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POPL
2015
ACM

Conjugate Hylomorphisms - Or: The Mother of All Structured Recursion Schemes

8 years 8 days ago
Conjugate Hylomorphisms - Or: The Mother of All Structured Recursion Schemes
The past decades have witnessed an extensive study of structured recursion schemes. A general scheme is the hylomorphism, which captures the essence of divide-and-conquer: a problem is broken into sub-problems by a coalgebra; sub-problems are solved recursively; the sub-solutions are combined by an algebra to form a solution. In this paper we develop a simple toolbox for assembling recursive coalgebras, which by definition ensure that their hylo equations have unique solutions, whatever the algebra. Our main tool is the conjugate rule, a generic rule parametrized by an adjunction and a conjugate pair of natural transformations. We show that many basic adjunctions induce useful recursion schemes. In fact, almost every structured recursion scheme seems to arise as an instance of the conjugate rule. Further, we adapt our toolbox to the more expressive setting of parametrically recursive coalgebras, where the original input is also passed to the algebra. The formal development is complem...
Ralf Hinze, Nicolas Wu, Jeremy Gibbons
Added 16 Apr 2016
Updated 16 Apr 2016
Type Journal
Year 2015
Where POPL
Authors Ralf Hinze, Nicolas Wu, Jeremy Gibbons
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