Intensionally stable functions
Our principal concern in this paper is to pave further the way towards a semantical version of Milner's fully abstract model of typed λ-calculi. Relying on Milner's results that show that the function-based model of PCF is unique (up to isomorphism) and is Scottordered, and taking into account the fact that the underlying domains of the model cannot be distributive, we introduce SK-domains and define SI-functions which generalize, by departing from the distributivity requirement, the stable functions already introduced by Berry. We then show that SK-domains and SI-functions constitute a cartesian closed category which can be order enrich with Scott's ordering ie: can be used to provide order extensional models for λ-calculus based languages.
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