A Tactic Language for the System Coq

Delahaye, David

doi:10.1007/3-540-44404-1_7

Cited by 134 publications

(107 citation statements)

References 5 publications

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“…We use Coq's built-in tactics for first-order inferences. Coq also has a language called Ltac for userdefined automated tactics (Delahaye, 2000). The additional axioms and tactics specialized for natural language constructions are written in Ltac.…”

Section: Inferences In Holmentioning

confidence: 99%

Higher-order logical inference with compositional semantics

Mineshima¹,

Martínez-Gómez²,

Miyao³

et al. 2015

Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing

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We present a higher-order inference system based on a formal compositional semantics and the wide-coverage CCG parser. We develop an improved method to bridge between the parser and semantic composition. The system is evaluated on the FraCaS test suite. In contrast to the widely held view that higher-order logic is unsuitable for efficient logical inferences, the results show that a system based on a reasonably-sized semantic lexicon and a manageable number of non-first-order axioms enables efficient logical inferences, including those concerned with generalized quantifiers and intensional operators, and outperforms the state-of-the-art firstorder inference system.

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Section: Inferences In Holmentioning

confidence: 99%

Higher-order logical inference with compositional semantics

Mineshima¹,

Martínez-Gómez²,

Miyao³

et al. 2015

Proceedings of the 2015 Conference on Empirical Methods in Natural Language Processing

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show abstract

“…These systems have also started to move the language where tactics are implemented from its implementation language (typically ML variants) to the proof language (e.g. LTac for Coq [12] and EisBach for Isabelle [27]). Autexier and Dietrich [3] has taken this even further and developed a declarative tactic language where tactics are written schematically.…”

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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“…Other improvements include a better readability of the Coq scripts by the definition of tactics using Ltac [8], the redefinition of the term algebra, and the separation between the specification (static) and proof (dynamic) parts.…”

Section: Improvementsmentioning

confidence: 99%

Automated Certification of Implicit Induction Proofs

Stratulat¹,

Demange²

2011

Certified Programs and Proofs

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Abstract. Theorem proving is crucial for the formal validation of properties about user specifications. With the help of the Coq proof assistant, we show how to certify properties about conditional specifications that are proved using automated proof techniques like those employed by the Spike prover, a rewrite-based implicit induction proof system. The certification methodology is based on a new representation of the implicit induction proofs for which the underlying induction principle is an instance of Noetherian induction governed by an induction ordering over equalities. We propose improvements of the certification process and show that the certification time is reasonable even for industrial-size applications. As a case study, we automatically prove and certify more than 40% of the lemmas needed for the validation of a conformance algorithm for the ABR protocol.

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A Tactic Language for the System Coq

Cited by 134 publications

References 5 publications

Higher-order logical inference with compositional semantics

Higher-order logical inference with compositional semantics

Mechanised Verification Patterns for Dafny

Automated Certification of Implicit Induction Proofs

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