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Anonymous function

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An anonymous function is a function without a name. It is a Lambda abstraction and might look like this:
\x -> x + 1
. (That backslash is Haskell's way of expressing a λ and is supposed to look like a Lambda.)

1 Examples

That is a nameless function which increments its parameter, x. So in Hugs or GHCi, I might say:

Prompt> (\x -> x + 1) 4
5 :: Integer

Or I could make a nameless function of two parameters, x and y:

\x y -> x + y
, which could be applied like so:
Prompt> (\x y -> x + y) 3 5
8 :: Integer

You could also name a lambda expression if you wanted to for some reason:

addOne = \x -> x + 1

Of course, there are a variety of better ways to write that in Haskell, but you get the idea.

2 But why bother?

Sometimes it is more convenient to use a lambda expression rather than giving a function a name. This is often the case when using
map
and
foldl / foldr
. So if I wanted to add one to each element of a list, here's one way to do it (without anonymous functions):
addOneList lst = map addOne' lst
  where addOne' x = x + 1

But here's another way, where we pass the anonymous function into map rather than any named function.

addOneList' lst = map (\x -> x + 1) lst

For completeness it's worth mentioning that this could be better written using a section, in pointfree style:

addOneList'' = map (+1)

3 See also