Coalgebraic Monads
نویسندگان
چکیده
منابع مشابه
Coalgebraic Monads
This paper introduces coalgebraic monads as a unified model of term algebras covering fundamental examples such as initial algebras, final coalgebras, rational terms and term graphs. We develop a general method for obtaining finitary coalgebraic monads which allows us to generalise the notion of rational term and term graph to categories other than Set. As an application we sketch part of the c...
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Monads are extensively used nowadays to abstractly model a wide range of computational effects such as nondeterminism, statefulness, and exceptions. It turns out that equipping a monad with a (uniform) iteration operator satisfying a set of natural axioms allows for modelling iterative computations just as abstractly. The emerging monads are called complete Elgot monads. It has been shown recen...
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We study the construction of preorders on Set-monads by the semantic ⊤⊤-lifting. We show the universal property of this construction, and characterise the class of preorders on a monad as a limit of a Card-chain. We apply these theoretical results to identifying preorders on some concrete monads, including the powerset monad, maybe monad, and their composite monad. We also relate the constructi...
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Strong bisimulation for labelled transition systems is one ofthe most fundamental equivalences in process algebra, and has beengeneralised to numerous classes of systems that exhibit richer transi-tion behaviour. Nearly all of the ensuing notions are instances of themore general notion of coalgebraic bisimulation. Weak bisimulation, how-ever, has so far been much less amenab...
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ژورنال
عنوان ژورنال: Electronic Notes in Theoretical Computer Science
سال: 2002
ISSN: 1571-0661
DOI: 10.1016/s1571-0661(04)80360-8