You may be interested in the work of my colleagues: "Categorical semantics for Arrows" (2009) Bart Jacobs, Ichiro Hasuo and Chris Heunen Journal of Functional Programming, 19(3-4):403-438, 2009 http://www.comlab.ox.ac.uk/people/chris.heunen/publications/2008/arrows/arro... "Arrows, like Monads, are Monoids" (2006) Bart Jacobs and Chris Heunen (ENTCS 158:219-236) in the proceedings of MFPS 22 http://www.comlab.ox.ac.uk/people/chris.heunen/publications/2006/arrows/arro... Bas On Tue, Sep 28, 2010 at 1:45 AM, Mike Stay <metaweta@gmail.com> wrote:
On Mon, Sep 27, 2010 at 3:50 PM, Mike Stay <metaweta@gmail.com> wrote:
I'm trying to understand Arrows in Haskell, http://www.haskell.org/arrows/index.html but since I haven't become literate yet, I'm not sure I'm getting everything right. It looks to me like an Arrow is a monoidal closed category object in Hask. Is that all there is to it?
Hmm. After reading "Freyd is Kleisli, for Arrows", it now looks to me like an Arrow is an enrichment.
It consists of a V-profunctor - A:C^op x C -> V, where V is a monoidal category, together with a natural transformation - arr:Hom => A and dinatural transformations - compose:A(b,c) x A(a,b) => A(a,c) - first:A(a,b) => A(a tensor c, b tensor c) satisfying various coherence laws. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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