Elgot Algebras

Authors:
Jiří Adámek;Stefan Milius;Jiří Velebil
Affiliations:
Institute of Theoretical Computer Science, Technical University, Braunschweig, Germany;Institute of Theoretical Computer Science, Technical University, Braunschweig, Germany;Faculty of Electrical Engineering, Technical University, Prague, Czech Republic
Venue:
Electronic Notes in Theoretical Computer Science (ENTCS)
Year:
2006

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Abstract

Iterative algebras, i. e., algebras A in which flat recursive equations e have unique solutions e^@?, are generalized to Elgot algebras, where a choice e@?e^@? of solutions of all such equations e is specified. This specification satisfies two simple and well motivated axioms: functoriality (stating that solutions are ''uniform'') and compositionality (stating how to perform simultaneous recursion). These two axioms stem canonically from Elgot's iterative theories: We prove that the category of Elgot algebras is the Eilenberg-Moore category of the free iterative monad.