Abstract
We introduce a technique based on logical relations, which, given two models M and N of a simply typed lambda-calculus L, allows us to construct a model M/N whose L-theory is a superset of both Th(M) and Th(N).
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S. Abramsky, R. Jagadeesan, P. Malacaria. Full abstraction for PCF (Extended Abstract). Proc. of TACS 94, Lecture Notes in Computer Science 789, 1–15, Springer, 1994.
G. Berry. Modèles complètement adéquats et stables des λ-calculs typés, Thèse de Doctorat d'Etat, Université Paris VII, 1979.
G. Berry. Stable models of typed lambda-calculi. Proc. 5th Int. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science 62, 72–89, Springer, 1978.
G. Berry and P.L. Curien. Sequential algorithms on concrete data structures. Theoretical Computer Science 20, 265–231, 1982.
A. Bucciarelli. Logical relations and λ-theories. Proc. Imperial College Theory and Formal Methods Section Workshop, to appear, 1996.
A. Bucciarelli, T. Ehrhard. Sequentiality and Strong Stability. Proc. 6th Int. Symp. on Logic in Computer Science, 138–145, IEEE Computer Society Press, 1991.
A. Bucciarelli, T. Ehrhard. Extensional embedding of a strongly stable model of PCF. Proc. 18th Int. Coll. on Automata, Languages and Programming, Lecture Notes in Computer Science 510, 35–44, Springer, 1991.
A. Bucciarelli, T. Ehrhard. Sequentiality in an extensional framework. Information and Computation, Volume 110, Number 2, 265–296, 1994.
P.L. Curien. Categorical Combinators, Sequential Algorithms and Functional Programming. Revised edition, Birkhäuser, 1993.
T. Ehrhard. A relative definability result for strongly stable functions and some corollaries. Submitted paper, available at http://ida.dcs.qmw.ac.uk/authors/E/EhrhardT/, 1996.
H. Friedman. Equality between functionals. Proc. Logic Colloquium, Lecture Notes in Mathematics 453, 22–37, Springer, 1973.
J.M.E. Hyland, L. Ong. On full abstraction for PCF: I, II and III. 133pp, submitted paper, 1994.
T. Jim, A. Meyer. Full Abstraction and the Context Lemma. Proc. Theoretical Aspects of Comp. Sci. 1991, Lecture Notes in Computer Science 526, 131–151, Springer, 1991.
R. Loader. Finitary PCF is not decidable. Unpublished notes, available at http://info.ox.ac.uk/loader. 1996.
J.C. Mitchell. Type Systems for Programming Languages Handbook of Theoretical Computer Science, Volume B, edited by J. van Leeuwen, 365–458, Elsevier, 1990.
P. O'Hearn, J. Riecke. Kripke Logical Relations and PCF. To appear in Information and Computation.
G. Plotkin. LCF considered as a programming language. Theoretical Computer Science 5, 223–256, 1977.
D. Scott. A type theoretic alternative to CUCH, ISWIM, OWHY. Theoretical Computer Science 121, 411–440, 1993. Manuscript circulated since 1969.
G. Winskel. Stable Bistructure Models of PCF. BRICS Report Series 94-13, Departement of Computer Science, University of Aarhus, Denmark, 1994.
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Bucciarelli, A. (1997). Logical reconstruction of bi-domains. In: de Groote, P., Roger Hindley, J. (eds) Typed Lambda Calculi and Applications. TLCA 1997. Lecture Notes in Computer Science, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62688-3_31
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DOI: https://doi.org/10.1007/3-540-62688-3_31
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