Abstract

We present a realizability interpretation of co-inductive types based on partial equivalence relations (per's). We extract from the per's interpretation sound rules to type recursive definitions. These recursive definitions are needed to introduce "infinite" and "total" objects of co-inductive type such as an infinite stream or a non-terminating process. We show that the proposed type system enjoys the basic syntactic properties of subject reduction and strong normalization with respect to a confluent rewriting system first studied by Gimenez. We also compare the proposed type system with those studied by Coquand and Gimenez. In particular, we provide a semantic reconstruction of Gimenez's system which suggests a rule to type nested recursive definitions.

Citations