Abstract

This paper is an attempt to persuade you of my viewpoint by presenting a novel generic program for a certain class of optimisation problems, named sequential decision processes. This class was originally identified by Richard Bellman in his pioneering work on dynamic programming [4]. It is a perfect example of a class of problems which are very much alike, but which has until now escaped solution by a single program. Those readers who have followed some of the work that Richard Bird and I have been doing over the last five years [6, 7] will recognise many individual examples: all of these have now been unified. The point of this observation is that even when you are on the lookout for generic programs, it can take a rather long time to discover them. The presentation below will follow that earlier work, by referring to the calculus of relations and the relational theory of data types. I shall however attempt to be light on the formalism, as I do not regard it as essential to the main thesis of this paper. Undoubtedly there are other (perhaps more convenient) notations in which the same ideas could be developed. This paper does assume some degree of familiarity with a lazy functional programming language such as Haskell, Hope, Miranda

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