17th Estonian Winter School in Computer Science (EWSCS)
XVII Eesti Arvutiteaduse Talvekool

Palmse, Estonia, February 26 -March 2, 2012

Martín Escardó


School of Computer Science
University of Birmingham
UK

Topology for functional programming

Abstract

The central notion of topology is that of continuity of functions, closely followed in importance by that of compactness of sets. In computation with infinite objects, continuity amounts to the fact the finite parts of the output can depend only on finite parts of the input. This idea occurs in Brouwerian intuitionistic mathematics, and in Scott-style denotational semantics, and more recently also in operational semantics of programming languages. In this course I will explain continuity and compactness from a computational point of view, and show how they can be used to construct seemingly impossible functional programs that explore an infinite search space in a finite amount of time. I will also illustrate this with various applications.

Course materials

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