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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Vizzotto, Juliana Kaizer 2013. 2013 2nd Workshop-School on Theoretical Computer Science. p. 9.

    LIU, HAI CHENG, ERIC and HUDAK, PAUL 2011. Causal commutative arrows. Journal of Functional Programming, Vol. 21, Issue. 4-5, p. 467.

    Goranson, Harold T. 2015. Proceedings of the 26th ACM Conference on Hypertext & Social Media - HT '15. p. 267.

    Yallop, Jeremy and Liu, Hai 2016. Proceedings of the 9th International Symposium on Haskell - Haskell 2016. p. 21.

    Goranson, Ted Cardier, Beth and Devlin, Keith 2015. Pragmatic phenomenological types. Progress in Biophysics and Molecular Biology, Vol. 119, Issue. 3, p. 420.

    Winograd-Cort, Daniel and Hudak, Paul 2014. Settable and non-interfering signal functions for FRP. ACM SIGPLAN Notices, Vol. 49, Issue. 9, p. 213.


The arrow calculus

  • DOI:
  • Published online: 26 January 2010

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.

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P. Hudak , A. Courtney , H. Nilsson & J. Peterson (2003) Arrows, robots, and functional reactive programming. In Advanced Functional Programming, 4th International School, J. Jeuring & S. P. Jones (eds), LNCS, vol. 2638. Springer-Verlag, Oxford, UK.

J. Hughes (2000) Generalising monads to arrows, Sci Comput Program., 37: 67111.

E. Moggi (1991) Notions of computation and monads, Inf. Comput., 93 (1): 5592.

J. Power & E. Robinson (1997) Premonoidal categories and notions of computation, Math. Struct. Comput. Sci., 7 (5): 453468.

A. Sabry & M. Felleisen (1993) Reasoning about programs in continuation-passing style, Lisp Symbol. Comput., 6 (3/4): 289360.

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Journal of Functional Programming
  • ISSN: 0956-7968
  • EISSN: 1469-7653
  • URL: /core/journals/journal-of-functional-programming
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