[Haskell-cafe] Trouble with currying and uncurrying...

[Benedict Eastaugh]

On 25 April 2011 14:11, Angel de Vicente <angelv at iac.es> wrote:

> OK, I have tried it and it works, but I don't understand the syntax for
> curry. Until now I have encountered only functions that take the same number
> of arguments as the function definition or less (partial application), but
> this syntax looks a bit new to me. curry is supposed to have as its argument
> one function of type (a,b) -> c and produce another function, but then the
> second line gives three arguments to curry, the function itself and the
> variables x and y.
>
> What I'm missing here?

You can think of all functions in Haskell as taking only one argument.
So curry has one argument, which is a function that takes a pair (in
this case g). The value of curry g is another function (the curried
version of g) which takes two arguments.

This is clearer when written out like so:

g :: (a, b) -> c

h :: a -> b -> c
h = curry g

h x y = g (x, y)

So by simple substitution we can see that

curry g x y = g (x, y)

It might be even clearer if we add parentheses, since function
application associates to the left:

(curry g) x y = g (x, y)

Hope this clears things up. For more information you could have a look
at the Gentle Introduction's section on functions:

http://www.haskell.org/tutorial/functions.html

Benedict.