[Haskell-cafe] Monad/Functor Book

[Derek Elkins]

Creighton Hogg wrote:
> 
> 
> On 3/27/07, *Dan Piponi* <dpiponi at gmail.com <mailto:dpiponi at gmail.com>> 
> wrote:
> 
>     On 3/27/07, Dave at haskell.org <mailto:Dave at haskell.org>
>     <Dave at haskell.org <mailto:Dave at haskell.org>> wrote:
>      > Given the amount of material posted at haskell.org
>     <http://haskell.org> and elsewhere
>      > explaining IO, monads and functors, has anyone considered publishing
>      > a comprehensive book explaining those subjects?  (I am trying to
>      > read all the material online, but books are easier to read and don't
>      > require sitting in front of a computer to do so. Plus I can write in
>      > books :-). )
> 
>     I've thought about writing extended tutorials on the relationship
>     between Haskell programming and category theory but there's a problem
>     I run into. It's tempting to make the identifications:
>     types<->objects, Haskell function<->arrows, suitably polymorphic
>     functions<->natural transformations, and so on. But the fact is, this
>     doesn't really work in the obvious way even though it seems like it
>     should at first (eg. Haskell functions aren't always total functions
>     in the mathematical sense and if you allow partial functions you can
>     do weird stuff). So either:
> 
>     (1) we need some technical work to patch up the differences (and
>     unfortunately I don't know what the patch-up is),
>     (2) we restrict ourselves to certain types of Haskell function for
>     which the theory works or
>     (3) we deliberately leave things a little vague.
> 
>     I usually tend to go for option (3), but that wouldn't be satisfactory
>     for an extended treatment.
> 
>     Has anyone else given this subject much thought? 
> 
> 
> I consider myself to be distinctly in the target audience of a thorough 
> treatment of CT & it's relationship to Haskell, so I'll throw out there 
> that I think some superposition of options (2) and (3) would be the most 
> satisfying.  You can handwave a little bit, but knowing *where* the 
> naive mappings between category theoretic constructs and Haskell's 
> system breakdown would be very nice.  Personally, one of the biggest 
> things for me is not really having any intuition for what kind of 
> category the Haskell type system lives in.  I mean, it looks cartesian 
> closed because you can do currying but what more to it is there than that?

Actually it isn't Cartesian Closed (monoidally closed though should work).

But, I more or less agree.  Either just ignore it (3), or something somewhere 
between (2) and (3) would probably be best.  The kind of people that are going 
to care enough about the mismatches probably already know to be wary, but make 
sure you make -some- comment to the appropriate effect.  Most of the time you 
are just going for intuition and (either way) precision in this aspect is 
irrelevant.

A request: If you do write this, please show the CT being -used- for something 
and not just mapped to/from Haskell.