Slot games: a quantitative model of computation

Abstract

We present a games-based denotational semantics for a quantitative analysis of programming languages. We define a Hyland-Ong-style games framework called slot games, which consists of HO games augmented with a new action called token. We develop a slot-game model for the language Idealised Concurrent Algol by instrumenting the strategies in its HO game model with token actions. We show that the slot-game model is a denotational semantics induced by a notion of observation formalised in the operational theory of improvement of Sands, and we give a full abstraction result. A quantitative analysis of programs has many potential applications, from compiler optimisations to resource-constrained execution and static performance profiling. We illustrate several such applications with putative examples that would be nevertheless difficult, if not impossible, to handle using known operational techniques.