The arrow calculus

Authors:
Sam Lindley;Philip Wadler;Jeremy Yallop
Affiliations:
University of edinburgh (e-mail: sam.lindley@ed.ac.uk, philip.wadler@ed.ac.uk, jeremy.yallop@ed.ac.uk);University of edinburgh (e-mail: sam.lindley@ed.ac.uk, philip.wadler@ed.ac.uk, jeremy.yallop@ed.ac.uk);University of edinburgh (e-mail: sam.lindley@ed.ac.uk, philip.wadler@ed.ac.uk, jeremy.yallop@ed.ac.uk)
Venue:
Journal of Functional Programming
Year:
2010

Citing 7
Cited 5

Notions of computation and monads

Information and Computation
Reasoning about programs in continuation-passing style

Lisp and Symbolic Computation - Special issue on continuations—part I
Generalising monads to arrows

Science of Computer Programming - Special issue on mathematics of program construction
A new notation for arrows

Proceedings of the sixth ACM SIGPLAN international conference on Functional programming
A Mixed Linear and Non-Linear Logic: Proofs, Terms and Models (Extended Abstract)

CSL '94 Selected Papers from the 8th International Workshop on Computer Science Logic
Premonoidal categories and notions of computation

Mathematical Structures in Computer Science
Applicative programming with effects

Journal of Functional Programming

The Arrow Calculus as a Quantum Programming Language

WoLLIC '09 Proceedings of the 16th International Workshop on Logic, Language, Information and Computation
Embedding a functional hybrid modelling language in Haskell

IFL'08 Proceedings of the 20th international conference on Implementation and application of functional languages
Causal commutative arrows

Journal of Functional Programming - Dedicated to ICFP 2009
Correct looping arrows from cyclic terms

FLOPS'12 Proceedings of the 11th international conference on Functional and Logic Programming
Wormholes: introducing effects to FRP

Proceedings of the 2012 Haskell Symposium

Quantified Score

Hi-index	0.00

Visualization

Abstract

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.