Abstract
Subtyping in first order object calculi is studied with respect to the logical semantics obtained by identifying terms that satisfy the same set of predicates, as formalized through an assignment system. It is shown that equality in the full first order ς-calculus is modelled by this notion, which on turn is included in a Morris style contextual equivalence.
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References
Abadi, M., Cardelli, L.: A Theory of Objects. Springer, Heidelberg (1996)
Abramsky, S.: Domain theory in logical form. Annals of Pure and Applied Logic 51, 1–77 (1991)
Barendregt, H.P., Coppo, M., Dezani, M.: A filter lambda model and the completeness of type assignment. Journal of Symbolic Logic 48, 931–940 (1983)
Breazu-Tannen, V., Coquand, T., Gunter, C.A., Scedrov, A.: Inheritance as implicit coercion. Information and Computation 93, 172–221 (1991)
Bruce, K.B., Longo, G.: A modest model of records, inheritance and bounded quantification. Information and Computation 87, 196–240 (1990)
Bruce, K.B., Mitchell, J.C.: Per models of subtyping, recursive types and higher-order polymorphism. In: Proc. of POPL (1992)
de’Liguoro, U.: CICLing 2001. LNCS, vol. 2004, pp. 315–328. Springer, Heidelberg (2001)
de’Liguoro, U.: Subtyping in logical form. In: ITRS 2002. ENTCS 70. Elsevier, Amsterdam (2002)
Gordon, A., Rees, G.: Bisimilarity for first-order calculus of objects with subtyping. In: Proc. of POPL 1996, pp. 386–395 (1996)
Mitchell, J.C.: Foundations for Programming Languages. MIT Press, Cambridge (1996)
van Bakel, S.: Intersection Type Assignment Systems. Theoretical Computer Science 151(2), 385–435 (1995)
van Bakel, S., de’Liguoro, U.: Logical semantics of the first order sigma-calculus. In: Blundo, C., Laneve, C. (eds.) ICTCS 2003. LNCS, vol. 2841, pp. 202–215. Springer, Heidelberg (2003)
van Bakel, S., de’Liguoro, U. (eds.): Subtyping object and recursive types logically (July 2005), www.di.unito.it/~deligu/papers/
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van Bakel, S., de’Liguoro, U. (2005). Subtyping Object and Recursive Types Logically. In: Coppo, M., Lodi, E., Pinna, G.M. (eds) Theoretical Computer Science. ICTCS 2005. Lecture Notes in Computer Science, vol 3701. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11560586_7
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DOI: https://doi.org/10.1007/11560586_7
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-29106-0
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