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.)

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.

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)

@@ Line 3: / Line 3: @@
-An anonymous function is a [[Function]] without a name.  It is a [[Lambda abstraction]] and might look like this: <hask>\x -> x + 1</hask>.  (That backslash is supposed to look like a Lambda.)
+An anonymous function is a [[function]] without a name.  It is a [[Lambda abstraction]] and might look like this: <hask>\x -> x + 1</hask>.  (That backslash is Haskell's way of expressing a &lambda; and is supposed to look like a Lambda.)
 ==Examples==
@@ Line 43: / Line 43: @@
 addOneList' lst = map (\x -> x + 1) lst
 </haskell>
-For completeness it's worth mentioning that this could be better written:
+For completeness it's worth mentioning that this could be better written
+using a [[section]], in [[pointfree]] style:
 <haskell>
@@ Line 50: / Line 52: @@
 ==See also==
-* Section 3.1 in the [http://haskell.cs.yale.edu/tutorial/functions.html Haskell tutorial].
+* Section 3.1 in the [http://www.haskell.org/tutorial/functions.html Haskell tutorial].
 * [[Closure]]
 * [[Lambda calculus]]
+* [[Beta reduction]]