Nonfree Datatypes in Isabelle/HOL

Animating a Many-Sorted Metatheory
  • Andreas Schropp
  • Andrei Popescu
Conference paper

DOI: 10.1007/978-3-319-03545-1_8

Part of the Lecture Notes in Computer Science book series (LNCS, volume 8307)
Cite this paper as:
Schropp A., Popescu A. (2013) Nonfree Datatypes in Isabelle/HOL. In: Gonthier G., Norrish M. (eds) Certified Programs and Proofs. CPP 2013. Lecture Notes in Computer Science, vol 8307. Springer, Cham

Abstract

Datatypes freely generated by their constructors are well supported in mainstream proof assistants. Algebraic specification languages offer more expressive datatypes on axiomatic means: nonfree datatypes generated from constructors modulo equations. We have implemented an Isabelle/HOL package for nonfree datatypes, without compromising foundations. The use of the package, and its nonfree iterator in particular, is illustrated with examples: bags, polynomials and λ-terms modulo α-equivalence. The many-sorted metatheory of nonfree datatypes is formalized as an ordinary Isabelle theory and is animated by the package into user-specified instances. HOL lacks a type of types, so we employ an ad hoc construction of a universe embedding the relevant parameter types.

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  • Andreas Schropp
    • 1
    • 3
  • Andrei Popescu
    • 1
    • 2
  1. 1.Technische Universität MünchenGermany
  2. 2.Institute of Mathematics Simion Stoilow of the Romanian AcademyRomania
  3. 3.COMSA GmbHGermany

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