category theory from 10,000 feet

[Shannon -jj Behrens]

I hate to sound like a total newbie, but can anyone give me the 10
second run down on category theory and why it keeps coming up on
functional programming mailing lists? It seems like a new model or
approach, similar to lambda calculus or monads. I peeked at
Wikipedia, but it didn't help me get the big picture. Does category
theory apply to all the functional programming languages, or is it
just something happening in, say, Haskell or Scala?

I apologize if this has been covered before.

Thanks,
-jj

--
In this life we cannot do great things. We can only do small things
with great love. -- Mother Teresa

[Jason Dusek]

Category Theory and related disciplines provide many of the
"design patterns" of typed functional programming.

It is quite reasonable that we draw patterns from math,
given the prevalence (and relative ease) of "equational
reasoning" in sorting out the meaning of functional
programs.

--
Jason Dusek
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[Valeria de Paiva]

Let me try my 'lift pitch':
The best mathematical theorems are the ones that connect fields that seem unrelated, at first sight. We have one such theorem that says that the collection of all functional programs that can be written is "the same" as  certain categories and their morphisms. Knowing this bridge-like theorem (The Curry-Howard iso) allows you to solve problems wherever they might be easier and then transfer solutions to the other side. It's a 2-for-the-price-of-one situation!

Valeria

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Valeria de Paiva
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