "lemmas".…”

Section: Experimental Evaluationmentioning

confidence: 99%

Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

Brotherston

Gorogiannis

2015

Lecture Notes in Computer Science

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Abstract. We give a procedure for establishing the invalidity of logical entailments in the symbolic heap fragment of separation logic with user-defined inductive predicates, as used in program verification. This disproof procedure attempts to infer the existence of a countermodel to an entailment by comparing computable model summaries, a.k.a. bases (modified from earlier work), of its antecedent and consequent. Our method is sound and terminating, but necessarily incomplete. Experiments with the implementation of our disproof procedure indicate that it can correctly identify a substantial proportion of the invalid entailments that arise in practice, at reasonably low time cost. Accordingly, it can be used, e.g., to improve the output of theorem provers by returning "no" answers in addition to "yes" and "unknown" answers to entailment questions, and to speed up proof search or automated theory exploration by filtering out invalid entailments.

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Automating Inductive Proofs Using Theory Exploration

Cited by 83 publications

References 17 publications

Mechanised Verification Patterns for Dafny

Mechanised Verification Patterns for Dafny

TIP: Tons of Inductive Problems

Disproving Inductive Entailments in Separation Logic via Base Pair Approximation

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