A beta reduction (also written β reduction) is the process of calculating a result from the application of a function to an expression.
For example, suppose we apply the function
(\x -> 2*x*x + y)
to the value
7. To calculate the result, we substitute
7 for every occurrence of
x, and so the application of the function
(\x -> 2*x*x + y)(7)
is reduced to the result
2*7*7 + y
This is a beta reduction.
(Further reductions could be applied to reduce
98. Although the lambdas are not explicit, they exist hidden in the definition of
Also see Lambda calculus and the wikipedia lambda calculus article.