Categorical models of polymorphism

asperti, andrea; Martini, Simone

doi:10.1016/0890-5401(92)90024-A

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Categorical models of polymorphism

Author(s): Andrea Asperti , Simone Martini

Publication date Created: July 1992

Publication date (Print): July 1992

Journal: Information and Computation

Publisher: Elsevier BV

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The system F of variable types, fifteen years later

Jean-Yves Girard (1986)

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Categorical semantics for higher order polymorphic lambda calculus

R. A. G. Seely (1987)

A categorical structure suitable for interpreting polymorphic lambda calculus (PLC) is defined, providing an algebraic semantics for PLC which is sound and complete. In fact, there is an equivalence between the theories and the categories. Also presented is a definitional extension of PLC including “subtypes”, for example, equality subtypes, together with a construction providing models of the extended language, and a context for Girard's extension of the Dialectica interpretation.