# Difference between revisions of "Eta conversion"

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m (Reverted edits by Tomjaguarpaw (talk) to last revision by Lemming) |
(aka eta expansion) |
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An ''eta conversion'' (also written ''η-conversion'') is adding or dropping of abstraction over a function. For example, the following two values are equivalent under η-conversion: <haskell>\x -> abs x | An ''eta conversion'' (also written ''η-conversion'') is adding or dropping of abstraction over a function. For example, the following two values are equivalent under η-conversion: <haskell>\x -> abs x | ||

</haskell>and <haskell>abs</haskell> | </haskell>and <haskell>abs</haskell> | ||

− | Converting from the first to the second would constitute an eta ''reduction'', and moving from the second to the first would be an eta ''abstraction''. The term 'eta conversion' can refer to the process in either direction. | + | Converting from the first to the second would constitute an eta ''reduction'', and moving from the second to the first would be an eta ''abstraction'' (also known as eta ''expansion''). The term 'eta conversion' can refer to the process in either direction. |

Extensive use of η-reduction can lead to [[Pointfree]] programming. It is also typically used in certain compile-time optimisations. | Extensive use of η-reduction can lead to [[Pointfree]] programming. It is also typically used in certain compile-time optimisations. |

## Latest revision as of 18:06, 15 February 2021

An *eta conversion* (also written *η-conversion*) is adding or dropping of abstraction over a function. For example, the following two values are equivalent under η-conversion:

```
\x -> abs x
```

and

```
abs
```

Converting from the first to the second would constitute an eta *reduction*, and moving from the second to the first would be an eta *abstraction* (also known as eta *expansion*). The term 'eta conversion' can refer to the process in either direction.

Extensive use of η-reduction can lead to Pointfree programming. It is also typically used in certain compile-time optimisations.

## See also

- Haskell-Cafe on What's the motivation for η rules?