Primitive (Co)Recursion and Course-of-Value (Co)Iteration, Categorically (1999) [9 citations — 3 self]
http://www.cs.ioc.ee/~tarmo/papers/inf.ps.gz
http://www.it.kth.se/~tarmo/papers/histofutu.ps.gz
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author = {Tarmo Uustalu and Varmo Vene},
title = {Primitive (Co)Recursion and Course-of-Value (Co)Iteration, Categorically},
journal = {Informatica},
year = {1999},
volume = {10},
pages = {5--26}
}
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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. Key words: typed (total) functional programming, category theory, program calculation, (co)datatypes, forms of (co)recursion 1. Introduction This paper is about a well-known categorical approach to typed (total) functional programming popular in t...
