Personal tools

Beta reduction

From HaskellWiki

Revision as of 18:22, 3 February 2007 by Nedervold (Talk | contribs)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to: navigation, search

A beta reduction (also written β reduction) is the process of calculating a result from the application of a function to an expression.

Haskell theoretical foundations

General:
Mathematics - Category theory
Research - Curry/Howard/Lambek

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

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

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 free 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
2*7*7
to
98
. Although the lambdas are not explicit, they exist hidden in the definition of
(*)
.)

Also see Lambda calculus and the wikipedia lambda calculus article.