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Comprehending monads†

Published online by Cambridge University Press:  04 March 2009

Philip Wadler
Philip Wadler
Affiliation:
Department of Computing Science, University of Glasgow, G12 8QQ, Scotland.waldler@dcs.glasgow.ac.uk.
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Abstract

Category theorists invented monads in the 1960's to express concisely certain aspects of universal algebra. Functional programmers invented list comprehensions in the 1970's to express concisely certain programs involving lists. This paper shows how list comprehensions may be generalised to an arbitrary monad, and how the resulting programming feature can express concisely in a pure functional language some programs that manipulate state, handle exceptions, parse text, or invoke continuations. A new solution to the old problem of destructive array update is also presented. No knowledge of category theory is assumed.

Type
Research Article
Information
Mathematical Structures in Computer Science , Volume 2 , Issue 4 , December 1992 , pp. 461 - 493
Copyright
Copyright © Cambridge University Press 1992

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