## Recursion over realizability structures.(English)Zbl 0760.03012

Author’s summary: 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 they 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.

### MSC:

 03D80 Applications of computability and recursion theory 03B40 Combinatory logic and lambda calculus 68Q55 Semantics in the theory of computing 03F50 Metamathematics of constructive systems 18D15 Closed categories (closed monoidal and Cartesian closed categories, etc.)
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