Full abstraction for functional languages with control

This paper considers the consequences of relaxing the bracketing condition on ‘dialoguegames’, showing that this leads to a category of games which can be ‘factorized ’ into a well-bracketed substructure, and a set of classically typed morphisms. These are shown to be sound denotations for control operators, allowing the factorization to be used to extend the definability result for PCF to one for PCF with control operators at atomic types. Thus we define a fully abstract and effectively presentable model of a functional language with non-local control as part of a modular ap-proach to modelling non-functional features using games. 1