Skip to main content Accessibility help
×
Home
Hostname: page-component-684899dbb8-ct24h Total loading time: 0.265 Render date: 2022-05-20T23:50:44.233Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "useRatesEcommerce": false, "useNewApi": true }

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)
Rights & Permissions[Opens in a new window]

Abstract

HTML view is not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

Atkey, R. (2008) What is a categorical model of arrows? In Mathematical Structures in Functional Programming, Capreta, V. & McBride, C. (eds), Electronic Notes in Theoretical Computer Science, Reykjavic, Iceland.Google Scholar
Benton, N. (1995) A mixed linear and non-linear logic: Proofs, terms and models. In Computer Science Logics, Pacholski, L. & Tiuryn, J. (eds), Lecture Notes in Computer Science, vol. 933. Springer–Verlag, Kazimierz, Poland.Google Scholar
Courtney, A. & Elliott, C. (2001) Genuinely Functional User Interfaces. Haskell workshop, 4169.Google Scholar
Hudak, P., Courtney, A., Nilsson, H. & Peterson, J. (2003) Arrows, robots, and functional reactive programming. In Advanced Functional Programming, 4th International School, Jeuring, J. & Jones, S. P. (eds), LNCS, vol. 2638. Springer-Verlag, Oxford, UK.Google Scholar
Hughes, J. (2000) Generalising monads to arrows, Sci Comput Program., 37: 67111.CrossRefGoogle Scholar
Jansson, P. & Jeuring, J. (1999) Polytypic compact printing and parsing. Pages 273–287 of: European Symposium on Programming, LNCS, vol. 1576. Springer-Verlag, Amsterdam, The Netherlands.Google Scholar
Lindley, S., Wadler, P. & Yallop, J. (2008a) The Arrow Calculus. Tech. rept. EDI-INF-RR-1258. School of Informatics, University of Edinburgh.Google Scholar
Lindley, S., Wadler, P. & Yallop, J. (2008b) Idioms are oblivious, arrows are meticulous, monads are promiscuous. In Mathematical Structures in Functional Programming, Capreta, V. & McBride, C. (eds), Electronic Notes in Theoretical Computer Science, Reykjavic, Iceland.Google Scholar
McBride, C. & Paterson, R. (2008) Applicative programming with effects, J. Funct. Program., 18 (1): 113.CrossRefGoogle Scholar
Moggi, E. (1991) Notions of computation and monads, Inf. Comput., 93 (1): 5592.CrossRefGoogle Scholar
Paterson, R. (2001) A new notation for arrows. Pages 229–240 of: International Conference on Functional Programming, ACM Press, Florence, Italy.Google Scholar
Power, J. & Robinson, E. (1997) Premonoidal categories and notions of computation, Math. Struct. Comput. Sci., 7 (5): 453468.CrossRefGoogle Scholar
Power, J. & Thielecke, H. (1999) Closed Freyd- and kappa-categories. In International colloquium on automata, languages, and programming, LNCS, vol. 1644. Springer, Prague, Czech Republic.Google Scholar
Sabry, A. & Felleisen, M. (1993) Reasoning about programs in continuation-passing style, Lisp Symbol. Comput., 6 (3/4): 289360.CrossRefGoogle Scholar
Submit a response

Discussions

No Discussions have been published for this article.
You have Access
17
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

The arrow calculus
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

The arrow calculus
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

The arrow calculus
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *