Fixed Points in Metrified Quasi Ordered Sets: Modelling Escaping in Functional Programs

The standard denotational semantics of a programming language, being based on Tarski’s Theorem, is often not capable of expressing program properties. Annotated semantic domains and corresponding semantic functions capacitate us to express the properties, but the resulting structures may no longer be partially ordered sets. Instead we obtain quasi ordered sets, which lack the antisymmetry of partially ordered sets. To cater with these structures, we introduce a new kind of structure called metrified quasi ordered sets and develop a generalisation of Tarski’s Theorem for these structures. We demonstrate the techniques for a simple lazy functional language F by modelling the escape behaviour of F programs.