research-article

Dijkstra monads for free

Authors:

Cătălin Hriţcu,

Kenji Maillard,

Guido Martínez,

Gordon Plotkin,

Jonathan Protzenko,

Nikhil SwamyAuthors Info & Claims

ACM SIGPLAN Notices, Volume 52, Issue 1

Pages 515 - 529

https://doi.org/10.1145/3093333.3009878

Published: 01 January 2017 Publication History

Abstract

Dijkstra monads enable a dependent type theory to be enhanced with support for specifying and verifying effectful code via weakest preconditions. Together with their closely related counterparts, Hoare monads, they provide the basis on which verification tools like F*, Hoare Type Theory (HTT), and Ynot are built. We show that Dijkstra monads can be derived "for free" by applying a continuation-passing style (CPS) translation to the standard monadic definitions of the underlying computational effects. Automatically deriving Dijkstra monads in this way provides a correct-by-construction and efficient way of reasoning about user-defined effects in dependent type theories. We demonstrate these ideas in EMF*, a new dependently typed calculus, validating it via both formal proof and a prototype implementation within F*. Besides equipping F* with a more uniform and extensible effect system, EMF* enables a novel mixture of intrinsic and extrinsic proofs within F*.

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Carnier DPottier FKeuchel S(2024)Type Inference LogicsProceedings of the ACM on Programming Languages10.1145/36897868:OOPSLA2(2125-2155)Online publication date: 8-Oct-2024
https://doi.org/10.1145/3689786
Charguéraud AChlipala AErbsen AGruetter S(2023)Omnisemantics: Smooth Handling of NondeterminismACM Transactions on Programming Languages and Systems10.1145/357983445:1(1-43)Online publication date: 24-Jan-2023
https://dl.acm.org/doi/10.1145/3579834
Yoon IZakowski YZdancewic S(2022)Formal reasoning about layered monadic interpretersProceedings of the ACM on Programming Languages10.1145/35476306:ICFP(254-282)Online publication date: 31-Aug-2022
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Index Terms

Dijkstra monads for free
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation

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Information

Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 52, Issue 1

POPL '17

January 2017

901 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/3093333

Editor:
Matthew Fluet

Issue’s Table of Contents

POPL '17: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages
January 2017
901 pages
ISBN:9781450346603
DOI:10.1145/3009837
General Chair:
Giuseppe Castagna
Paris Diderot University, France / CNRS, France
,
Program Chair:
Andrew D. Gordon
Microsoft Research, UK / University of Edinburgh, UK

Copyright © 2017 ACM.

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Association for Computing Machinery

New York, NY, United States

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Published: 01 January 2017

Published in SIGPLAN Volume 52, Issue 1

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Carnier DPottier FKeuchel S(2024)Type Inference LogicsProceedings of the ACM on Programming Languages10.1145/36897868:OOPSLA2(2125-2155)Online publication date: 8-Oct-2024
https://doi.org/10.1145/3689786
Charguéraud AChlipala AErbsen AGruetter S(2023)Omnisemantics: Smooth Handling of NondeterminismACM Transactions on Programming Languages and Systems10.1145/357983445:1(1-43)Online publication date: 24-Jan-2023
https://dl.acm.org/doi/10.1145/3579834
Yoon IZakowski YZdancewic S(2022)Formal reasoning about layered monadic interpretersProceedings of the ACM on Programming Languages10.1145/35476306:ICFP(254-282)Online publication date: 31-Aug-2022
https://dl.acm.org/doi/10.1145/3547630
Protzenko JBeurdouche BMerigoux DBhargavan K(2019)Formally Verified Cryptographic Web Applications in WebAssembly2019 IEEE Symposium on Security and Privacy (SP)10.1109/SP.2019.00064(1256-1274)Online publication date: May-2019
https://doi.org/10.1109/SP.2019.00064
Kura SUnno H(2024)Automated Verification of Higher-Order Probabilistic Programs via a Dependent Refinement Type SystemProceedings of the ACM on Programming Languages10.1145/36746628:ICFP(973-1002)Online publication date: 15-Aug-2024
https://dl.acm.org/doi/10.1145/3674662
Zhou ZYe QDelaware BJagannathan S(2024)A HAT Trick: Automatically Verifying Representation Invariants using Symbolic Finite AutomataProceedings of the ACM on Programming Languages10.1145/36564338:PLDI(1387-1411)Online publication date: 20-Jun-2024
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Andrici CCiobâcă ȘHriţcu CMartínez GRivas ETanter ÉWinterhalter T(2024)Securing Verified IO Programs Against Unverified Code in F*Proceedings of the ACM on Programming Languages10.1145/36329168:POPL(2226-2259)Online publication date: 5-Jan-2024
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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
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Ho SFromherz AProtzenko J(2023)Modularity, Code Specialization, and Zero-Cost Abstractions for Program VerificationProceedings of the ACM on Programming Languages10.1145/36078447:ICFP(385-416)Online publication date: 31-Aug-2023
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