Titlebook: Semantics of Data Types; International Sympos Gilles Kahn,David B. MacQueen,Gordon Plotkin Conference proceedings 1984 Springer-Verlag Berl

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https://doi.org/10.1007/3-540-13346-1Datentyp; Semantik; lambda calculus; logic; proof theory; semantics

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Polymorphism is not set-theoretic,The polymorphic, or second-order, typed lambda calculus is an extension of the typed lambda calculus in which polymorphic functions can be defined. In this paper, we will prove that the standard set-theoretic model of the ordinary typed lambda calculus cannot be extended to model this language extension.

COLIC

Towards a proof theory of parameterized specifications,It is shown that certain parameterized data types have a "typical" initial algebra which captures the equational theory of the data type. Hence the characteristic of initial algebras, namely that term induction and rewriting provide a proof method for equational theorems, also applies to parameterized data types.

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