Recursion over Realizability Structures

Abstract Realizability structures play a major role in the metamathematics of intuitionistic systems and they are a basic tool in the extraction of the computational content of constructive proofs. Besides their rich categorical structure and effectiveness properties provide a privileged mathematical setting for the semantics of data types of programming languages. In this paper we emphasize the modelling of recursive definitions of programs and types. A realizability model for a language including Girard's system F and an operator of recursion on types is given and some of its local properties are studied.

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