A Coalgebraic Theory of Reactive Systems | Zendy

Filippo Bonchi | Zendy; Ugo Montanari | Zendy

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A Coalgebraic Theory of Reactive Systems

Author(s) -

Filippo Bonchi,

Ugo Montanari

Publication year - 2008

Publication title -

electronic notes in theoretical computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.242

H-Index - 60

ISSN - 1571-0661

DOI - 10.1016/j.entcs.2009.02.012

Subject(s) - coalgebra , principle of compositionality , morphism , monad (category theory) , semantics (computer science) , mathematics , functor , denotational semantics , lift (data mining) , computer science , pure mathematics , algebra over a field , operational semantics , programming language , artificial intelligence , data mining

In this paper we investigate the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, under rather restrictive conditions, the compositionality of the abstract semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure.Here we show that for every reactive system we can build a coalgebra. Furthermore, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra

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