nLab
corecursion
Corecursion
Context
Induction
Rules
Categorical semantics
Examples
Corecursion
Idea
Corecursion exploits the existence of a morphism from a coalgebra for an endofunctor to a terminal coalgebra for the same endofunctor to define an operation. It is dual to recursion. See also coinduction.
Examples
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For the endofunctor on Set, the terminal coalgebra is , the extended natural number system. Define a function :
where is as defined at extended natural number.
Then is an -coalgebra. The unique coalgebra morphism (to the terminal coalgebra ) is addition on the extended natural numbers.
Reference
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Jiří Adámek, Introduction to Coalgebra (pdf)
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Lawrence Moss, Norman Danner, On the Foundations of Corecursion (journal, pdf)
Last revised on September 28, 2012 at 16:18:36.
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