H. Tews. Coalgebras for binary methods: Properties of bisimulations and invariants. Theoretical Informatics and Applications, 35(1):83--111, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Bisimulations for Binary Methods Hendrik Tews Inst. Theor. Informatik, TU Dresden, D 01062 Dresden, Germany. tews tcs.inf.tu dresden.de A generalised notion of coalgebra that is capable of modelling binary methods as they occur in object oriented programming has been introduced in [14]. An important problem with this generalisation is that bisimulations are not closed under union and that a greatest bisimulation does not exists in general. There are two possible approaches to improve this situation: First, to strengthen the definition of bisimulation, and second, to place ....

....binary methods that have a codomain of Self (so the canonical example equal is excluded) and whose behaviour is completely determined by the operations in the coalgebraic signature. A rigorous solution that allows to model methods of arbitrary types has been proposed by the present author in [14]. The idea is to use bivariant functors Set op Set ## Set to model signatures and to work with appropriately generalised notions of coalgebra and bisimulation. If H is such a bivariant functor then a H coalgebra is a function X ## H(X;X) This allows to model exotic method types like 1 ....

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H. Tews. Coalgebras for binary methods: Properties of bisimulations and invariants. Theoretical informatics and applications, 35(1):83--111, February 2001. 16

....a class speci cation. All the example speci cations from the preceding sections are valid ccsl speci cations (modulo the use of symbols like 8) However, ccsl allows more general coalgebraic signatures. Currently it supports signatures that correspond to the higher order polynomial functors from [28]. ccsl uses a higher order logic extended with in nitary modal operators. The main reference on ccsl is [26] but see also the older reference [9] In order to get theorem proving support, ccsl can be translated into the higher order logics of pvs [24] and isabelle hol [25] The translation is ....

H. Tews. Coalgebras for binary methods: Properties of bisimulations and invariants. Theoretical informatics and applications, 35(1):83-111, February 2001.

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H. Tews. Coalgebras for binary methods: Properties of bisimulations and invariants. Theoretical Informatics and Applications, 35(1):83--111, 2001.

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H. Tews. Coalgebras for binary methods: Properties of bisimulations and invariants. Theoretical informatics and applications, 35(1):83--111, Feb. 2001.

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