A Semantic Characterization Of Full Abstraction For Typed Lambda Calculi

Full abstraction is a well known issue in denotational semantics. For a special case of typed lambda calculus, PCF, Plotkin showed that the classical model consisting of domains of continuous functions is not fully abstract. Milner constructed a fully abstract model of typed lambda calculus syntactically. However, its precise relationship with the classical model was not clear, and hence it remained open whether a fully abstract model can be constructed which is related to the classical model in a pleasant way. In this paper we show that a fully abstract, extensional model of typed lambda calculus can be constructed as a homomorphic retraction of the classical model.