Abstract
We present a fully abstract and effectively presentable model of unary FPC (a version of FPC with lifting rather than lifted sums) in a category of bicpos and continuous and stable functions. We show universality for the corresponding model of unary PCF, and then show that this implies full abstraction for unary FPC. We use a translation into this metalanguage to show that the “canonical” bidomain model of the lazy λ-calculus (with seqential convergence testing) is fully abstract.
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References
S. Abramsky. The lazy λ-calculus. In D. Turner, editor, Research Topics in Functional Programming, pages 65–117. Addison Wesley, 1990.
S. Abramsky and G. McCusker. Games and full abstraction for the lazy λ-calculus. In Proceedings of the Tenth Annual IEEE Symposium on Logic in Computer Science, pages 234–243. IEEE Computer Society Press, 1995.
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. Tennent, editors, Algol-like languages. Birkhauser, 1997.
S. Abramsky and C.-H. L. Ong. Full abstraction in the lazy λ-calculus. Information and Computation, 105:159–267, 1993.
S. Abramsky, R. Jagadeesan and P. Malacaria. Full abstraction for PCF. Information and Computation, 163:409–470, 2000.
G. Berry. Stable models of typed λ-calculi. In Proceedings of the 5th International Colloquium on Automata, Languages and Programming, number 62 in LNCS, pages 72–89. Springer, 1978.
G. Berry. Modèles complètement adéquats et stables des lambda-calculs typés. PhD thesis, Université Paris 7, 1979.
A. Bucciarelli and T. Ehrhard. A theory of sequentiality. Theoretical Computer Science, 113:273–292, 1993.
R. Cartwright and M. Felleisen. Observable sequentiality and full abstraction. In Proceedings of POPL’ 92, 1992.
R. Cartwright, P.-L. Curien and M. Felleisen. Fully abstract semantics for observably sequential languages. Information and Computation, 1994.
P.-L. Curien. Categorical combinators, sequential algorithms and functional programming. Progress in Theoretical Computer Science series. Birkhauser, 1993.
P.-L. Curien, G. Winskell, and G. Plotkin. Bistructures, bidomains and linear logic. In Milner Festschrift. MIT Press, 1997.
N. Dershowitz and Z. Manna. Proving termination with multiset orderings. Communications of the ACM, 22:465–476, 1979.
P. di Gianantonio. Games semantics for the pure lazy λ-calculus. In S. Abramsky, editor, Proceedings of TLCA’ 01, number 2044 in LNCS. Springer, 2001.
M. Fiore and G. Plotkin. An axiomatisation of compuationally adequate domain thoeretic models of FPC. In Proceedings of LICS’ 94, pages 92–102. IEEE Computer Society Press, 1994.
J. M. E. Hyland and C.-H. L. Ong. On full abstraction for PCF: I, II and III. Information and Computation, 163:285–408, 2000.
J. Laird. Bistability and bisequentiality. Available from the author’s home page, 2002.
R. Loader. Unary PCF is decidable. Theoretical Computer Science, 206, 1998.
R. Loader. Finitary PCF is undecidable. Annals of Pure and Applied Logic, 2000.
J. Longley. The sequentially realizable functionals. Technical Report ECS-LFCS-98-402, LFCS, Univ. of Edinburgh, 1998.
G. McCusker. Games and full abstraction for a functional metalanguage with recursive types. PhD thesis, Imperial College London, 1996.
P.W. O’Hearn and R. Tennent. Kripke logical relations and PCF. Information and Computation, 120(1):107–116, 1995.
A. M. Pitts. Relational properties of domains. Information and Computation, 127:66–90, 1996.
G. Plotkin. LCF considered as a programming language. Theoretical Computer Science, 5:223–255, 1977.
G. Plotkin. Postgraduate lecture notes in advanced domain theory (incorporating the ‘Pisa notes’). Available from http://www.dcs.ed.ac.uk/home/gdp/publications/, 1981.
G. Plotkin. Lectures on predomains and partial functions, 1985. Notes for a course given at the Center for the study of Language and Information, Stanford.
J. Riecke and A. Sandholm. A relational account of call-by-value sequentiality. In Proceedings of the Twelfth Annual Symposium on Logic in Computer Science, LICS’ 97. IEEE Computer Society Press, 1997.
M. Schmidt-Schauß. Decidability of behavioural equivalence in unary PCF. Theoretical Computer Science, 216:363–373, 1999.
M. Smyth and G. Plotkin. The category-theoretic solution of recursive domain equations. SIAM Journal on Computing, 11(4):761–783, 1982.
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Laird, J. (2003). A Fully Abstract Bidomain Model of Unary FPC. In: Hofmann, M. (eds) Typed Lambda Calculi and Applications. TLCA 2003. Lecture Notes in Computer Science, vol 2701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-44904-3_15
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DOI: https://doi.org/10.1007/3-540-44904-3_15
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