[Haskell-cafe] Monad/Functor Book

[Dan Piponi]

On 3/27/07, Dave at haskell.org <Dave at haskell.org> wrote:
> Given the amount of material posted at 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?
--
Dan