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The arrow calculus

Published online by Cambridge University Press:  26 January 2010

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.

Type
Articles
Copyright
Copyright © Cambridge University Press 2010

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