Beta reduction

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A beta reduction (also written β reduction) is where you actually apply a lambda function to an expression to generate a result.

For example, suppose we have

(\x y -> 2*x*x + y) 7

If we now replace every occurance of x with 7, we arrive at

\y -> 2*7*7 + y

We have thus performed a beta reduction.

Also see Lambda calculus and the wikipedia lambda calculus article.