A Tutorial on the Universality and Expressiveness of Fold
Hutton, Graham (1999) A Tutorial on the Universality and Expressiveness of Fold. Journal of Functional Programming, 9 (4). pp. 355-372.
In functional programming, fold is a standard operator that encapsulates a simple pattern of recursion for processing lists. This article is a tutorial on two key aspects of the fold operator for lists. First of all, we emphasize the use of the universal property of fold both as a proof principle that avoids the need for inductive proofs, and as a definition principle that guides the transformation of recursive functions into definitions using fold. Secondly, we show that even though the pattern of recursion encapsulated by fold is simple, in a language with tuples and functions as first-class values the fold operator has greater expressive power than might first be expected.
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