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 coinductive type such as an infinite stream, a digital transducer, or a nonterminating process. We show that the proposed type system subsumes those studied by Coquand and Gimenez while still enjoying the basic syntactic properties of subject reduction and strong normalization with respect to a confluent rewriting system first put forward by Gimenez.
We investigate how to take advantage of the particular features of the calculus of inductive constructions in the framework of hardware verification. First, we emphasize in a short case study the use of dependent types and of the constructive aspect of the logic for specifying and synthesizing combinatorial circuits. Then, co-inductive types are introduced to model the temporal aspects of sequential synchronous devices. Moore and Mealy automata are co-inductively axiomatized and are used to represent uniformly both the structures and the behaviors of the circuits. This leads to clear, general and elegant proof processes as is illustrated on the example of a realistic circuit: the ATM Switch Fabric. All the proofs are carried out using Coq.
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