Pi-Calculus, Dialogue Games and PCF.
J. M. E. Hyland, C.-H. Luke Ong · 1995
Game semantics is an unusual denotational semantics in that it captures the intensional (or algorithmic) and dynamical aspects of the computation. This makes it an ideal semantical framework in which to seek to unify analyses of both the qualitative (correctness) as well as the quantitative (efficiency) properties of programming languages. This paper reports work arising from a recent construction of an order (or inequationally) fully abstract model for Scott's functional programming language pcf based on a kind of two-person (Player and Opponent) dialogue game of questions and answers [HO94]. In this model types are interpreted as games and terms as innocent strategies. The fully abstract game model may be said to be canonical for the semantical analysis of sequential functional languages. Unfortunately even for relatively simple pcf-terms, precise description of their denotations as strategies in [HO94] very rapidly becomes unwieldy and opaque. What is needed to remedy the situation ...