J. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J. de Bakker et al., editors, Proc. of the REX workshop A Decade of Concurrency -- Reflections and Perspectives, volume 803 of LNCS, pages 530--582. Springer-Verlag, 1994.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....Work The work reported in this section is by no means the only attempt to systematically derive denotational models from SOS language specifications. The main precursors to this work in the field of the metatheory of process description languages may be found in the work by Bloom [47] and Rutten [189, 190, 191, 192]. In his unpublished paper [47] Bloom gives operational, logical, relational, and three denotational semantics for GSOS languages without negative premises and unguarded recursion, and shows that they coincide. Bloom s work is based on the behavioural notion of simulation [124] and two of his ....

....models from transition rules. Rutten s general processes as terms approach could have been applied to yield an equivalent formulation of the semantic operations on finite synchronization trees given above. The work presented in the aforementioned papers has been generalized by Rutten and Turi [192]. Ibidem it is shown how TSSs in tyft tyxt format induce a denotational semantics, and the essential properties of semantic domains that make their definitions possible are investigated in a categorical perspective. Abramsky and Vickers [3] consider various notions of process observations in a ....

J. Rutten and D. Turi, Initial algebra and final coalgebra semantics for concurrency, in de Bakker et al. [73], pp. 530--581.

....a concrete definition of bisimulation. A cornerstone of the coalgebraic approach to bisimulation is the correspondence of bisimilarity of deterministic and non deterministic transition systems given in concrete terms of transfer properties or given in categorical terms of a mediating coalgebra [RT93]. In [VR99] it is shown that the concrete notion of bisimulation for Markov chains coincides with the coalgebraic notion. The proof technique extends to most other contexts involving the # functor, viz. Str, Alt, React, SSeg, Seg, and Gen as well. The bundle probabilistic transition systems of ....

J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In REX School/Symposium, pages 530--582. LNCS 666, 1993.

....a concrete definition of bisimulation. A cornerstone of the coalgebraic approach to bisimulation is the correspondence of bisimilarity of deterministic and non deterministic transition systems given in concrete terms of transfer properties or given in categorial terms of a mediating coalgebra [RT93]. In [VR99] it is shown that the concrete notion of bismulation for Markov chains coincides with the coalgebraic notion. The proof technique extends to most other contexts involving the # functor, viz. Str, Alt, React, SSeg, Seg, and Gen as well. The bundle probabilistic transition systems of ....

J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In REX School/Symposium, pages 530--582. LNCS 666, 1993.

....coalgebras are of particular interest because of the following property which is the coinductive proof principle (cpp) Here a predicate P on U describes the states satisfies P , the set of all such states forms a subset of U . Therefore, P can be encoded as a subset of U equally. Theorem 2. 1 ([RT94]) A final coalgebra (U; is strongly extensional: 8u; u 2 U; u U u ) u = u where the relation U is the union of F bisimulations: U = fR U U j R is a F bisimulation on (U; g With this principle, it suffices to establish the existence of a bisimulation between two ....

Jan Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. In J. W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proceedings of the REX School/Symposium `A decade of concurrency', volume 803 of LNCS, pages 530--582. Springer, 1994.

....(Y; Gamma ) a2Act ; U) such that U(fx) V (x) A fundamental property of a final ETS is that it is strongly extensional in the sense of Theorem 4.1. The proof of the theorem below is given in Hartonas [12] The proof is along the lines of similar results in Aczel [4] and Rutten and Turi [28]. Theorem 4.1 (Strong Extensionality for a Final ETS) If F = F; Gamma ) a2Act ; V ) is a final ETS and p; q 2 F , then p q iff p = q. We regard an ETS as a coalgebra for the functor Phi j (Act Theta Gamma) Theta (Act ) j Theta Theta (Act What we are interested in is a ....

J.J.M.M. Rutten and D. Turi. Initial Algebra and Final Coalgebra Semantics for Concurrency. J. de Bakker et al. (eds) Proc. REX workshop, A Decade of Concurrency -- Reflections and Perspectives, Lecture Notes in Computer Science 803 (1994) 530-582, Springer-Verlag.

....the model can capture the notion of admissibility but full abstractness must fail in this framework. In producing here a fully abstract model for fair bisimilarity we extend the framework developed by Aczel [1, 3] and then also investigated by J. Rutten in [23, 25] and J. Rutten and D. Turi in [24, 26]. Since we work within a non standard set theory, we have collected our set theoretic assumptions in Appendix A, where we also review some of the technical aspects of Aczel s approach to modeling processes as hypersets. 2 Transition Systems as Coalgebras A transition system over A is a ....

....defined as the largest fortification relation OE= fRj R is a fortification relation g A fundamental property of a final ETS is that it is strongly extensional in the sense of Theorem 3.2. The proof of the theorem can be given along the lines of similar results in Aczel [3] and Rutten and Turi [26]. Theorem 3.2 If F = F; Gamma ) a2A ; V ) is a final ETS and p; q 2 F , then p q iff p = q. Proof: The proof is an immediate consequence of the following Proposition, taking f X to be the identity on F . 12 Proposition 3.3 Assume F = F; Gamma ) a2A ; V ) is a final ETS and let X ....

