# Interfaces, components, formal spaces and continuous functions

## Peter Hancock

(Edinburgh University)

Quite a bit of programming consists in implementing high-level procedural interfaces in terms of low-level interfaces. One approach to modelling this is with a category in which the objects are interfaces, and the morphisms are components.

In collaboration with Pierre Hyvernat and Anton Setzer, I have succeeded in ironing some wrinkles out of such a model. Unexpectedly, the category turns out to be (the opposite of) a category of generalised formal topologies and continuous functions figured out by Giovanni Sambin and others at Padua. Components are continuous functions.

So as not to paint too rosy a picture, I shall indicate some of the problems that arise when one confronts such a model with component-based architectures that arise in practice.

**Thursday 29th May 2003, 14:00**

Robert Recorde Room

Department of Computer Science