Skip to main content
SpringerLink
Log in

Nonfree Datatypes in Isabelle/HOL

Animating a Many-Sorted Metatheory

  • Conference paper
Certified Programs and Proofs (CPP 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8307))

Included in the following conference series:

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. The Coq Proof Assistant (2013), http://coq.inria.fr

  2. Maude ITP (2013), http://maude.cs.uiuc.edu/tools/itp

  3. Altenkirch, T., McBride, C., Morris, P.: Generic programming with dependent types. In: Backhouse, R., Gibbons, J., Hinze, R., Jeuring, J. (eds.) SSDGP 2006. LNCS, vol. 4719, pp. 209–257. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  4. Blanqui, F., Hardin, T., Weis, P.: On the implementation of construction functions for non-free concrete data types. In: De Nicola, R. (ed.) ESOP 2007. LNCS, vol. 4421, pp. 95–109. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Bove, A., Dybjer, P.: Dependent types at work. In: Bove, A., Barbosa, L.S., Pardo, A., Pinto, J.S. (eds.) LerNet ALFA Summer School 2008. LNCS, vol. 5520, pp. 57–99. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  6. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Quesada, J.F.: The Maude system. In: Narendran, P., Rusinowitch, M. (eds.) RTA 1999. LNCS, vol. 1631, pp. 240–243. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  7. CoFI task group on semantics, CASL — The Common Algebraic Specification Language, Semantics (1999), http://www.informatik.uni-bremen.de/cofi/wiki/index.php/CASL

  8. Coquand, T., Danielsson, N.A.: Isomorphism is equality. Draft (2013)

    Google Scholar 

  9. Haftmann, F., Wenzel, M.: Constructive type classes in Isabelle. In: Altenkirch, T., McBride, C. (eds.) TYPES 2006. LNCS, vol. 4502, pp. 160–174. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Harrison, J.: HOL Light: A tutorial introduction. In: Srivas, M., Camilleri, A. (eds.) FMCAD 1996. LNCS, vol. 1166, pp. 265–269. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  11. Homeier, P.V.: A design structure for higher order quotients. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 130–146. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  12. Huffman, B., Kuncar, O.: Lifting and transfer: A modular design for quotients in Isabelle/HOL. In: Isabelle Users Workshop (2012)

    Google Scholar 

  13. Huffman, B., Urban, C.: A new foundation for Nominal Isabelle. In: Kaufmann, M., Paulson, L.C. (eds.) ITP 2010. LNCS, vol. 6172, pp. 35–50. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  14. Kaliszyk, C., Urban, C.: Quotients revisited for Isabelle/HOL. In: SAC, pp. 1639–1644 (2011)

    Google Scholar 

  15. Kammüller, F., Wenzel, M., Paulson, L.C.: Locales - A sectioning concept for Isabelle. In: Bertot, Y., Dowek, G., Hirschowitz, A., Paulin, C., Théry, L. (eds.) TPHOLs 1999. LNCS, vol. 1690, pp. 149–166. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  16. Nadathur, G., Miller, D.: An overview of Lambda-Prolog. In: ICLP/SLP, pp. 810–827 (1988)

    Google Scholar 

  17. Nipkow, T., Paulson, L.C., Wenzel, M.: Isabelle/HOL: A Proof Assistant for Higher-Order Logic. LNCS, vol. 2283. Springer, Heidelberg (2002)

    Google Scholar 

  18. Norrish, M.: Recursive function definition for types with binders. In: Slind, K., Bunker, A., Gopalakrishnan, G.C. (eds.) TPHOLs 2004. LNCS, vol. 3223, pp. 241–256. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  19. Popescu, A., Gunter, E.L.: Recursion principles for syntax with bindings and substitution. In: ICFP, pp. 346–358 (2011)

    Google Scholar 

  20. Schropp, A.: Instantiating deeply embedded many-sorted theories into HOL types in Isabelle. Master’s thesis, Technische Universität München (2012), http://home.in.tum.de/~schropp/master-thesis.pdf

  21. Schropp, A., Popescu, A.: Nonfree datatypes: metatheory, implementation and examples, http://bitbucket.org/isaspecops/nonfree-data/downloads/cpp2013_bundle.zip

  22. Shulman, M., Licata, D., Lumsdaine, P.L., et al.: Higher inductive types on the homotopy type theory blog, http://homotopytypetheory.org/category/higher-inductive-types/

  23. Breazu-Tannen, V., Subrahmanyam, R.: Logical and computational aspects of programming with sets/bags/lists. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 60–75. Springer, Heidelberg (1991)

    Chapter  Google Scholar 

  24. Traytel, D., Popescu, A., Blanchette, J.C.: Foundational, compositional (co)datatypes for higher-order logic—Category theory applied to theorem proving. In: LICS 2012, pp. 596–605 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Technische Universität München, Germany

    Andreas Schropp & Andrei Popescu

  2. Institute of Mathematics Simion Stoilow of the Romanian Academy, Romania

    Andrei Popescu

  3. COMSA GmbH, Germany

    Andreas Schropp

Authors
  1. Andreas Schropp
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrei Popescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Microsoft Research Cambridge, 21 Station Road, CB1 2FB, Cambridge, UK

    Georges Gonthier

  2. Canberra Research Lab., NICTA, PO Box 8001, 2601, Canberra, ACT, Australia

    Michael Norrish

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer International Publishing Switzerland

About this paper

Cite this paper

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. https://doi.org/10.1007/978-3-319-03545-1_8

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-03545-1_8

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-03544-4

  • Online ISBN: 978-3-319-03545-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation