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Unifying structured recursion schemes

An Extended Study

Part of: JFP Research Articles

Published online by Cambridge University Press:  03 February 2016

RALF HINZE  and
NICOLAS WU
RALF HINZE
Affiliation:
Department of Computer Science, University of Oxford, Oxford, UK (e-mail: ralf.hinze@cs.ox.ac.uk)
NICOLAS WU
Affiliation:
Department of Computer Science, University of Bristol, Bristol, UK (e-mail: nicolas.wu@bristol.ac.uk)
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Abstract

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Folds and unfolds have been understood as fundamental building blocks for total programming, and have been extended to form an entire zoo of specialised structured recursion schemes. A great number of these schemes were unified by the introduction of adjoint folds, but more exotic beasts such as recursion schemes from comonads proved to be elusive. In this paper, we show how the two canonical derivations of adjunctions from (co)monads yield recursion schemes of significant computational importance: monadic catamorphisms come from the Kleisli construction, and more astonishingly, the elusive recursion schemes from comonads come from the Eilenberg–Moore construction. Thus, we demonstrate that adjoint folds are more unifying than previously believed.

Type
Articles
Information
Journal of Functional Programming , Volume 26 , 2016 , e1
Copyright
Copyright © Cambridge University Press 2016 

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