Bananas in space: extending fold and unfold to exponential types
Meijer, Erik and Hutton, Graham (1995) Bananas in space: extending fold and unfold to exponential types. In: International Conference on Functional Programming Languages and Computer Architecture (7th), 26-28 June 1995, La Jolla, California, USA.
Official URL: http://dl.acm.org/citation.cfm?doid=224164.224225
Fold and unfold are general purpose functionals for process-ing and constructing lists. By using the categorical approach of modelling recursive datatypes as fixed points of functors, these functionals and their algebraic properties were generalised from lists to polynomial (sum-of-product) datatypes. However, the restriction to polynomial datatypes is a serious limitation: it precludes the use of exponentials (function-spaces), whereas it is central to functional programming that functions are first-class values, and so exponentials should be able to be used freely in datatype definitions. In this paper we explain how Freyd’s work on modelling recursive datatypes as fixed points of difunctors shows how to generalise fold and unfold from polynomial datatypes to those involving exponentials. Knowledge of category theory is not required; we use Gofer throughout as our meta-language, making extensive use of constructor classes
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