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.

References

[1]

Alexander Aiken. Introduction to set constraint-based program analysis. Sci. Comput. Program., 35(2-3):79-111, 1999.

Digital Library

[2]

Roy Dyckhoff. Contraction-free sequent calculi for intuitionistic logic. The Journal of Symbolic Logic, 57(3), September 1992.

[3]

The eclipse project. www.eclipse.org.

[4]

Stacy E. Finkelstein, Peter Freyd, and James Lipton. A new framework for declarative programming. Theor. Comput. Sci., 300(1-3):91-160, 2003.

Digital Library

[5]

Robert Fuhrer, Frank Tip, and Adam Kiezun. Advanced refactorings in eclipse. In OOPSLA '04: Companion to the 19th annual ACM SIGPLAN conference on Objectoriented programming systems, languages, and applications, pages 8-8, New York, NY, USA, 2004. ACM Press.

Digital Library

[6]

Miguel Garcia-Diaz and Susana Nieva. Providing declarative semantics for hh extended constraint logic programs. In PPDP '04: Proceedings of the 6th ACM SIGPLAN international conference on Principles and practice of declarative programming, pages 55-66, New York, NY, USA, 2004. ACM Press.

Digital Library

[7]

Nevin Charles Heintze. Set based program analysis. PhD thesis, Carnegie Mellon University, Pittsburgh, PA, USA, 1992.

Digital Library

[8]

S. Haridi and S. Janson. Kernel andorra Prolog and its computation model. In David H. D. Warren and Peter Szeredi, editors, Proceedings of the Seventh International Conference on Logic Programming, pages 31-46, Jerusalem, 1990. The MIT Press.

Digital Library

[9]

J. Jaffar and J.-L. Lassez. Constraint Logic Programming. In Proceedings of the 14th Annual ACM Symposium on Principles of Programming Languages (POPL'87), Munich, Germany, pages 111-119. ACM Press, New York (NY), USA, 1987.

Digital Library

[10]

Sorin Lerner, Todd Millstein, Erika Rice, and Craig Chambers. Automated soundness proofs for dataflow analyses and transformations via local rules. In POPL '05: Proceedings of the 32nd ACM SIGPLAN-SIGACT symposium on Principles of programming languages, pages 364-377, New York, NY, USA, 2005. ACM Press.

Digital Library

[11]

Javier Leach, Susana Nieva, and Mario Rodrguez-Artalejo. Constraint logic programming with hereditary harrop formulas. Theory Pract. Log. Program., 1(4):409-445, 2001.

Digital Library

[12]

Pablo López, Frank Pfenning, Jeff Polakow, and Kevin Watkins. Monadic concurrent linear logic programming. In Pedro Barahona and Amy P. Felty, editors, PPDP, pages 35-46. ACM, 2005.

Digital Library

[13]

Patrick Lincoln and Vijay Saraswat. Proofs as concurrent processes. Technical report, PARC, 1993.

[14]

Dale Miller, Gopalan Nadathur, Frank Pfenning, and Andre Scedrov. Uniform proofs as a foundation for logic programming. Annals of Pure and Applied Logic, 51:125-157, 1991.

[15]

Nathaniel Nystrom, Michael R. Clarkson, and Andrew C. Myers. Polyglot: An extensible compiler framework for java. In Proceedings of the Conference on Compiler Construction (CC'03), pages 1380-152, April 2003.

Digital Library

[16]

Gopalan Nadathur and Dale Miller. Higher-order logic programming. In C. Hogger D. Gabbay and A. Robinson, editors, Handbook of Logic in Artificial Intelligence and Logic Programming, volume 5, pages 499-590. Oxford University Press, 1998.

[17]

P.W. O'Hearn and D. J. Pym. The logic of bunched implications. Bulletin of Symbolic Logic, 5(2):215-244, 1999.

[18]

Martin Odersky, Martin Sulzmann, and Martin Wehr. Type inference with constrained types. Theor. Pract. Object Syst., 5(1):35-55, 1999.

