[Haskell-beginners] Functional programming principles at higher levels?

[Christopher Howard]

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.

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