Article

Monad-independent Hoare logic in HasCasl

Authors:

Lutz Schröder,

Till MossakowskiAuthors Info & Claims

FASE'03: Proceedings of the 6th international conference on Fundamental approaches to software engineering

Pages 261 - 277

Published: 07 April 2003 Publication History

Abstract

Monads have been recognized by Moggi as an elegant device for dealing with stateful computation in functional programming languages. It is thus natural to develop a Hoare calculus for reasoning about computational monads. While this has previously been done only for the state monad, we here provide a generic, monad-independent approach, which applies also to further computational monads such as exceptions, input/output, and non-determinism. All this is formalized within the logic of HASCASL, a higher-order language for functional specification and programming. Combination of monadic features can be obtained by combining their loose specifications. As an application, we prove partial correctness of Dijkstra's nondeterministic version of Euclid's algorithm in a monad with nondeterministic dynamic references.

References

[1]

K. Claessen and J. Hughes, Testing monadic code with QuickCheck, Haskell Workshop, ACM, 2002, pp. 65-77.

Digital Library

[2]

CoFI, The Common Framework Initiative for algebraic specification and development, electronic archives, http://www.brics.dk/Projects/CoFI.

[3]

CoFI Language Design Task Group, Casl - The CoFI Algebraic Specification Language - Summary, version 1.0, Documents/CASL/Summary, in {2}, July 1999.

[4]

E. W. Dijkstra, A discipline of programming, Prentice Hall, 1976.

Digital Library

[5]

J.-C. Filliâtre, Proof of imperative programs in type theory, Types for Proofs and Programs, LNCS, vol. 1657, Springer, 1999, pp. 78-92.

Digital Library

[6]

R. Goldblatt, Logics of time and computation, CSLI, 1992.

Digital Library

[7]

The Haskell mailing list, http://www.haskell.org/mailinglist.html, May 2002.

[8]

S. P. Jones, J. Hughes, L. Augustsson, D. Barton, B. Boutel, W. Burton, J. Fasel, K. Hammond, R. Hinze, P. Hudak, T. Johnsson, M. Jones, J. Launchbury, E. Meijer, J. Peterson, A. Reid, C. Runciman, and P. Wadler, Haskell 98: A non-strict, purely functional language, (1999), http://www.haskell.org/onlinereport.

[9]

C. Lüth and N. Ghani, Monads and modularity, Frontiers of Combining Systems, LNAI, vol. 2309, Springer, 2002, pp. 18-32.

Digital Library

[10]

S. Mac Lane, Categories for the working mathematician, Springer, 1997.

[11]

E. Moggi, Notions of computation and monads, Inform. and Comput. 93 (1991), 55-92.

Digital Library

[12]

P. D. Mosses, Casl: A guided tour of its design, Workshop on Abstract Datatypes, LNCS, vol. 1589, Springer, 1999, pp. 216-240.

Digital Library

[13]

F. Regensburger, HOLCF: Higher order logic of computable functions, Theorem Proving in Higher Order Logics, LNCS, vol. 971, 1995, pp. 293-307.

Digital Library

[14]

L. Schröder and T. Mossakowski, HASCASL: Towards integrated specification and development of Haskell programs, Algebraic Methodology and Software Technology, LNCS, vol. 2422, Springer, 2002, pp. 99-116.

Digital Library

[15]

Philip Wadler, How to declare an imperative, ACM Computing Surveys 29 (1997), 240-263.

