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Games In The Semantics Of Programming Languages – An Elementary Introduction

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Abstract

Mathematical models are an important tool in the development ofsoftware technology, including programming languages and algorithms.During the last few years, a new class of such models has beendeveloped based on the notion of a mathematical game that isespecially well-suited to address the interactions between thecomponents of a system. This paper gives an introduction to thesegame-semantical models of programming languages, concentrating onmotivating the basic intuitions and putting them into context.

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REFERENCES

  • Abramsky, S.: 1999, ‘Retracing Some Paths in Process Algebra’, in CONCUR’ 96: Concurrency Theory (Pisa), Springer Verlag, Berlin, pp. 1–17.

    Google Scholar 

  • Abramsky, S.: 1997a, ‘Semantics of Interaction: An Introduction to Game Semantics’, in A. Pitts and P. Dybjer (eds.), Semantics and Logics of Computation, Cambridge, 1995), Cambridge, pp.1–31.

  • Abramsky, S.: 1997b, ‘Games in the Semantics of Programming Languages’, in P. Dekker, M. Stokhof and Y. Venema (eds.), Proceedings of the 11th Amsterdam Colloquium, ILLC, Department of Philosophy, University of Amsterdam 1997, pp. 1–6.

  • Abramsky, S.: 1999a, A note on Reactive Refinement.

  • Abramsky, S.: 1999b, ‘Process Realizability/Concurrent Games & Full Completeness of Linear Logic’, Lecture Notes for the Lectures at the Marktoberdorf Summer School.

  • Abramsky, S.: 1999c, ‘Game Semantics and Full Abstraction for Sequential Programming Languages’, Course at LFCS, University of Edinburgh.

  • Abramsky, S., Honda, K., and McCusker, G.: 1998, ‘A Fully Abstract Game Semantics for General References’, in Proceedings of the Thirteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE, pp. 334–344.

  • Abramsky, S. and Jagadeesan, R.: 1992, ‘Games and Full Completeness for Multiplicative Linear Logic (extended abstract)’, in R. Shyamsunder (ed.), Foundations of Software Technology and Theoretical Computer Science, New Delhi, 1992, Berlin, pp. 291–301.

  • Abramsky, S. and Jagadeesan, R.: 1994, ‘Games and Full Completeness for Multiplicative Linear Logic’, Journal of Symbolic Logic 59, 543–574.

    Google Scholar 

  • Abramsky, S., Jagadeesan, R., and Malacaria, P.: 1994, ‘Full Abstraction for PCF (extended abstract)’, in M. Hagiya and J. C. Mitchell (eds.), Theoretical Aspects of Computer Software, Sendai, 1994) Berlin, pp. 1–15.

  • Abramsky, S., Jagadeesan, R., and Malacaria, P.: 2000, ‘Full Abstraction for PCF, Information and Computation. 163, 409–470.

    Google Scholar 

  • Abramsky, S. and McCusker, G.: 1997, ‘Linearity, Sharing and State: A Fully Abstract Game Semantics for IDEALIZED ALGOL with Active Expressions’, in P. O’Hearn and R. Tennent (eds.), ALGOL-like Languages, Volume 2, Boston, pp. 297–329.

  • Abramsky, S. and McCusker, G.: 1999a, ‘Game Semantics’, in H. Schwichtenberg and U. Berger (eds.), Logic and Computation: Proceedings of the 1997 Marktoberdorf Summer School, Berlin, pp. 1–55.

  • Abramsky, S. and McCusker, G.: 1999b, ‘Full Abstraction for Idealized Algol with Passive Expressions’, Theoretical Computer Science 227, 3–42.

    Google Scholar 

  • Abramsky, S. and Melliès, P. A.: 1999, ‘Concurrent Games and Full Completeness’, in Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE, pp. 431–442.

  • Berry, G. and Curien, P. L.: 1982, ‘Sequential Algorithms on Concrete Data Structures’, Theoretical Computer Science 20, 265–321

    Google Scholar 

  • Blass, A.: 1992, ‘A game Semantics for Linear Logic’, Annals of Pure and Applied Logic 56, 183–220.

    Google Scholar 

  • Felscher, W.: 1986, ‘Dialogues as a Foundation for Intuitionistic Logic’, in D. Gabbay and F. Guenther (eds.), Handbook of Philosophical Logic, vol. III, D. Reidel Publishing Company, pp. 341–372.

