Eta reduction

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Eta-reduction or η-reduction is the process of removing a “pointless” abstraction. The name originally comes from considerations about the lambda calculus ; however, the concept per se is not limited to this. In a function definition such as , which could also be written as , the introduction of a name for the function argument of is of no use. The eta-reduced variant is . ${\displaystyle f(x):=\sin(x)}$ ${\displaystyle f:=x\mapsto \sin(x)}$ ${\displaystyle f}$ ${\displaystyle f:=\sin }$

The reverse process (explicitly naming a parameter of a function) is called η-expansion and is used, for example, when this enables further useful transformations.

Example from programming ( Haskell )

The following two function definitions are synonymous:

addiereZehnZu x = (+) 10 x
addiereZehnZu = (+) 10  
 -- in beiden Fällen ergibt die Ausführung von ...
addiereZehnZu 5
 -- ... das Ergebnis 15.
 -- auch dies ist eine Eta-Reduktion.

Web links

• http://www.haskell.org/haskellwiki/Eta_conversion