Abstract
Pure, lazy functional languages like Haskell provide a sound basis for formal reasoning about programs in an equational style. In practice, however, equational reasoning about correctness proofs is underutilized. In the context of Haskell, we suggest that part of the reason for this is the lack of accessible tools for machine-checked equational reasoning. This paper outlines the design of MProver, a proof checker which fills just that niche. MProver features first-class support for reasoning about potentially undefined computations (particularly important in a lazy setting), and an extended notion of Haskell-like type classes, enabling a highly modular style of program verification that closely follows familiar functional programming idioms.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
The Coq development team: The Coq Proof Assistant Reference Manual. LogiCal Project, Version 8.3 (2010)
de Mol, M., van Eekelen, M., Plasmeijer, R.: Theorem Proving for Functional Programmers. In: Arts, T., Mohnen, M. (eds.) IFL 2002. LNCS, vol. 2312, pp. 55–71. Springer, Heidelberg (2002)
Gibbons, J., Hinze, R.: Just do it: Simple monadic equational reasoning. In: ICFP (September 2011)
Peyton Jones, S. (ed.): Haskell 98 Language and Libraries, the Revised Report. Cambridge University Press (2003)
Giménez, C.E.: Un calcul de constructions infinies et son application a la verification de systemes communicants, Ph.D. thesis (1996)
Yorgey, B.: Typeclassopedia, http://www.haskell.org/haskellwiki/Typeclassopedia (accessed May 31, 2012)
Stump, A., Deters, M., Petcher, A., Schiller, T., Simpson, T.: Verified Programming in Guru. In: PLPV 2008 (2008)
Benton, N., Kennedy, A., Varming, C.: Some Domain Theory and Denotational Semantics in Coq. In: Berghofer, S., Nipkow, T., Urban, C., Wenzel, M. (eds.) TPHOLs 2009. LNCS, vol. 5674, pp. 115–130. Springer, Heidelberg (2009)
Nanevski, A., Morrisett, G., Shinnar, A., Govereau, P., Birkedal, L.: Ynot: Reasoning with the awkward squad. In: ICFP 2008 (2008)
Nanevski, A., Morrisett, G., Birkedal, L.: Hoare Type Theory, Polymorphism and Separation. J. Funct. Program. 18(5-6), 865–911 (2008)
van Kesteren, R., van Eekelen, M., de Mol, M.: Proof support for general type classes. In: TFP 2004, pp. 1–16 (2004)
van Eekelen, M., de Mol, M.: Proof tool support for explicit strictness. In: Butterfield, A., Grelck, C., Huch, F. (eds.) IFL 2005. LNCS, vol. 4015, pp. 37–54. Springer, Heidelberg (2006)
Wadler, P., Blott, S.: How to make ad-hoc polymorphism less ad hoc. In: POPL 1989, pp. 60–76 (1989)
Sozeau, M., Oury, N.: First-class type classes. In: Mohamed, O.A., Muñoz, C., Tahar, S. (eds.) TPHOLs 2008. LNCS, vol. 5170, pp. 278–293. Springer, Heidelberg (2008)
Huffman, B., Matthews, J., White, P.: Axiomatic constructor classes in Isabelle/HOLCF. In: Hurd, J., Melham, T. (eds.) TPHOLs 2005. LNCS, vol. 3603, pp. 147–162. Springer, Heidelberg (2005)
Hallgren, T.: Haskell Tools from the Programatica Project. In: Haskell 2003, pp. 103–106 (2003)
Xu, D.N.: Extended static checking for Haskell. In: Haskell 2006, pp. 48–59 (2006)
Xu, D.N., Peyton Jones, S., Claessen, K.: Static contract checking for Haskell. In: POPL 2009, pp. 41–52 (2009)
Runciman, C., Naylor, M., Lindblad, F.: SmallCheck and Lazy SmallCheck: Automatic Exhaustive Testing for Small Values. In: Haskell 2008, pp. 37–48 (2008)
Claessen, K., Hughes, J.: QuickCheck: A Lightweight Tool for Random Testing of Haskell Programs. In: ICFP 2000, pp. 268–279 (2000)
Gill, A.: Introducing the Haskell Equational Reasoning Assistant. In: Haskell 2006, pp. 108–109 (2006)
Schröder, L., Mossakowski, T.: HasCasl: Integrated higher-order specification and program development. Theor. Comput. Sci. 410, 1217–1260 (2009)
Kieburtz, R.B.: P-logic: property verification for Haskell programs (2002)
Harrison, W.L., Kieburtz, R.B.: The Logic of Demand in Haskell. J. Funct. Program. 15, 837–891 (2005)
Howard, B.T.: Inductive, coinductive, and pointed types. In: ICFP 1996: Proceedings of the First ACM SIGPLAN International Conference on Functional Programming, pp. 102–109. ACM, New York (1996)
Casinghino III, C., Eades, H.D., Kimmell, G., Sjoberg, V., Sheard, T., Stump, A., Weirich, S.: The preliminary design of the Trellys core language Talk and discussion session at PLPV 2011 (2011)
Norell, U.: Towards a practical programming language based on dependent type theory. Department of Computer Science and Engineering, Chalmers University of Technology (September 2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Procter, A., Harrison, W.L., Stump, A. (2013). The Design of a Practical Proof Checker for a Lazy Functional Language. In: Loidl, HW., Peña, R. (eds) Trends in Functional Programming. TFP 2012. Lecture Notes in Computer Science, vol 7829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40447-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-40447-4_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-40446-7
Online ISBN: 978-3-642-40447-4
eBook Packages: Computer ScienceComputer Science (R0)