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Tactics and Certificates in Meta Dedukti

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Interactive Theorem Proving (ITP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10895))

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Abstract

Tactics are often featured in proof assistants to simplify the interactive development of proofs by allowing domain-specific automation. Moreover, tactics are also helpful to check the output of automatic theorem provers because they can rebuild details that the provers omit.

We use meta-programming to define a tactic language for the Dedukti logical framework which can be used both for checking certificates produced by automatic provers and for developing proofs interactively.

More precisely, we propose a dependently-typed tactic language for first-order logic in Meta Dedukti and an untyped tactic language built on top of the typed one. We show the expressivity of these languages on two applications: a transfer tactic and a resolution certificate checker.

This work has been supported in part by the VECOLIB project of the French national research organization ANR (grant ANR-14-CE28-0018).

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Notes

  1. 1.

    By “untyped” we do not mean that no type is assigned to the Dedukti terms of the language but that typing is trivial: all the tactics have the same type (tactic).

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Authors and Affiliations

  1. University Paris Diderot, Irif, Paris, France

    Raphaël Cauderlier

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  1. Raphaël Cauderlier
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Correspondence to Raphaël Cauderlier .

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Editors and Affiliations

  1. Carnegie Mellon University, Pittsburgh, PA, USA

    Jeremy Avigad

  2. Inria, Nantes, France

    Assia Mahboubi

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Cauderlier, R. (2018). Tactics and Certificates in Meta Dedukti. In: Avigad, J., Mahboubi, A. (eds) Interactive Theorem Proving. ITP 2018. Lecture Notes in Computer Science(), vol 10895. Springer, Cham. https://doi.org/10.1007/978-3-319-94821-8_9

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  • DOI: https://doi.org/10.1007/978-3-319-94821-8_9

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