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<title>Apomorphism</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Apomorphism</span></span>

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<div id="mw-content-text" class="mw-body-content mw-content-ltr" lang="en" dir="ltr"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><p>In <a href="Formal_methods" title="Formal methods">formal methods</a> of <a href="Computer_science" title="Computer science">computer science</a>, an <b>apomorphism</b> (from <i><a href="https://en.wiktionary.org/wiki/%E1%BC%80%CF%80%CF%8C" class="extiw external" title="wikt:ἀπό">ἀπό</a></i> — <a href="Greek_(language)" class="mw-redirect" title="Greek (language)">Greek</a> for "apart") is the <a href="Categorical_dual" class="mw-redirect" title="Categorical dual">categorical dual</a> of a <a href="Paramorphism" title="Paramorphism">paramorphism</a> and an extension of the concept of <a href="Anamorphism" title="Anamorphism">anamorphism</a> (<a href="Coinduction" title="Coinduction">coinduction</a>). Whereas a paramorphism models <a href="Primitive_recursion" class="mw-redirect" title="Primitive recursion">primitive recursion</a> over an <a href="Recursive_data_type" title="Recursive data type">inductive data type</a>, an apomorphism models primitive <a href="Corecursion" title="Corecursion">corecursion</a> over a coinductive data type.

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<div class="mw-heading mw-heading2"><h2 id="Origins">Origins</h2></div>

<p>The term "apomorphism" was introduced in <i>Functional Programming with Apomorphisms (Corecursion)</i>.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup>

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<ul><li><a href="Morphism" title="Morphism">Morphism</a></li>

<li>Morphisms of <a href="F-algebra" title="F-algebra">F-algebras</a>

<ul><li>From an initial algebra to an algebra: <a href="Catamorphism" title="Catamorphism">Catamorphism</a></li>

<li>From a coalgebra to a final coalgebra: <a href="Anamorphism" title="Anamorphism">Anamorphism</a></li>

<li>An anamorphism followed by an catamorphism: <a href="Hylomorphism_(computer_science)" title="Hylomorphism (computer science)">Hylomorphism</a></li>

<li>Extension of the idea of catamorphisms: <a href="Paramorphism" title="Paramorphism">Paramorphism</a></li></ul></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite id="CITEREFVeneUustalu1998" class="citation cs2">Vene, Varmo; Uustalu, Tarmo (1998), <a rel="nofollow" class="external text" href="https://cs.ioc.ee/~tarmo/papers/vene-uustalu-nwpt97-peas.pdf">"Functional Programming with Apomorphisms (Corecursion)"</a> <span class="cs1-format">(PDF)</span>, <i>Proceedings of the Estonian Academy of Sciences: Physics, Mathematics</i>, <b>47</b> (3): <span class="nowrap">147–</span>161</cite></span>

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This article is issued from <a class="external text" title="Last edited on 2025-07-07" href="https://en.wikipedia.org/wiki/?title=Apomorphism&oldid=1299255683">Wikipedia</a>. The text is available under <a class="external text" href="https://creativecommons.org/licenses/by-sa/4.0/deed.en">Creative Commons Attribution-Share Alike 4.0</a> unless otherwise noted. Additional terms may apply for the media files.

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