Abstract

. This paper presents a polytypic implementation of memo functions that are based on digital search trees. A memo function can be seen as the composition of a tabulation function that creates a memo table and a look-up function that queries the table. We show that tabulation can be derived from look-up by inverse function construction. The type of memo tables is dened by induction on the structure of argument types and is parametric with respect to the result type of memo functions. A memo table for a xed argument type is then a functor and look-up and tabulation are natural isomorphisms. We provide simple polytypic proofs of these properties. 1 Introduction A memo function [11] is like an ordinary function except that it caches previously computed values. If it is applied a second time to a particular argument, it immediately returns the cached result, rather than recomputing it. For storing arguments and results a memo function internally employs an index structure, the ...

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