research-article

Dijkstra and Hoare monads in monadic computation

Author:

Bart JacobsAuthors Info & Claims

Theoretical Computer Science, Volume 604, Issue C

Pages 30 - 45

https://doi.org/10.1016/j.tcs.2015.03.020

Published: 02 November 2015 Publication History

Abstract

The Dijkstra and Hoare monads have been introduced recently for capturing weakest precondition computations and computations with pre- and post-conditions, within the context of program verification, supported by a theorem prover. Here we give a more general description of such monads in a categorical setting. We first elaborate the recently developed view on program semantics in terms of a triangle of computations, state transformers, and predicate transformers. Instantiating this triangle for different computational monads T shows how to define the Dijkstra monad associated with T, via the logic involved.Subsequently we give abstract definitions of the Dijkstra and Hoare monad, parametrised by a computational monad. These definitions presuppose a suitable (categorical) predicate logic, defined on the Kleisli category of the underlying monad. When all this structure exists, we show that there are maps of monads (Hoare) (State) (Dijkstra), all parametrised by a monad T.

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Cited By

Wang ZCao QTao Y(2024)Verifying Programs with Logic and Extended Proof Rules: Deep Embedding vs. Shallow EmbeddingJournal of Automated Reasoning10.1007/s10817-024-09706-568:3Online publication date: 10-Aug-2024
https://dl.acm.org/doi/10.1007/s10817-024-09706-5
Maillard KHriţcu CRivas EVan Muylder A(2019)The next 700 relational program logicsProceedings of the ACM on Programming Languages10.1145/33710724:POPL(1-33)Online publication date: 20-Dec-2019
https://dl.acm.org/doi/10.1145/3371072
Maillard KAhman DAtkey RMartínez GHriţcu CRivas ETanter É(2019)Dijkstra monads for allProceedings of the ACM on Programming Languages10.1145/33417083:ICFP(1-29)Online publication date: 26-Jul-2019
https://dl.acm.org/doi/10.1145/3341708
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Index Terms

Dijkstra and Hoare monads in monadic computation
1. Theory of computation
  1. Logic

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Published In

cover image Theoretical Computer Science

Theoretical Computer Science Volume 604, Issue C

November 2015

133 pages

ISSN:0304-3975

Issue’s Table of Contents

Copyright © Elsevier B.V.

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Elsevier Science Publishers Ltd.

United Kingdom

Publication History

Published: 02 November 2015

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Cited By

Wang ZCao QTao Y(2024)Verifying Programs with Logic and Extended Proof Rules: Deep Embedding vs. Shallow EmbeddingJournal of Automated Reasoning10.1007/s10817-024-09706-568:3Online publication date: 10-Aug-2024
Maillard KHriţcu CRivas EVan Muylder A(2019)The next 700 relational program logicsProceedings of the ACM on Programming Languages10.1145/33710724:POPL(1-33)Online publication date: 20-Dec-2019
Maillard KAhman DAtkey RMartínez GHriţcu CRivas ETanter É(2019)Dijkstra monads for allProceedings of the ACM on Programming Languages10.1145/33417083:ICFP(1-29)Online publication date: 26-Jul-2019
Ahman DHriţcu CMaillard KMartínez GPlotkin GProtzenko JRastogi ASwamy N(2017)Dijkstra monads for freeACM SIGPLAN Notices10.1145/3093333.300987852:1(515-529)Online publication date: 1-Jan-2017
Ahman DHriţcu CMaillard KMartínez GPlotkin GProtzenko JRastogi ASwamy NCastagna GGordon A(2017)Dijkstra monads for freeProceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages10.1145/3009837.3009878(515-529)Online publication date: 1-Jan-2017
Castagna GGordon A(2017)Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming LanguagesundefinedOnline publication date: 1-Jan-2017
Hino WKobayashi HHasuo IJacobs BKoskinen EGrohe MShankar N(2016)Healthiness from DualityProceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/2933575.2935319(682-691)Online publication date: 5-Jul-2016

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