Abstract

We construct a small arithmetic package operating on discrete sequences: u0 , u1 , u2 , . . . treated as single mathematical entities. Applying functions to sequences by the generalized map, or adding them element-wise is quite trivial, but if the sequences are regular, e.g. if they are arithmetic or geometric progressions, a much more compact and in several cases much more e#cient representation is possible. For example any polynomial of an arithmetic infinite sequence has an easily coded, and e#ciently processed finite representation through its forward di#erences. Even in more general cases, the lazy manipulation of sequences results in a remarkable compactness of coding, especially where the processing algorithms are iterative. The main motivation of this paper is methodologic. 1 Indexless Sequence Processing and Generation This is a light-weight essay on practical use of functional programming methods in the domain of coding of numeric computations, useful for pedagogy and for ...

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