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Functional Pearls

The Third Homomorphism Theorem

Part of: JFP Research Articles

Published online by Cambridge University Press:  07 November 2008

Jeremy Gibbons
Jeremy Gibbons
Affiliation:
Department of Computer Science, University of AucklandPrivate Bag 92019, Auckland, New Zealand (e-mail:jeremy@cs.auckland.ac.nz)
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Abstract

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The Third Homomorphism Theorem is a folk theorem of the constructive algorithmics community. It states that a function on lists that can be computed both from left to right and from right to left is necessarily a list homomorphism – it can be computed according to any parenthesization of the list. We formalize and prove the theorem, and use it to improve an O(n2) sorting algorithm to O(n log n).

Type
Articles
Information
Journal of Functional Programming , Volume 6 , Issue 4 , July 1996 , pp. 657 - 665
Copyright
Copyright © Cambridge University Press 1996

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