Re: Potluck dish -- a game

[Mateusz Kowalczyk <fuuzetsu@fuuzetsu.co.uk>]

On 19/02/14 08:52, Ścisław Dercz wrote:
> Hi Mateusz!
> 
> Nice to meet someone mathematically-oriented! I'm delighted with your care
> about the proper use of algebraic language and am always eager to be
> corrected. However this time there is no need to do so -- it IS a monoid,
> one of those you meet almost everywhere, i.e. a monoid of X->X
> transformations. The identity map is it's neutral element (identity, unit)
> and composition (X->X)x(X->X)->(X->X) is its action. Notice that it is not
> a group since some transformations cannot be reverted -- e.g. the ones
> produced with mk-remover.
> The code is a bit messy and it mostly comes from a one-night hackaton, and
> I will not be able to polish it until next weekend for sure.
> I will translate the Polish comments. At the moment I can only provide you
> with the last one, a neat mixture of Gombrowicz and Maslowska: "koniec
> bomba a kto czytal ten ssie galy eurocwelom" -- the translation does not
> seem trivial, perhaps something like "The end and the bomb, who read is an
> euro-pansy cocksucker" -- however it might look a bit homophobic (as many
> Polish curses do), perhaps you or Panicz could propose something better?

Personally I'd just remove it but it's fully up to you. I simply thought
that you might have forgotten to remove some comments as some are in
English and some aren't.

> Greeting,
> d.
> 
> PS I just found your answer, so now I guess we do agree on the monoid
> thing?

Yes, I inspected it again when posting again and I can now see what you
were going for. I imagine that commenting on code shouldn't have been
the first thing I did after waking up. My apologies.

> As of monads I do understand that the class of endofunctors with
> composition and identity as unit form a monoid, no doubt, that's the
> construction I mentioned at the beginning.

My only gripe is that I'm unsure whether guile functions can be
considered (endo-)functors and if they do, I'd love to see what kind of
category Guile forms. I can't find any material exploring this. With
Haskell, the deal is simple, we have Hask (which is admittedly a bit
boring due to presence of ‘undefined’)[1].

> But that's the monad-monoid relation in the direction opposite to what I
> was asking for. And technically I am not sure whether "the endofunctor
> definition" applies to Kleisli triplets (which you probably meant) that
> easily, as it seems either broader, or that the "all told" part hides some
> important constraints, like that the category C you consider has enough
> means (perhaps binary products or some other universal constructions) to
> represent "the new type" T(A) for any A in C... But again, I am an ignorant
> so please do correct me.

It was only a remark that such monoids can indeed have something to do
with monads, I meant nothing more. There's an interesting blog post on
embedding the endofunctor monoid inside of Haskell[2] and presenting its
laws, which give us the monad laws. I imagine you know this already but
someone else might find it a nice read.

[1]: http://www.haskell.org/haskellwiki/Hask
[2]: http://blog.sigfpe.com/2008/11/from-monoids-to-monads.html

-- 
Mateusz K.