Categorical semantics for higher order polymorphic lambda calculus

Journal of Symbolic Logic 52 (4):969-989 (1987)
Abstract
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
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DOI 10.2307/2273831
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References found in this work BETA
The „Dialectica” Interpretation and Categories.Philip J. Scott - 1978 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 24 (31-36):553-575.
The „Dialectica”︁ Interpretation and Categories.Philip J. Scott - 1978 - Mathematical Logic Quarterly 24 (31‐36):553-575.

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Citations of this work BETA
Second-Order Type Isomorphisms Through Game Semantics.Joachim de Lataillade - 2008 - Annals of Pure and Applied Logic 151 (2-3):115-150.
A Game Semantics for Generic Polymorphism.Samson Abramsky & Radha Jagadeesan - 2005 - Annals of Pure and Applied Logic 133 (1-3):3-37.
On Church's Formal Theory of Functions and Functionals.Giuseppe Longo - 1988 - Annals of Pure and Applied Logic 40 (2):93-133.

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