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

[Carter Schonwald]

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-idioms.pdf

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 <mike at izbicki.me> 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 <ruben.astud at gmail.com>
> 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...
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