Digital Library

Cited By

Silva RVasconcellos CRoggia KCavalcante EDantas FBatista T(2020)Monadic W in CoqProceedings of the 24th Brazilian Symposium on Context-Oriented Programming and Advanced Modularity10.1145/3427081.3427085(25-32)Online publication date: 19-Oct-2020
https://dl.acm.org/doi/10.1145/3427081.3427085
Goncharov SSchroder L(2013)A Relatively Complete Generic Hoare Logic for Order-Enriched EffectsProceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS.2013.33(273-282)Online publication date: 25-Jun-2013
https://dl.acm.org/doi/10.1109/LICS.2013.33
Schröder LMossakowski T(2009)HasCaslTheoretical Computer Science10.1016/j.tcs.2008.11.020410:12-13(1217-1260)Online publication date: 20-Mar-2009
https://dl.acm.org/doi/10.1016/j.tcs.2008.11.020
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Monad-independent Hoare logic in HasCasl
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
2. Theory of computation
  1. Formal languages and automata theory
    1. Formalisms
  2. Semantics and reasoning

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Published In

cover image Guide Proceedings

FASE'03: Proceedings of the 6th international conference on Fundamental approaches to software engineering

April 2003

403 pages

ISBN:3540008993

Editor:
Mauro Pezzè
Università degli Studi di Milano Bicocca, Dipartimento di Informatica, Sistemistica e Comunicazione, Milano, Italy

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 07 April 2003

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Cited By

Silva RVasconcellos CRoggia KCavalcante EDantas FBatista T(2020)Monadic W in CoqProceedings of the 24th Brazilian Symposium on Context-Oriented Programming and Advanced Modularity10.1145/3427081.3427085(25-32)Online publication date: 19-Oct-2020
https://dl.acm.org/doi/10.1145/3427081.3427085
Goncharov SSchroder L(2013)A Relatively Complete Generic Hoare Logic for Order-Enriched EffectsProceedings of the 2013 28th Annual ACM/IEEE Symposium on Logic in Computer Science10.1109/LICS.2013.33(273-282)Online publication date: 25-Jun-2013
https://dl.acm.org/doi/10.1109/LICS.2013.33
Schröder LMossakowski T(2009)HasCaslTheoretical Computer Science10.1016/j.tcs.2008.11.020410:12-13(1217-1260)Online publication date: 20-Mar-2009
https://dl.acm.org/doi/10.1016/j.tcs.2008.11.020
Mossakowski TSchröder LGoncharov S(2008)A generic complete dynamic logic for reasoning about purity and effectsProceedings of the Theory and practice of software, 11th international conference on Fundamental approaches to software engineering10.5555/1792838.1792858(199-214)Online publication date: 29-Mar-2008
https://dl.acm.org/doi/10.5555/1792838.1792858
Schröder L(2007)Bootstrapping types and cotypes in HASCASLProceedings of the 2nd international conference on Algebra and coalgebra in computer science10.5555/1770730.1770762(447-461)Online publication date: 20-Aug-2007
https://dl.acm.org/doi/10.5555/1770730.1770762
Boulmé S(2007)Intuitionistic refinement calculusProceedings of the 8th international conference on Typed lambda calculi and applications10.5555/1770203.1770209(54-69)Online publication date: 26-Jun-2007
https://dl.acm.org/doi/10.5555/1770203.1770209
Saabas AUustalu T(2006)Compositional type systems for stack-based low-level languagesProceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 5110.5555/2523791.2523798(27-39)Online publication date: 16-Jan-2006
https://dl.acm.org/doi/10.5555/2523791.2523798
Harrison W(2006)Proof abstraction for imperative languagesProceedings of the 4th Asian conference on Programming Languages and Systems10.1007/11924661_6(97-113)Online publication date: 8-Nov-2006
https://dl.acm.org/doi/10.1007/11924661_6
Goncharov SSchröder LMossakowski T(2006)Completeness of global evaluation logicProceedings of the 31st international conference on Mathematical Foundations of Computer Science10.1007/11821069_39(447-458)Online publication date: 28-Aug-2006
https://dl.acm.org/doi/10.1007/11821069_39
Mossakowski T(2006)Monad-Based logics for computational effectsProceedings of the 11th international conference on Algebraic Methodology and Software Technology10.1007/11784180_3(3-4)Online publication date: 5-Jul-2006
https://dl.acm.org/doi/10.1007/11784180_3
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