# Beta reduction

### From HaskellWiki

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(I think my example actually included an eta-reduction as well as a beta conversion. Edited example.) |
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− | A ''beta reduction'' (also written ''β reduction'') is | + | 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 | + | {{Foundations infobox}} |

+ | For example, suppose we apply the function | ||

<haskell> | <haskell> | ||

− | 2*x*x + y | + | (\x -> 2*x*x + y) |

</haskell> | </haskell> | ||

− | + | to the value <hask>7</hask>. To calculate the result, we substitute <hask>7</hask> for every [[Free variable|free occurrence]] of <hask>x</hask>, and so the application of the function | |

+ | <haskell> | ||

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

+ | </haskell> | ||

+ | is ''reduced'' to the result | ||

<haskell> | <haskell> | ||

2*7*7 + y | 2*7*7 + y | ||

</haskell> | </haskell> | ||

− | + | This is a ''beta reduction''. | |

+ | |||

+ | (Further reductions could be applied to reduce <hask>2*7*7</hask> to <hask>98</hask>. Although the lambdas are not explicit, they exist hidden in the definition of <hask>(*)</hask>.) | ||

Also see [[Lambda calculus]] and the [http://en.wikipedia.org/wiki/Lambda_calculus wikipedia lambda calculus article]. | Also see [[Lambda calculus]] and the [http://en.wikipedia.org/wiki/Lambda_calculus wikipedia lambda calculus article]. | ||

[[Category:Glossary]] | [[Category:Glossary]] |

## Revision as of 18:22, 3 February 2007

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)

7

7

x

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

is *reduced* to the result

2*7*7 + y

This is a *beta reduction*.

2*7*7

98

(*)

Also see Lambda calculus and the wikipedia lambda calculus article.