[Haskell] Re: Teach theory then Haskell as example

[Max Rabkin]

On Fri, Jan 16, 2009 at 7:46 AM, Dave Bayer <bayer at cpw.math.columbia.edu> wrote:
> As a mathematician, Haskell has renewed my interest in category theory. I
> had thought one learns category theory most easily at age 20, because it
> paints such an eviscerated view of flesh-and-blood subjects like geometry,
> but at age 20 one doesn't care.

Yep, 20 year olds like me like to see the guts ripped out of geometry
(actually, my dislike of geometry probably peaked around 17, but
nevertheless I like what I've seen of category theory). Hopefully I'll
still like category theory when I'm 21 and I'm taking a course in it
:)

> I'm struck, reading various papers that translate functional programming
> constructs back to category theory, how messy something simple in Haskell
> has to look in classical category theory, because Haskell is "higher order"
> and classical category theory is not.

I believe this is what higher-dimensional category theory is about,
and my understanding is that even going a few dimensions up makes
things significantly more difficult (and things that are "obviously"
equivalent become hard to prove so). Haskell of course has no bounds
on the dimension (you can use millionth-order functions if you like,
though I don't know if you'll have success on a real-world compiler).

> Among the intro texts out there,
>
> \bib{MR1120026}{book}{
>   author={Pierce, Benjamin C.},
>   title={Basic category theory for computer scientists},
>   series={Foundations of Computing Series},
>   publisher={MIT Press},
>   place={Cambridge, MA},
>   date={1991},
>   pages={xiv+100},
>   isbn={0-262-66071-7},
>   review={\MR{1120026 (93c:18002)}},
> }
>
> is excellent, with a functional programming focus.

Good to have a recommendation -- my future CT lecturer has a hard time
recommending anything not written by Mac Lane.

--Max