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A Verified Decision Procedure for Orders in Isabelle/HOL

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Part of the Lecture Notes in Computer Science book series (LNPSE,volume 12971)


We present the first verified implementation of a decision procedure for the quantifier-free theory of partial and linear orders. We formalise the procedure in Isabelle/HOL and provide a specification that is made executable using Isabelle’s code generator. The procedure is already part of the development version of Isabelle as a sub-procedure of the simplifier.

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  • DOI: 10.1007/978-3-030-88885-5_9
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  1. 1.

    File path of the procedure in the Isabelle2021 distribution: src/Provers/order.ML.

  2. 2.

    Introduced in commit


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We thank Kevin Kappelmann and the anonymous reviewers for their comments.

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Correspondence to Lukas Stevens .

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Stevens, L., Nipkow, T. (2021). A Verified Decision Procedure for Orders in Isabelle/HOL. In: Hou, Z., Ganesh, V. (eds) Automated Technology for Verification and Analysis. ATVA 2021. Lecture Notes in Computer Science(), vol 12971. Springer, Cham.

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