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A Decision Procedure for (Co)datatypes in SMT Solvers

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Automated Deduction - CADE-25 (CADE 2015)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 9195))

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Abstract

We present a decision procedure that combines reasoning about datatypes and codatatypes. The dual of the acyclicity rule for datatypes is a uniqueness rule that identifies observationally equal codatatype values, including cyclic values. The procedure decides universal problems and is composable via the Nelson–Oppen method. It has been implemented in CVC4, a state-of-the-art SMT solver. An evaluation based on problems generated from theories developed with Isabelle demonstrates the potential of the procedure.

In memoriam Morgan Deters 1979–2015.

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Notes

  1. 1.

    http://lara.epfl.ch/~reynolds/CADE2015-cdt/.

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Acknowledgment

We owe a great debt to the development team of CVC4, including Clark Barrett and Cesare Tinelli, and in particular Morgan Deters, who jointly with the first author developed the initial version of the theory solver for datatypes in CVC4. Our present and former bosses, Viktor Kuncak, Stephan Merz, Tobias Nipkow, Cesare Tinelli, and Christoph Weidenbach, have either encouraged the research on codatatypes or at least benevolently tolerated it, both of which we are thankful for. Peter Gammie and Andreas Lochbihler provided useful benchmarks. Andrei Popescu helped clarify our thoughts regarding codatatypes and indicated related work. Dmitriy Traytel took part in discussions about degenerate codatatypes. Pascal Fontaine, Andreas Lochbihler, Andrei Popescu, Christophe Ringeissen, Mark Summerfield, Dmitriy Traytel, and the anonymous reviewers suggested many textual improvements. The second author’s research was partially supported by the Deutsche Forschungsgemeinschaft project “Den Hammer härten” (grant NI 491/14-1) and the Inria technological development action “Contre-exemples Utilisables par Isabelle et Coq” (CUIC).

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Authors and Affiliations

  1. École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland

    Andrew Reynolds

  2. Inria Nancy and LORIA, Villers-lès-Nancy, France

    Jasmin Christian Blanchette

  3. Max-Planck-Institut für Informatik, Saarbrücken, Germany

    Jasmin Christian Blanchette

Authors
  1. Andrew Reynolds
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  2. Jasmin Christian Blanchette
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Correspondence to Andrew Reynolds .

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Editors and Affiliations

  1. University of Ottawa, Ottawa, Canada

    Amy P. Felty

  2. University of Innsbruck, Innsbruck, Austria

    Aart Middeldorp

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Reynolds, A., Blanchette, J.C. (2015). A Decision Procedure for (Co)datatypes in SMT Solvers. In: Felty, A., Middeldorp, A. (eds) Automated Deduction - CADE-25. CADE 2015. Lecture Notes in Computer Science(), vol 9195. Springer, Cham. https://doi.org/10.1007/978-3-319-21401-6_13

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  • DOI: https://doi.org/10.1007/978-3-319-21401-6_13

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