Headline

Transformation of a function on multiple arguments to take one at a time

Illustration

In Language:Haskell, functions are typically in curried form. Consider, for example, the signature of addition:

> :t (+)
(+) :: Num a => a -> a -> a

Curried form is generally convenient as it directly enables partial application. For instance, we can define an increment function, just by passing one argument to addition:

inc :: Int -> Int
inc = (+) 1

If we were to define addition in uncurried form, then this would look as follows:

add :: Num a => (a, a) -> a
add (x,y) = x+y

We can easily perform currying:

add' :: Num a => a -> a -> a
add' x y = add (x,y)

In fact, the currying transformation can be represented by the following higher-order function:

curry :: ((a, b) -> c) -> a -> b -> c
curry f a b = f (a,b)

(We would need such a curry(ing) function for each number of arguments.) Thus, we can express the currying transformation as follows:

add'' :: Num a => a -> a -> a
add'' = curry add

Relationships

See uncurrying for the dual transformation.

Citation

(http://en.wikipedia.org/wiki/Currying, 18 May 2013)

In mathematics and computer science, currying is the technique of transforming a function that takes multiple arguments (or a tuple of arguments) in such a way that it can be called as a chain of functions, each with a single argument (partial application). It was originated by Moses Schönfinkel ... and later re-discovered by Haskell Curry.

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