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International Conference on Theorem Proving in Higher Order Logics

TPHOLs 2009: Theorem Proving in Higher Order Logics pp 310–326Cite as

Formalising FinFuns – Generating Code for Functions as Data from Isabelle/HOL

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5674))

Abstract

FinFuns are total functions that are constant except for a finite set of points, i.e. a generalisation of finite maps. We formalise them in Isabelle/HOL and present how to safely set up Isabelle’s code generator such that operations like equality testing and quantification on FinFuns become executable. On the code output level, FinFuns are explicitly represented by constant functions and pointwise updates, similarly to associative lists. Inside the logic, they behave like ordinary functions with extensionality. Via the update/constant pattern, a recursion combinator and an induction rule for FinFuns allow for defining and reasoning about operators on FinFuns that directly become executable. We apply the approach to an executable formalisation of sets and use it for the semantics for a subset of concurrent Java.

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Author information

Authors and Affiliations

  1. Universität Karlsruhe (TH), Germany

    Andreas Lochbihler

Authors
  1. Andreas Lochbihler
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Editors and Affiliations

  1. Institut für Informatik, Technische Universität München, Boltzmannstraße 3, 85748, Garching, Germany

    Stefan Berghofer , Tobias Nipkow , Christian Urban  & Makarius Wenzel , ,  & 

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Lochbihler, A. (2009). Formalising FinFuns – Generating Code for Functions as Data from Isabelle/HOL. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds) Theorem Proving in Higher Order Logics. TPHOLs 2009. Lecture Notes in Computer Science, vol 5674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03359-9_22

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  • DOI: https://doi.org/10.1007/978-3-642-03359-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03358-2

  • Online ISBN: 978-3-642-03359-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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