Abstract
A general construction of models of call-by-value from models of call-by-name computation is described. The construction makes essential use of the properties of sum types in common denotational models of call-by-name. When applied to categories of games, it yields fully abstract models of the call-by-value functional language PCFv, which can be extended to incorporate recursive types, and of a language with local references as in Standard ML.
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S. Abramsky, R. Jagadeesan, and P. Malacaxia. Full abstraction for PCF. Submitted for publication, 1996.
S. Abramsky. Axioms for full abstraction and full completeness. In G. Plotkin and C. Sterling, editors, Milner Festschrift. MIT Press, to appear.
S. Abramsky and G. McCusker. Linearity, sharing and state: a fully abstract game semantics for Idealized Algol with active expressions. In P. W. O'Hearn and R. D. Tennent, editors, Algol-like Languages, pages 297–329 of volume 2. Birkhaüser, 1997.
M. P. Fiore. Axiomatic Domain Theory in Categories of Partial Maps. Distinguished Dissertations in Computer Science. Cambridge University Press, 1996.
M. P. Fiore and G. D. Plotkin. An axiomatization of computationally adequate domain theoretic models of FPC. In Proceedings, Ninth Annual IEEE Symposium on Logic in Computer Science, pages 92–102. IEEE Computer Society Press, 1994.
P. J. Freyd. Recursive types reduced to inductive types. In Proceedings, Fifth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, 1990.
P. J. Freyd. Algebraically complete categories. In A. Carboni et al., editors, Proc. 1990 Como Category Theory Conference, pages 95–104, Berlin, 1991. Springer-Verlag. Lecture Notes in Mathematics Vol. 1488.
J.-Y. Girard. Linear Logic. Theoretical Computer Science, 50(1):1–102, 1987.
K. Honda and N. Yoshida. Game theoretic analysis of call-by-value computation. In P. Degano, R. Gorrieri, and A. Marchietti-Spaccamela, editors, Proceedings, 25th International Colloquium on Automata, Languages and Programming: ICALP '97, volume 1256 of Lecture Notes in Computer Science, pages 225–236. Springer-Verlag, 1997.
J. M. E. Hyland and C.-H. L. Ong. On full abstraction for PCF: I, II and III. Submitted for publication, 1996.
B. Jacobs. Semantics of weakening and contraction. Annals of Pure and Applied Logic, 69:73–106, 1994.
G. McCusker. Games and Full Abstraction for a Functional Metalanguage with Recursive Types. PhD thesis, Department of Computing, Imperial College, University of London, 1996.
G. McCusker. Games and full abstraction for FPC. In Proceedings, Eleventh Annual IEEE Symposium on Logic in Computer Science, pages 174–183. IEEE Computer Society Press, 1996.
E. Moggi. Notions of computation and monads. Information and Computation, 93:55–92, 1991.
H. Nickau. Hereditarily sequential functionals. In Proceedings of the Symposium on Logical Foundations of Computer Science: Logic at St. Petersburg, Lecture notes in Computer Science. Springer, 1994.
A. M. Pitts. Relational properties of domains. Information and Computation, 127:66–90, 1996.
A. M. Pitts and I. D. B. Stark. Observable properties of higher order functions that dynamically create local names, or: What's new? In Mathematical Foundations of Computer Science, Proc. 18th Int. Symp., Gdańsk, 1993, volume 711 of Lecture Notes in Computer Science, pages 122–141. Springer-Verlag, Berlin, 1993.
A. M. Pitts and I. D. B. Stark. On the observable properties of higher order functions that dynamically create local names (preliminary report). In Workshop on State in Programming Languages, Copenhagen, 1993, pages 31–45. ACM SIGPLAN, 1993. Yale Univ. Dept. Computer Science Technical Report YALEU/DCS/RR-968.
A. M. Pitts. Some notes on inductive and co-inductive techniques in the semantics of functional programs. Notes Series BRIGS-NS-94-5, BRIGS, Department of Computer Science, University of Aarhus, December 1994. vi+135 pp, draft version.
G. Plotkin. LCF considered as a programming language. Theoretical Computer Science, 5:223–255, 1977.
G. Plotkin. Lectures on predomains and partial functions. Notes for a course given at the Center for the Study of Language and Information, Stanford, 1985.
J. Power and E. Robinson. Premonoidal categories and notions of computation. Mathematical Structures in Computer Science, 11, 1993.
J. C. Reynolds. Syntactic control of interference. In Conf. Record 5th ACM Symposium on Principles of Programming Languages, pages 39–46, 1978.
J. C. Reynolds. The essence of Algol. In Proceedings of the 1981 International Symposium on Algorithmic Languages, pages 345–372. North-Holland, 1981.
K. Sieber. Relating full abstraction results for different programming languages. In Proceedings of 10th Conference on Foundations of Software Technology and Theoretical Computer Science, Bangalore, 1990. Springer LNCS 472.
I. Stark. Names and Higher-Order Functions. PhD thesis, University of Cambridge, Dec 1994.
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Abramsky, S., McCusker, G. (1998). Call-by-value games. In: Nielsen, M., Thomas, W. (eds) Computer Science Logic. CSL 1997. Lecture Notes in Computer Science, vol 1414. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0028004
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DOI: https://doi.org/10.1007/BFb0028004
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