Abstract
System F is a well-known typed λ-calculus with polymorphic types, which provides a basis for polymorphic programming languages. We study an extension of F, called F <:, that combines parametric polymorphism with subtyping.
The main focus of the paper is the equational theory of F <:, which is related to PER models and the notion of parametricity. We study some categorical properties of the theory when restricted to closed terms, including interesting categorical isomorphisms. We also investigate proof-theoretical properties, such as the conservativity of typing judgments with respect to F.
We demonstrate by a set of examples how a range of constructs may be encoded in F <:. These include record operations and subtyping hierarchies that are related to features of object-oriented languages.
This author is partially supported by the CNR-Stanford collaboration grant 89.00002.26.
This author is partially supported by the ONR Contract N00014-88-K-0635 and by NSF Grant CCR-87-05596.
Simone Martini and Andre Scedrov would like to thank John C. Mitchell, the Computer Science Department, and the Center for the Study of Language and Information at Stanford University for their hospitality during those authors' extended stay in 1989–1990, when much of this research was done.
Luca Cardelli and Simone Martini would like to thank Pierre-Louis Curien, Giorgio Ghelli, and Giuseppe Longo for many stimulating discussions related to this work. In particular, Curien helped in the early proof of Top ∼ ∃(X)X.
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Cardelli, L., Martini, S., Mitchell, J.C., Scedrov, A. (1991). An extension of system F with subtyping. In: Ito, T., Meyer, A.R. (eds) Theoretical Aspects of Computer Software. TACS 1991. Lecture Notes in Computer Science, vol 526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-54415-1_73
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DOI: https://doi.org/10.1007/3-540-54415-1_73
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