  • Girard, J.-Y.: 1987, ‘Linear Logic’, Theoretical Computer Science 50, 1–101.

    Google Scholar 

  • Girard, J.-Y.: 1989, ‘Towards a geometry of Interaction’, in John W. Gray and Andre Scedrov (eds.), Categories in Computer Science and Logic, Proceedings of the AMS-IMS-SIAM joint summer research conference held June 14–20, 1987, University of Colorado, Boulder, with support from the National Science Foundation, Providence [Contemporary Mathematics 92], pp. 69–108.

  • Harmer, R. and McCusker, G.: 1999, ‘A Fully Abstract Game Semantics for Finite Non-determinism’, in Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE.

  • Hintikka, J. and Sandu, G.: 1997, ‘Game-theoretical Semantics’, in J. van Benthem (ed.), Handbook of Logic and Language, Elsevier Science.

  • Hoare, C. A. R.: 1985, Communicating Sequential Processes, Prentice-Hall International.

  • Honda, K., and Yoshida, N.: 1997, ‘Game Theoretic Analysis of Call-by-value Computation’, in P. Degano, R. Gorrieri and A. Marchietti-Spaccamela (eds.), Proceedings, 25th International Colloquium on Automata, Languages and Programming: ICALP’ 97, Berlin [Lecture Notes in Computer Science 1256], pp. 225–236.

  • Hyland, J. M. E. and Ong, C. H. L.: 1993, ‘Fair Games and Full Completeness for Multiplicative Linear Logic without the Mix-Rule’, Unpublished Manuscript.

  • Hyland, J. M. E. and Ong, C. H. L.: 2000, ‘On Full Abstraction for PCF: I, II and III’, Information and Computation 163, 285–408.

    Google Scholar 

  • Joyal, A.: 1977, ‘Remarques sur la Théorie des Jeux a Deux Personnes’, Gazette des Sciences Mathématiques du Quebec 1(4).

  • Jürjens, J.: 1999a, ‘Towards Reactive Refinement’, contributed talk at the Marktoberdorf Summer School.

  • Jürjens, J.: 1999b, ‘A Category of Processes, Specifications and Refinement’, talk at the workshop “Categorical Models of Concurrency”, Dresden, October 1999.

  • Lafont, Y. and Streicher, T.: 1991, ‘Game Semantics for Linear Logic’, in Proceedings of the Sixth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE, pp. 43–50.

  • Laird, J.: 1997, ‘Full Abstraction for Functional Languages with Control’, in Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE, pp. 58–67.

  • Lamarche, F.: 1994, ‘Sequentiality, Games and Linear Logic (Announcement)’, in Workshop on Categorical Logic in Computer Science.

  • Lorenzen, P.: 1960, ‘Logik und Agon’, in Atti del Congresso Internazionale di Filosofia, Sansoni, Firenze, pp. 187–194.

    Google Scholar 

  • Malacaria, P. and Hankin, C.: 1999, ‘Non-deterministic Games and Program Analysis: An Application to Security’, in Proceedings of the Fourteenth International Symposium on Logic in Computer Science, Computer Society Press of the IEEE, pp. 443–452.

  • McCusker, G.: 1998, ‘Games and Full Abstraction for a Functional Metalanguage with Recursive Types’, Berlin [Distinguished Dissertations in Computer Science].

  • Matthes, R.: 2002, ‘Tarski’s Fixed-point Theorem and Higher-order Term Rewrite Sys-tems’, this volume.

  • Merz, S.: 2002, ‘Model Checking and Beyond: On the Analysis of Reactive Systems’, this volume.

  • Mey, D.: 1994, ‘Finite games for a Predicate Logic without Contractions’, Theoretical Computer Science 123, 341–349.

    Google Scholar 

  • Nickau, H.: 1996, ‘Hereditarily Sequential Functionals: A Game-Theoretic Approach to Sequentiality’, Dissertation, Universität Gesamthochschule Siegen.

  • Plotkin, G. D.: 1977, ‘LCF Considered as a Programming Language’, Theoretical Computer Science 5, 223–255.

    Google Scholar 

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Jürjens, J. Games In The Semantics Of Programming Languages – An Elementary Introduction. Synthese 133, 131–158 (2002). https://doi.org/10.1023/A:1020883810034

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