Digital Library

[19]

Jens Palsberg. Closure analysis in constraint form. ACM Trans. Program. Lang. Syst., 17(1):47-62, 1995.

Digital Library

[20]

Frank Pfenning and Conal Elliott. Higher-order abstract syntax. In Proceedings of the ACM-SIGPLAN Conference on Programming Language Design and Implementation, pages 199-208. ACM Press, June 1988.

Digital Library

[21]

Jens Palsberg and Michael I. Schwartzbach. Object-oriented type systems. John Wiley and Sons Ltd., Chichester, UK, UK, 1994.

Digital Library

[22]

Prakash Panangaden, Vijay A. Saraswat, P. J. Scott, and R. A. G. Seely. A hyperdoctrinal view of concurrent constraint programming. In J.W. de Bakker, Willem P. de Roever, and Grzegorz Rozenberg, editors, REX Workshop, volume 666 of Lecture Notes in Computer Science, pages 457-476. Springer, 1992.

Digital Library

[23]

William Pugh and David Wonnacott. Constraint-based array dependence analysis. ACM Trans. Program. Lang. Syst., 20(3):635-678, 1998.

Digital Library

[24]

Atanas Rountev, Ana Milanova, and Barbara G. Ryder. Points-to analysis for java using annotated constraints. In OOPSLA '01: Proceedings of the 16th ACM SIGPLAN conference on Object oriented programming, systems, languages, and applications, pages 43-55, New York, NY, USA, 2001. ACM Press.

Digital Library

[25]

Vijay A. Saraswat. The category of constraint systems is cartesian closed. In Proceedings of the IEEE Symposium on Logic in Computer Science, 1992.

[26]

V. Saraswat. Concurrent Constraint Programming. Doctoral Dissertation Award and Logic Programming. MIT Press, 1993.

Digital Library

[27]

Natarajan Shankar. Proof search in the intuitionistic sequent calculus. In Deepak Kapur, editor, Automated Deduction - CADE-11, number 607 in Lecture Notes in Computer Science, pages 522-536. Springer Verlag, June 1992.

Digital Library

[28]

V Saraswat, R Jagadeesan, and V Gupta. jcc: Integrating timed default concurrent constraint programming into Java. Number 2902 in Lecture Notes in Computer Science, pages 156-170. Springer Verlag, 2003.

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
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
https://dl.acm.org/doi/10.1145/2629678
Show More Cited By

Recommendations

Reasoning about inconsistent concurrent systems: a non-classical temporal logic
SOFSEM'06: Proceedings of the 32nd conference on Current Trends in Theory and Practice of Computer Science

It has been widely recognized that inconsistencies often appear and are inevitable when specifying large and complex concurrent systems. The logic QCL (quasi-classical logic) has therefore been developed for handling such specifications. But, on the one ...
Interactive proofs in higher-order concurrent separation logic
POPL '17

When using a proof assistant to reason in an embedded logic -- like separation logic -- one cannot benefit from the proof contexts and basic tactics of the proof assistant. This results in proofs that are at a too low level of abstraction because they ...
Interactive proofs in higher-order concurrent separation logic
POPL '17: Proceedings of the 44th ACM SIGPLAN Symposium on Principles of Programming Languages

When using a proof assistant to reason in an embedded logic -- like separation logic -- one cannot benefit from the proof contexts and basic tactics of the proof assistant. This results in proofs that are at a too low level of abstraction because they ...

Comments

Information & Contributors

Information

Published In

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

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

10
Total Citations
View Citations
0
Total Downloads

Downloads (Last 12 months)0
Downloads (Last 6 weeks)0

Reflects downloads up to 26 Sep 2024

Other Metrics

View Author Metrics

Citations

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
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
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
https://dl.acm.org/doi/10.1016/j.tcs.2009.07.041
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
https://dl.acm.org/doi/10.1145/1449955.1449800
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
https://dl.acm.org/doi/10.5555/2392389.2392432
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
https://dl.acm.org/doi/10.5555/2392389.2392429
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
https://dl.acm.org/doi/10.5555/1770203.1770223

View Options

View options

Media

Figures

Other

Tables

View Table of Contents