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$ \eta $-Reduction

$ \eta $-reduction is useful to eliminate redundant lambda abstractions. The following rule can be interpreted like this:

If the sole purpose of a lambda abstraction is to pass its argument to another function, then the lambda abstraction is redundant and can be stripped via $ \eta $-reduction.

In an environment where `eager evaluation' is used like in Scheme such redundant lambda abstractions are used as a wrapper around a lambda expression to prevent immediate evaluation.

{\sc Rule 8 (Eta Reduction)} \\
The following transfor...
...ightarrow} M$\ ,
\end{center}where $x$\ may not be a free variable in $M$.

Georg P. Loczewski 2004-03-05

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