Abstract

We discuss the use of the lazy evaluation scheme as coding tool in some algebraic manipulations. We show --- on several examples --- how to process the infinite power series or other open-ended data structures with co-recurrent algorithms, which simplify enormously the coding of recurrence relations or solving equations in the power series domain. The important point is not the "infinite" length of the data, but the fact that the algorithms use open recursion, and the user never thinks about the truncation. 1 Introduction This article develops some applications of the functional lazy evaluation schemes to symbolic calculus. Neither the idea of non-strict semantics, nor its application to generate infinite, open structures such as power series, are new, see for example [1, 2], some books on functional programming ([3, 4]), etc. The lazy evaluation (or call by need is a protocol which delays the evaluation of the arguments of a function: while evaluating f(x) the code for f is entered, ...

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