A lambda abstraction is another name for an anonymous function. It gets its name from the usual notation for writing it - for example, . (Note: some sources write it as .)
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 must more ugly 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 occurrence of the parameter variable (in this case ) with the parameter value (in this case 7). This is an eta reduction.