Stable models of typed λ-calculi

Abstract

Following Scott, the denotational semantics of programming languages are usually built from the notion of continuous functions. The need for restricted models has been emphasized by Plotkin and Milner, which showed thats continuous function models did not capture all operational properties of ALGOL-like sequential languages. We present new model constructions from a notion of stable function. This requires the introduction of two different orderings between stable functions which give very different cpo structures to the function spaces. We show that Milner's fully abstract model of Plotkin's PCP language only contains stable functions.