# Apomorphism

> Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Apomorphism
> Markdown URL: https://mediated.wiki/source/Apomorphism.md
> Source: https://en.wikipedia.org/wiki/Apomorphism
> Source revision: 1334691500
> License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/)

{{About|the computer science term|the term in biology|Apomorphy}}
In [formal methods](/source/formal_methods) of [computer science](/source/computer_science), an '''apomorphism''' (from ''ἀπό'' — [Greek](/source/Greek_(language)) for "apart") is the [categorical dual](/source/categorical_dual) of a [paramorphism](/source/paramorphism) and an extension of the concept of [anamorphism](/source/anamorphism) ([coinduction](/source/coinduction)). Whereas a paramorphism models [primitive recursion](/source/primitive_recursion) over an [inductive data type](/source/Recursive_data_type), an apomorphism models primitive [corecursion](/source/corecursion) over a coinductive data type.

==Origins==
The term "apomorphism" was introduced in ''Functional Programming with Apomorphisms (Corecursion)''.<ref>{{citation|
 last=Vene|
 first=Varmo|
 first2=Tarmo|
 last2=Uustalu|
 title=Functional Programming with Apomorphisms (Corecursion)|
 journal=Proceedings of the Estonian Academy of Sciences: Physics, Mathematics|
 volume=47|
 pages=147–161|
 year=1998|
 url=https://cs.ioc.ee/~tarmo/papers/vene-uustalu-nwpt97-peas.pdf|
 issue=3}}</ref>

==See also==
* [Morphism](/source/Morphism)
* Morphisms of [F-algebras](/source/F-algebra)
** From an initial algebra to an algebra: [Catamorphism](/source/Catamorphism)
** From a coalgebra to a final coalgebra: [Anamorphism](/source/Anamorphism)
** An anamorphism followed by an catamorphism: [Hylomorphism](/source/Hylomorphism_(computer_science))
** Extension of the idea of catamorphisms: [Paramorphism](/source/Paramorphism)

==References==
<references/>

Category:Recursion schemes

{{formalmethods-stub}}

---
Adapted from the Wikipedia article [Apomorphism](https://en.wikipedia.org/wiki/Apomorphism) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Apomorphism?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.