A semantic model for graphical user interfaces

Abstract

We give a denotational model for graphical user interface (GUI) programming using the Cartesian closed category of ultrametric spaces. The ultrametric structure enforces causality restrictions on reactive systems and allows well-founded recursive definitions by a generalization of guardedness. We capture the arbitrariness of user input (e.g., a user gets to decide the stream of clicks she sends to a program) by making use of the fact that the closed subsets of an ultrametric space themselves form an ultrametric space, allowing us to interpret nondeterminism with a "powerspace" monad.