Abstract

Formal reasoning is notoriously long and arduous; in order to use it to reason effectively in the construction of programs it is, therefore, paramount that we design our notations to be both clear and economical. Taking examples from AI, from imperative programming, from the use of the Bird-Meertens formalism and from category theory we demonstrate how the right choice of what to denote and how it is denoted can make significant improvements to formal calculations. Brief mention is also made of the connection between economical notation and properties of type. 1 2 Foreword Earlier this year I was an invited speaker at the 5th British Computer Society Theoretical Computer Science Colloquium held at Royal Holloway and Bedford New College, London. Before you is the text of my lecture, almost but not quite as given at the conference. (Perhaps the best way to describe the present paper is as the lecture that I should have given.) The publication of the text of the lecture will, ...

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