4 results
Jiří Adámek ; Stefan Milius ; Lawrence S Moss ; Lurdes Sousa.
For endofunctors of varieties preserving intersections, a new description of the final coalgebra and the initial algebra is presented: the former consists of all well-pointed coalgebras. These are the pointed coalgebras having no proper subobject and no proper quotient. The initial algebra consists […]
Published on August 9, 2013
Jiří Adámek ; Mahdie Haddadi ; Stefan Milius.
An algebra is called corecursive if from every coalgebra a unique coalgebra-to-algebra homomorphism exists into it. We prove that free corecursive algebras are obtained as coproducts of the terminal coalgebra (considered as an algebra) and free algebras. The monad of free corecursive algebras is […]
Published on September 11, 2014
Stefan Milius ; Lawrence S Moss ; Daniel Schwencke.
Terminal coalgebras for a functor serve as semantic domains for state-based systems of various types. For example, behaviors of CCS processes, streams, infinite trees, formal languages and non-well-founded sets form terminal coalgebras. We present a uniform account of the semantics of recursive […]
Published on September 30, 2013
Jiri Adamek ; Stefan Milius ; Jiri Velebil.
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 […]
Published on November 8, 2006