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The arrow calculus

Part of: JFP Research Articles

Published online by Cambridge University Press:  26 January 2010

SAM LINDLEY ,
PHILIP WADLER  and
JEREMY YALLOP
SAM LINDLEY
Affiliation:
University of Edinburgh (e-mail: Sam.Lindley@ed.ac.uk, Philip.Wadler@ed.ac.uk, Jeremy.Yallop@ed.ac.uk)
PHILIP WADLER
Affiliation:
University of Edinburgh (e-mail: Sam.Lindley@ed.ac.uk, Philip.Wadler@ed.ac.uk, Jeremy.Yallop@ed.ac.uk)
JEREMY YALLOP
Affiliation:
University of Edinburgh (e-mail: Sam.Lindley@ed.ac.uk, Philip.Wadler@ed.ac.uk, Jeremy.Yallop@ed.ac.uk)
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Abstract

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We introduce the arrow calculus, a metalanguage for manipulating Hughes's arrows with close relations both to Moggi's metalanguage for monads and to Paterson's arrow notation. Arrows are classically defined by extending lambda calculus with three constructs satisfying nine (somewhat idiosyncratic) laws; in contrast, the arrow calculus adds four constructs satisfying five laws (which fit two well-known patterns). The five laws were previously known to be sound; we show that they are also complete, and hence that the five laws may replace the nine.

Information

Type
Articles
Information
Journal of Functional Programming , Volume 20 , Issue 1 , January 2010 , pp. 51 - 69
Copyright
Copyright © Cambridge University Press 2010

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