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A HOL Conversion for Translating Linear Time Temporal Logic to ω-Automata

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Theorem Proving in Higher Order Logics (TPHOLs 1999)

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Abstract

We present an embedding of linear time temporal logic LTL in HOL together with an elegant translation of LTL formulas into equivalent ω-automata. The translation is completely implemented by HOL rules and is therefore safe. Its implementation is mainly based on preproven theorems such that the conversion works very efficiently. In particular, it runs in linear time in terms of the given formula. The main application of this conversion is the sound integration of symbolic model checkers as (unsafe) decision procedures in the HOL theorem prover. On the other hand, the conversion also enables HOL users to directly verify temporal properties by means of HOL’s induction rules.

This work has been financed by DFG project ‘Verification of embedded systems’ and the ESPRIT LTR Project 26241 (Prosper).

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Authors and Affiliations

  1. Department of Computer Science Institute for Computer Design and Fault Tolerance, University of Karlsruhe, P.O. Box 6980, 76128, Karlsruhe, Germany

    Klaus Schneider & Dirk W. Hoffmann

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  1. Klaus Schneider
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  2. Dirk W. Hoffmann
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Editors and Affiliations

  1. INRIA Sophia Antipolis, 2004 Route des Lucioles, F-06902, Sophia Antipolis Cedex, France

    Yves Bertot , Gilles Dowek  & Laurent Théry ,  & 

  2. University of Nice - Sophia Antipolis, Parc Valrose, F-06108, Nice Cedex 2, France

    André Hirschowitz

  3. University of Paris XI, 15, rue Georges Clemenceau, F-91405, Orsay Cedex, France

    Christine Paulin

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Schneider, K., Hoffmann, D.W. (1999). A HOL Conversion for Translating Linear Time Temporal Logic to ω-Automata. In: Bertot, Y., Dowek, G., Théry, L., Hirschowitz, A., Paulin, C. (eds) Theorem Proving in Higher Order Logics. TPHOLs 1999. Lecture Notes in Computer Science, vol 1690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48256-3_17

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  • DOI: https://doi.org/10.1007/3-540-48256-3_17

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