On Sat, Sep 24, 2011 at 10:45 PM, Christopher Howard
<christopher.howard@frigidcode.com> wrote:
On 09/24/2011 09:12 PM, Mike Meyer wrote:
Actually, functional programming and the higher math are separate
things. Haskell (and I expect the similar languages) have a lot of
math in their documentation. But that's not true for other functional
languages, like Clojure or Scheme. With a background in those
languages, I didn't have much trouble with the functional nature of
haskell. But I'm still trying to recall the graduate math courses I
took long time ago in a state far, far different from today.
Really? I'll confess I'm a bit surprised to hear that perspective. I don't know anything about Clojure or Scheme. But I found in trying to understand Haskell that it really is all about higher math. Once I finally gave up on "learnyouahaskell" and other ridiculous tutorials, I found the real functional programming textbooks, and discovered that it all starts with lambda calculus; all the explanations are given in set theory notation, with occasionally comparisons to integral and differential calculus for illustration, with very specific rules regarding substitution and reduction and normal forms. I'm still trying to figure out what all those combinators are about! And it is all rested on mathematical proofs, usually inductive.
And that is just the lambda calculus aspect. Then we move on to type theory (!!!) plus the various types of polymorphism, and then on to a number of other topics that I don't know enough about to even mention intelligibly.