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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 interpretationLinks
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Citations of this work
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A game semantics for generic polymorphism.Samson Abramsky & Radha Jagadeesan - 2005 - Annals of Pure and Applied Logic 133 (1-3):3-37.
On some connections between logic and category theory.J. Lambek - 1989 - Studia Logica 48 (3):269 - 278.
Alpha-conversion, conditions on variables and categorical logic.Pierre-Louis Curien - 1989 - Studia Logica 48 (3):319 - 360.
References found in this work
Hyperdoctrines, Natural Deduction and the Beck Condition.Robert A. G. Seely - 1983 - Mathematical Logic Quarterly 29 (10):505-542.
The „Dialectica”︁ Interpretation and Categories.Philip J. Scott - 1978 - Mathematical Logic Quarterly 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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