Computer Science – Logic in Computer Science
Scientific paper
2006-09-08
LMCS 2 (5:4) 2006
Computer Science
Logic in Computer Science
Scientific paper
10.2168/LMCS-2(5:4)2006
Denotational semantics can be based on algebras with additional structure (order, metric, etc.) which makes it possible to interpret recursive specifications. It was the idea of Elgot to base denotational semantics on iterative theories instead, i.e., theories in which abstract recursive specifications are required to have unique solutions. Later Bloom and Esik studied iteration theories and iteration algebras in which a specified solution has to obey certain axioms. We propose so-called Elgot algebras as a convenient structure for semantics in the present paper. An Elgot algebra is an algebra with a specified solution for every system of flat recursive equations. That specification satisfies two simple and well motivated axioms: functoriality (stating that solutions are stable under renaming of recursion variables) 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 monad given by a free iterative theory.
Adamek Jiri
Milius Stefan
Velebil Jiří
No associations
LandOfFree
Elgot Algebras does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Elgot Algebras, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Elgot Algebras will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-112000