research-article

Step-indexed kripke models over recursive worlds

Authors:

Jan Schwinghammer,

Kristian Støvring,

Jacob Thamsborg,

Hongseok YangAuthors Info & Claims

ACM SIGPLAN Notices, Volume 46, Issue 1

Pages 119 - 132

https://doi.org/10.1145/1925844.1926401

Published: 26 January 2011 Publication History

Abstract

Over the last decade, there has been extensive research on modelling challenging features in programming languages and program logics, such as higher-order store and storable resource invariants. A recent line of work has identified a common solution to some of these challenges: Kripke models over worlds that are recursively defined in a category of metric spaces. In this paper, we broaden the scope of this technique from the original domain-theoretic setting to an elementary, operational one based on step indexing. The resulting method is widely applicable and leads to simple, succinct models of complicated language features, as we demonstrate in our semantics of Charguéraud and Pottier's type-and-capability system for an ML-like higher-order language. Moreover, the method provides a high-level understanding of the essence of recent approaches based on step indexing.

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Cited By

Skorstengaard LDevriese DBirkedal L(2019)Reasoning about a Machine with Local CapabilitiesACM Transactions on Programming Languages and Systems10.1145/336351942:1(1-53)Online publication date: 10-Dec-2019
https://doi.org/10.1145/3363519
Birkedal LBizjak AClouston RGrathwohl HSpitters BVezzosi A(2019)Guarded Cubical Type TheoryJournal of Automated Reasoning10.1007/s10817-018-9471-763:2(211-253)Online publication date: 2-Aug-2019
https://dl.acm.org/doi/10.1007/s10817-018-9471-7
Skorstengaard LDevriese DBirkedal L(2018)Reasoning About a Machine with Local CapabilitiesProgramming Languages and Systems10.1007/978-3-319-89884-1_17(475-501)Online publication date: 14-Apr-2018
https://doi.org/10.1007/978-3-319-89884-1_17
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Index Terms

Step-indexed kripke models over recursive worlds
1. Software and its engineering
  1. Software notations and tools
    1. Formal language definitions
2. Theory of computation

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Published In

cover image ACM SIGPLAN Notices

ACM SIGPLAN Notices Volume 46, Issue 1

POPL '11

January 2011

624 pages

ISSN:0362-1340

EISSN:1558-1160

DOI:10.1145/1925844

Issue’s Table of Contents

POPL '11: Proceedings of the 38th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages
January 2011
652 pages
ISBN:9781450304900
DOI:10.1145/1926385
General Chair:
Thomas Ball
Microsoft Research, USA
,
Program Chair:
Mooly Sagiv
Tel Aviv University, Israel

Copyright © 2011 ACM.

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Association for Computing Machinery

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Publication History

Published: 26 January 2011

Published in SIGPLAN Volume 46, Issue 1

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Cited By

Skorstengaard LDevriese DBirkedal L(2019)Reasoning about a Machine with Local CapabilitiesACM Transactions on Programming Languages and Systems10.1145/336351942:1(1-53)Online publication date: 10-Dec-2019
https://doi.org/10.1145/3363519
Birkedal LBizjak AClouston RGrathwohl HSpitters BVezzosi A(2019)Guarded Cubical Type TheoryJournal of Automated Reasoning10.1007/s10817-018-9471-763:2(211-253)Online publication date: 2-Aug-2019
https://dl.acm.org/doi/10.1007/s10817-018-9471-7
Skorstengaard LDevriese DBirkedal L(2018)Reasoning About a Machine with Local CapabilitiesProgramming Languages and Systems10.1007/978-3-319-89884-1_17(475-501)Online publication date: 14-Apr-2018
https://doi.org/10.1007/978-3-319-89884-1_17
Balabonski TPottier FProtzenko J(2016)The Design and Formalization of Mezzo, a Permission-Based Programming LanguageACM Transactions on Programming Languages and Systems10.1145/283702238:4(1-94)Online publication date: 2-Aug-2016
https://doi.org/10.1145/2837022
Severi Pde Vries F(2013)Completeness of Conversion between Reactive Programs for Ultrametric ModelsTyped Lambda Calculi and Applications10.1007/978-3-642-38946-7_17(221-235)Online publication date: 2013
https://doi.org/10.1007/978-3-642-38946-7_17
Schwinghammer JBirkedal LReus BYang H(2011)Nested Hoare Triples and Frame Rules for Higher-order StoreLogical Methods in Computer Science10.2168/LMCS-7(3:21)20117:3Online publication date: 28-Sep-2011
https://doi.org/10.2168/LMCS-7(3:21)2011
Charlton N(2011)Hoare Logic for Higher Order Store Using Simple SemanticsLogic, Language, Information and Computation10.1007/978-3-642-20920-8_10(52-66)Online publication date: 2011
https://doi.org/10.1007/978-3-642-20920-8_10
Qian KSmith SStride BWeng SWu K(2024)Semantic-Type-Guided Bug FindingProceedings of the ACM on Programming Languages10.1145/36897888:OOPSLA2(2183-2210)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689788
Jacobs JHinrichsen JKrebbers R(2024)Deadlock-Free Separation Logic: Linearity Yields Progress for Dependent Higher-Order Message PassingProceedings of the ACM on Programming Languages10.1145/36328898:POPL(1385-1417)Online publication date: 5-Jan-2024
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Spies SGäher LTassarotti JJung RKrebbers RBirkedal LDreyer D(2022)Later credits: resourceful reasoning for the later modalityProceedings of the ACM on Programming Languages10.1145/35476316:ICFP(283-311)Online publication date: 31-Aug-2022
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