Full Abstraction for PCF

Abstract

The denotational semantics of a programming language gives a mathematical model of its types and terms. The Scott-domain model for the programming language PCF (Programming Computable Functions) uses Scott-domains with Scott-continuous functions (ordered pointwise). However, this model is not fully abstract: there are functions in the model that can not be represented in PCF. Hyland and Ong developed a model that is fully abstract by modeling types as dialogue games and terms as innocent strategies in those games.