# Currying

### From HaskellWiki

Currying is the process of transforming a function that takes multiple arguments into a function that takes just a single argument and returns another function if any arguments are still needed.

f :: a -> b -> c

is the **curried** form of

g :: (a, b) -> c

f = curry g g = uncurry f

Both forms are equally expressive. It holds

f x y = g (x,y) ,

however the curried form is usually more convenient because it allows partial application.

In Haskell, *all* functions are considered curried: That is, *all functions in Haskell take just single arguments.*

div :: Int -> Int -> Int

div 11

*returns a function*of type

Int -> Int

Int -> Int -> Int

*really*saying is "takes an

Much of the time, currying can be ignored by the new programmer. The major advantage of considering all functions as curried is theoretical: formal proofs are easier when all functions are treated uniformly (one argument in, one result out). Having said that, there *are* Haskell idioms and techniques for which you need to understand currying.

Currying provides a convenient way of writing some functions without having to explicitly name them:

- (unsugared:(1+)) is the "increment" function,(+) 1
- is the "double" function,(2*)
- is the "indent" function,("\t"++)
- is the "is-capital-vowel-in-English" function (ignoring the "sometimes Y").(`elem` "AEIOU")

These are examples of partial application (and of a Section of an infix operator).

Sometimes it's valuable to think about functions abstractly without specifically giving all their arguments: this is the Pointfree style.

Sometimes half the work of the function can be done looking only at the first argument (but there really *is* only one argument, remember?): see functional dispatch.

## Exercises

- Simplify curry id
- Write the function without lambda and with only Prelude functions\(x,y) -> (y,x)