Article

Testing concurrent systems: an interpretation of intuitionistic logic

Authors:

Radha Jagadeesan,

Gopalan Nadathur,

Vijay SaraswatAuthors Info & Claims

FSTTCS '05: Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science

Pages 517 - 528

https://doi.org/10.1007/11590156_42

Published: 15 December 2005 Publication History

Abstract

We present a natural confluence of higher-order hereditary Harrop formulas (HH formulas), Constraint Logic Programming (CLP, [JL87]), and Concurrent Constraint Programming (CCP, [Sar93]) as a fragment of (intuitionistic, higher-order) logic. This combination is motivated by the need for a simple executable, logical presentation for static and dynamic semantics of modern programming languages. The power of HH formulas is needed for higher-order abstract syntax, and the power of constraints is needed to naturally abstract the underlying domain of computation. Underpinning the combination is a sound and complete operational interpretation of a two-sided sequent presentation of (a large fragment of) intuitionistic logic in terms of behavioral testing of concurrent systems. Formulas on the left hand side of a sequent style presentation are viewed as a system of concurrent agents, and formulas on the right hand side as tests against this evolving system. The language permits recursive definitions of agents and tests, allows tests to augment the system being tested and allows agents to be contingent on the success of a test. We present a condition on proofs, operational derivability (OD), and show that the operational semantics generates only operationally derivable proofs. We show that a sequent in this logic has a proof iff it has an operationally derivable proof.

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https://dl.acm.org/doi/10.1145/2851141.2851153
Simmons R(2014)Structural FocalizationACM Transactions on Computational Logic10.1145/262967815:3(1-33)Online publication date: 8-Sep-2014
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cover image Guide Proceedings

FSTTCS '05: Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science

December 2005

566 pages

ISBN:3540304959

Editors:
Sundar Sarukkai
National Institute of Advanced Studies, Indian Institute of Science Campus, Bangalore, India
,
Sandeep Sen
Department of Comp. Sc. & Engg., Indian Institute of Technology Delhi, New Delhi, India

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 December 2005

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Cited By

Cruz FRocha RGoldstein S(2016)Declarative coordination of graph-based parallel programsACM SIGPLAN Notices10.1145/3016078.285115351:8(1-12)Online publication date: 27-Feb-2016
https://dl.acm.org/doi/10.1145/3016078.2851153
Cruz FRocha RGoldstein SAsenjo RHarris T(2016)Declarative coordination of graph-based parallel programsProceedings of the 21st ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming10.1145/2851141.2851153(1-12)Online publication date: 27-Feb-2016
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Simmons R(2014)Structural FocalizationACM Transactions on Computational Logic10.1145/262967815:3(1-33)Online publication date: 8-Sep-2014
https://dl.acm.org/doi/10.1145/2629678
Nigam VMiller DPorto ALópez-Fraguas F(2009)Algorithmic specifications in linear logic with subexponentialsProceedings of the 11th ACM SIGPLAN conference on Principles and practice of declarative programming10.1145/1599410.1599427(129-140)Online publication date: 7-Sep-2009
https://dl.acm.org/doi/10.1145/1599410.1599427
Liang CMiller D(2009)Focusing and polarization in linear, intuitionistic, and classical logicsTheoretical Computer Science10.1016/j.tcs.2009.07.041410:46(4747-4768)Online publication date: 1-Nov-2009
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Nystrom NSaraswat VPalsberg JGrothoff C(2008)Constrained types for object-oriented languagesACM SIGPLAN Notices10.1145/1449955.144980043:10(457-474)Online publication date: 19-Oct-2008
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Nystrom NSaraswat VPalsberg JGrothoff CHarris GKiczales GRiehle DBlack A(2008)Constrained types for object-oriented languagesProceedings of the 23rd ACM SIGPLAN conference on Object-oriented programming systems languages and applications10.1145/1449764.1449800(457-474)Online publication date: 19-Oct-2008
https://dl.acm.org/doi/10.1145/1449764.1449800
Liang CMiller D(2007)Focusing and polarization in intuitionistic logicProceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic10.5555/2392389.2392432(451-465)Online publication date: 11-Sep-2007
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Miller DSaurin A(2007)From proofs to focused proofsProceedings of the 21st international conference, and Proceedings of the 16th annuall conference on Computer Science Logic10.5555/2392389.2392429(405-419)Online publication date: 11-Sep-2007
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Lipton JNieva S(2007)Higher-order logic programming languages with constraintsProceedings of the 8th international conference on Typed lambda calculi and applications10.5555/1770203.1770223(272-289)Online publication date: 26-Jun-2007
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