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Second-order type isomorphisms through game semantics

Joachim de Lataillade

Annals of Pure and Applied Logic 151 (2-3):115-150 (2008)

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Categorical semantics for higher order polymorphic lambda calculus.R. A. G. Seely - 1987 - Journal of Symbolic Logic 52 (4):969-989.details 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. Download Export citation Bookmark 8 citations
A game semantics for generic polymorphism.Samson Abramsky & Radha Jagadeesan - 2005 - Annals of Pure and Applied Logic 133 (1-3):3-37.details Genericity is the idea that the same program can work at many different data types. Longo, Milstead and Soloviev proposed to capture the inability of generic programs to probe the structure of their instances by the following equational principle: if two generic programs, viewed as terms of type , are equal at any given instance A[T], then they are equal at all instances. They proved that this rule is admissible in a certain extension of System F, but finding a semantically (...) Download Export citation Bookmark 2 citations

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