AW: slide: useful function?

Christopher Milton
Mon, 2 Dec 2002 12:50:10 -0800 (PST)

--- Mark Carroll <> wrote:
> On Mon, 2 Dec 2002, David Bergman wrote:
> (snip)
> > Till then, we "Haskellers" will probably continue expressing our
> > patterns either directly in Haskell or using highly formal language,
> > with terms such as "catamorphisms".
> >
> > The virtue, and weakness, of traditional design patterns is their
> > vagueness and informal character, making them (1) comprehensible to the
> > 90% of the developer community not familiar with category theory but (2)
> (snip)
> If there are any good ways in which non-mathematicians can get to grips
> with these terms from category theory, they would be well worth promoting.
> For example, despite having a good computer science degree (in which I was
> at least introduced to FP, proof, etc. and even learned to draw the dual
> graph of hypercubes) I'm really not equipped to understand catamorphisms
> in terms of algebras and homomorphisms, and don't currently have time to
> take the math degree I fear I'd need in order to do so. Last time I was
> looking at category theory books I think I came to the conclusion that
> Lawvere and Schanuel cover things kindly but Pierce seemed to get the
> syllabus right, so the "right" book wasn't quite out there.
> My understanding of monads is already a matter of record. Does anyone know
> of a friendly text that might help new Haskellers to understand functors,
> etc. and what they mean for program design? I'm not averse to the formal
> language per se if it can be easily acquired; right now, I worry that I'm
> using Haskell suboptimally because, not only do I not know the terminology
> well, but I fear that I'm not even cognisant of the concepts that these
> terms represent.
> In a nutshell: if these category theory concepts indeed have an important
> impact in Haskell land, how to introduce them to working Haskell
> programmers well enough that they can use them in engineering software
> that's at least half as good as it could be?
> (I'm making the assumption here that it would be good for Haskell to be
> much more widely used - it shouldn't solely be for researchers.)

Here's some of what I've come across:

Jonathan M. D. Hill, and Keith Clarke
"An introduction to category theory, category theory monads, and their
relationship to functional programming"

Tom Leinster's Part III Category Theory course given in Cambridge in the
academic year 2000-2001:

John Baez
Categories, Quantization, and Much More
(see the links at the bottom of this page, too.)

Baez also has interesting info in his series,
This Week's Finds in Mathematical Physics


Christopher Milton

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