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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.

Haskell theoretical foundations

Mathematics - Category theory
Research - Curry/Howard/Lambek

Lambda calculus:
Alpha conversion - Beta reduction
Eta conversion - Lambda abstraction

Recursion - Combinatory logic
Chaitin's construction - Turing machine
Relational algebra

For example, suppose we have

2*x*x + y
If we now replace every occurance of
with 7, we arrive at
2*7*7 + y

We have thus performed a beta reduction.

Also see Lambda calculus and the wikipedia lambda calculus article.