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A Tactic Language for Declarative Proofs

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Interactive Theorem Proving (ITP 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6172))

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Abstract

Influenced by the success of the Mizar system many declarative proof languages have been developed in the theorem prover community, as declarative proofs are more readable, easier to modify and to maintain than their procedural counterparts. However, despite their advantages, many users still prefer the procedural style of proof, because procedural proofs are faster to write. In this paper we show how to define a declarative tactic language on top of a declarative proof language. The language comes along with a rich facility to declaratively specify conditions on proof states in the form of sequent patterns, as well as ellipses (dot notation) to provide a limited form of iteration. As declarative tactics are specified using the declarative proof language, they offer the same advantages as declarative proof languages. At the same time, they also produce declarative justifications in the form of a declarative proof script and can thus be seen as an attempt to reduce the gap between procedural and declarative proofs.

This work was supported by German Ministry for Research and Education (BMBF) under grant 01 IW 07002 (project FormalSafe).

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Authors and Affiliations

  1. German Research Center for Artificial Intelligence (DFKI), Bremen, Germany

    Serge Autexier & Dominik Dietrich

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  1. Serge Autexier
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  2. Dominik Dietrich
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Editors and Affiliations

  1. Department of Computer Sciences, University of Texas, Austin, Talyor Hall 2.124, 78712-1188, Austin, TX, USA

    Matt Kaufmann

  2. Computer Laboratory, University of Cambridge, CB3 0FD, Cambridge,, UK

    Lawrence C. Paulson

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Autexier, S., Dietrich, D. (2010). A Tactic Language for Declarative Proofs. In: Kaufmann, M., Paulson, L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-14052-5_9

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  • DOI: https://doi.org/10.1007/978-3-642-14052-5_9

  • Publisher Name: Springer, Berlin, Heidelberg

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  • Online ISBN: 978-3-642-14052-5

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