# Uncurrying

Transformation of a function to take its multiple arguments at once

## Illustration

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

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

Thus, addition takes one argument at a time. 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
```

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

```uncurry :: (a -> b -> c) -> (a, b) -> c
uncurry f (a,b) = f a b
```

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

```add' :: Num a => (a, a) -> a
```

## Relationships

See currying for the dual transformation.

## Citation

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

Uncurrying is the dual transformation to currying, and can be seen as a form of defunctionalization. It takes a function f(x) which returns another function g(y) as a result, and yields a new function fâ˛(x,y) which takes a number of additional parameters and applies them to the function returned by function f.

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