Re: [Haskell-cafe] Applicative & Monad as interaction between categories

huh, that looks neat, i'll have to check it out when i have time. I'd actually argue that the paper by Sam Lindley, Philip Wadler and Jeremy Yallop is another interesting take http://homepages.inf.ed.ac.uk/wadler/papers/arrows-and-idioms/arrows-and-idi... therein, the authors relate Applicatives, Monads and Arrows and their respective expressivity in a categorical setting On Tue, Aug 5, 2014 at 10:57 AM, Mike Izbicki wrote:

I have a github repo called subhask that does this. It uses the ConstraintKinds extension and some other tricks to let us work in subcategories of hask, and build endofunctors, applicatives, and monads in those categories. My particular application is building a dsl for machine learning, so there's a category for linear maps, and a category for lipschitz maps, among many others. (Normal distributions are monads in the category Vect, and most metric-based algorithms are monads in the category of lipshitz maps.) It's not quite ready for release, but you can check out the in progress work if you want.

The most interesting bits for you are probably the category instances: https://github.com/mikeizbicki/subhask/blob/master/src/SubHask/Category.hs

and the monad hierarchy: https://github.com/mikeizbicki/subhask/blob/master/src/SubHask/Functor.hs

The monad definitions currently lack adequate documentation because some things will still have to change to get the type checker to do what I want. For example, do notation doesn't work properly yet in some subcategories.

On Tue, Aug 5, 2014 at 1:46 AM, Ruben Astudillo wrote:

...

Hi all,

I recently came across of two blog posts[1][2] by Gabriel Gonzales where he shows motivation for writing compositional functions -- and thus why the concept of category is useful -- and motivation to write functors between them.

I wanted to know if something similar for has been done to `Applicative' and `Monad' as design pattern and interaction between categories. I've searching but I always hit the Monad tutorials and more info on how to use them.

Thanks in advance. Excuse my English.

[1]: http://www.haskellforall.com/2012/08/the-category-design-pattern.html [2]: http://www.haskellforall.com/2012/09/the-functor-design-pattern.html

-- Ruben Astudillo. pgp: 0x3C332311 , usala en lo posible :-) Crear un haiku, en diecisiete silabas, es complica... _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe

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