[Haskell-beginners] A post about Currying and Partial application

[Petar Radosevic]

Chaddaï Fouché wrote the following on Sun, Oct 02, 2011 at 12:48:31AM +0200:
> On Sat, Oct 1, 2011 at 2:40 PM, Petar Radosevic <petar at wunki.org> wrote:
> > Peter Hall wrote the following on Sat, Oct 01, 2011 at 10:49:31AM +0100:
> >> I think this sentence isn't right:
> >>
> >> "Curried functions are functions that only take one parameter."
> >>
> >> The way I understand it, a non-curried function takes only one
> >> parameter. Currying is syntactic sugar so you don't have to use
> >> higher-order functions every time you want multiple parameters.
> >>
> >> Without currying, if you wanted a function like:
> >>
> >>     f a b c = 2 * a + b - c
> >>
> >> , you'd have to write it something like:
> >>
> >>   f a = f1
> >>       where f1 b = f2
> >>           where f2 c = 2 * a + b - c
> >>
> >> or
> >>
> >>    f a = (\b -> (\c ->  2*a + b -c))
> >
> > You are right, I changed the sentence to better reflect wat currying
> > really is. Thank you for your input.
> 
> Sorry but you are mistaken on the sense of currying. Basically to
> curry the function f is to transform it from the type "(a,b) -> c" to
> the type "a -> (b -> c)", in other words instead of function from a
> cartesian product to a set, you get a function from the first element
> of the product to the set of function from the second element of the
> product to the original final set. This is a mathematical
> transformation that Curry noted was always possible whatever the
> function.
> In a CS context, this transformation is only possible in languages
> that handle functions as first-class data types, Haskell (or the ML
> family) is only special in that it encourage you to write every
> functions in an already curried style instead of the uncurried fashion
> that is used in most other languages. Every single example you give in
> your blog is curried, uncurried would be :
> 
> > sumTwo :: (Int,Int) -> Int
> > sumTwo (x,y) = x + y
> 
> and
> 
> > f :: (Int,Int,Int) -> Int
> > f (a,b,c) = 2 * a + b - c
> 
> See the function "curry" and "uncurry" to see that passing from one
> style to another can be automated (though only elegantly for two
> parameters).
> 
> Still it is true that currying functions ease the partial application
> of function (at least if your parameters are ordered sensibly).

Thank you for your explanation. I was also corrected on reddit[1] on the
matter. Since my post is wrong on the subject I have decided chuck it
and write a new one. I'm collecting all the comments people made as we
speak and am going to make good use of them in a post which hopefully
_does_ explain currying.

[1]: http://www.reddit.com/r/haskell/comments/kxdh7/curry_and_its_partial_application/

-- 
Petar Radošević, Programmer
wunki.org | @wunki
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