Categorical Semantics for Higher Order Polymorphic Lambda Calculus

@article{Seely1987CategoricalSF,
  title={Categorical Semantics for Higher Order Polymorphic Lambda Calculus},
  author={R. A. G. Seely},
  journal={J. Symb. Log.},
  year={1987},
  volume={52},
  pages={969-989}
}
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. ?0… CONTINUE READING
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Girard's type theory and categories, Unpublished lecture notes, McGill University, Montreal

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