Nonfree datatypes in Isabelle/HOL: animating a many-sorted metatheory

Schropp, Andreas and Popescu, Andrei (2013) Nonfree datatypes in Isabelle/HOL: animating a many-sorted metatheory. Certified Programs and Proofs: third international conference, CPP 2013, Melbourne, VIC, Australia, December 11-13, 2013, Proceeding. In: Certified Programs and Proofs (CPP), 11-13 Dec 2013, Melbourne, Australia. ISBN 9783319035444. ISSN 0302-9743 [Conference or Workshop Item] (doi:10.1007/978-3-319-03545-1_8)

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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.

Item Type: Conference or Workshop Item (Paper)
Additional Information: Volume 8307 of the series Lecture Notes in Computer Science
Research Areas: A. > School of Science and Technology > Computer Science > Foundations of Computing group
Item ID: 15368
Notes on copyright: The final publication is available at Springer via
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Depositing User: Andrei Popescu
Date Deposited: 27 Apr 2015 12:30
Last Modified: 09 Jun 2021 17:23

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