[Haskell-beginners] Beginners Digest, Vol 56, Issue 22

[Brent Yorgey]

On Wed, Feb 13, 2013 at 10:27:12AM -0500, Patrick Lynch wrote:
> Good morning Brent.
> 
> Thank you for your recomendation.
> I went to Amazon and checked the Table of Contents on the book you
> mentioned...
> It costs $90 and its not really what I'm looking for.

Hi Patrick,

I was not suggesting that you buy the book.  I included a link in my
email where there is a PDF of the particular chapter I mentioned
available for free:

  http://www.cs.ox.ac.uk/publications/publication2360-abstract.html

> 
> I'm going to approach this from a different direction. It is:
>   1. I'm looking for a the Haskell definition of the category
> Hask...If you can help me out here, I'd appreciate it.

The objects in the category Hask are Haskell types.

The morphisms (arrows) in Hask between two objects (i.e. types) A and
B are functions of type A -> B.

Bottom/undefined actually causes problems in this category so usually
when we talk about Hask we pretend that bottom/undefined does not
exist, as if we were working in a total (terminating) subset of
Haskell.

The Functor class is for functors (in the mathematical sense) from
Hask to Hask.

>   2. Functor, Monoid and Monad are all classes in Haskell...I'm going
> to try to determine how they are related to Hask and to each other.

You seem to have a rigidly preconceived idea of a few narrow questions
that you want the answers to.  I advise you to broaden your idea of
what you would like to learn -- and eventually you will come round to
an understanding of the answers to your original questions.  I still
strongly recommend the Gibbons chapter I mentioned.  You say it is not
what you are looking for but I think it really is -- it does not
contain *explicit* answers to your specific questions but it will
start you down the path to understanding them, and from a programming
rather than a math perspective like you wanted.

-Brent