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Primitive (Co)Recursion and Course-of-Value (Co)Iteration, Categorically
Volume 10, Issue 1 (1999): Special Issue on Programming Theory, Information System Engineering, Software Engineering, and Artificial Intelligence, pp. 5–26
Tarmo Uustalu   Varmo Vene  

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https://doi.org/10.3233/INF-1999-10102
Pub. online: 1 January 1999      Type: Research Article     

Received
1 December 1999
Published
1 January 1999

Abstract

In the mainstream categorical approach to typed (total) functional programming, datatypes are modelled as initial algebras and codatatypes as terminal coalgebras. The basic function definition schemes of iteration and coiteration are modelled by constructions known as catamorphisms and anamorphisms. Primitive recursion has been captured by a construction called paramorphisms. We draw attention to the dual construction of apomorphisms, and show on examples that primitive corecursion is a useful function definition scheme. We also put forward and study two novel constructions, viz., histomorphisms and futumorphisms, that capture the powerful schemes of course-of-value iteration and its dual, respectively, and argue that even these are helpful.

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Keywords
typed (total) functional programming category theory program calculation (co)data-types forms of (co)recursion

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INFORMATICA

  • Online ISSN: 1822-8844
  • Print ISSN: 0868-4952
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