A lambda abstraction is another name for an anonymous function. It gets its name from the usual notation for writing it: for example, . (Another common but equivalent notation is: .)
In Haskell source code, the Greek letter lambda is replaced by a backslash character ('
\') instead, since this is easier to type and requires only the basic 7-bit ASCII character set. Similarly, the arrow is replaced with the much more ugly (but strictly ASCII) character sequence '
->'. So, for example, the lambda abstraction above would be written in Haskell as
\ x -> x * x
There is actually a whole mathematical theory devoted to expressing computation entirely using lambda abstractions: the lambda calculus. Most functional programming languages (including Haskell) are based upon some extension of this idea.
When a lambda abstraction is applied to a value—for instance, —the result of the expression is determined by replacing every free occurrence of the parameter variable (in this case ) with the parameter value (in this case ). This is a beta reduction.