J.J.M.M. Rutten and D. Turi. Initial Algebra and Final Coalgebra Semantics for Concurrency. J. de Bakker et al. (eds) Proc. REX workshop, A Decade of Concurrency -- Reflections and Perspectives, Lecture Notes in Computer Science 803 (1994) 530-582, Springer-Verlag.

....reported in this paper is by no means the first attempt to systematically derive denotational models from SOS language specifications. The main precursors to this work in the field of the meta theory of process description languages may be found in the work by Bloom [20] and by Rutten and Turi [72, 73, 74, 75]. In his unpublished paper [20] Bloom gives operational, logical, relational and three denotational semantics for GSOS languages without negative premises and unguarded recursion, and shows that they coincide. Bloom s work is based on the behavioural notion of simulation [43] and two of his ....

....semantic operations on finite synchronization trees we present in Sect. 6.2; in this study, however, we have plumped for the more direct construction of the operations given in Def. 6.9. The work presented in the aforementioned papers by Rutten has recently been generalized by Rutten and Turi in [75]. In that paper, the authors show how to give denotational semantics to languages specified by transition system specifications in full tyft tyxt format [36] and investigate in a categorical perspective the essential properties of semantic domains that make their definitions possible. In [3] ....

J. Rutten and D. Turi, Initial algebra and final coalgebra semantics for concurrency, in A decade of concurrency, J. de Bakker, W. de Roever, and G. Rozenberg, eds., vol. 803 of Lecture Notes in Computer Science, Springer-Verlag, 1994, pp. 530-- 581. Also available as Technical Report CS-R9409, CWI, Amsterdam.

....same speculative level we should also mention the possibility, suggested in [64] of incorporating fairness constraints in the models by moving from presheaves to sheaves. Finally, it is not clear to us how our approach relates to the abstract understanding of bisimulation provided by coalgebras [4, 114]. The hope is that the recent work and ongoing research of Turi and Plotkin [131, 132] will help provide the missing links. Recall that PomL is the category of (finite) pomsets over L. Appendix A Basic Definitions of Enriched Category Theory A.1 Enriched categories In this appendix we review ....

Jan Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. In J. de Bakker et al., editor, Proceedings of the REX workshop: A decade of concurrency - Reflections and perspectives, volume 660 of Lecture Notes

....alternative characterisations, more di#erent to the first characterisation above. One is via Hennessy Milner temporal logic [56] Another is by games as in e.g. 96] Strong bisimulation has also been shown to arise naturally in quite di#erent settings: within final coalgebra semantics (e.g. [117]) and from span of open maps ( 71] as we will describe in Ch. 2. 1.2.2 Some Dichotomies in Concurrency Theory As mentioned earlier, there exists many other choices of observable behaviours, primitive operations and mathematical models, than the choice represented by CCS and its standard ....

Jan Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. In J. de Bakker et al., editor, Proceedings of the REX workshop A Decade of Concurrency - Reflections and Perspectives, volume 803 of LNCS, pages 530--582.

....behavior of concurrent processes. In general the category of coalgebras for an endofunctor on Set does not always have final coalgebras. It is well known that for the powerset functor , as a typical case, the final coalgebra does not exist because of Cantor s diagonal method. Rutten and Turi [9, 10, 11] showed the existence of final coalgebras following Barr [4] Their study of final semantics of processes made use of preservation of kernel pairs for the functor f (A 2 0) which is known to formulate processes as coalgebra. Their construction of final coalgebras, however, requires the ....

....equivalence relations on labeled transition systems due to D. Park. Then a well known fundamental fact [2, Theorem 2.4] and [3, Lemma 4.3] that every coalgebra has the maximum congruence will be proved. The terminology congruence was initially used for algebras, for examples, in [9] and [10]. However, we reuse this terminology for coalgebras in the sense of Aczel and Mendler[3] In Section 5 we state the main result of the paper. First we introduce tree congruences on coalgebras using the notion of trees. Then we show that, whenever all trees of coalgebras are bounded to a set, there ....

[Article contains additional citation context not shown here]

Jan J.M.M. Rutten and Daniel Turi, Initial algebra and final coalgebra semantics for concurrency, In J.W. de Bakker, W.--P. de Roever, and G. Rosenberg, editors, Lecture Notes in Computer Science 803 (1994).

....This relatively new field has been recognized as a natural setting to deal with state based dynamic systems where observations 1 2 and their patterns seem far more relevant than data construction. In particular, coalgebraic methods have been used to approach the semantics of concurrent systems [17] and the specification of object oriented programs [15, 8] Although adopting a model oriented approach to specification, instead of the axiomatic setting common to the above mentioned references, our contribution has a similar motivation. In particular, we discuss how software components can be ....

J. Rutten and D. Turi. Initial algebra and final co-algebra semantics for concurrency. In Proc. REX School: A Decade of Concurrency, pages 530-- 582. Springer Lect. Notes Comp. Sci. (803), 1994.

....distributes over an endofunctor F arises in the context of the coalgebraic approach to coinduction. The gist of the coalgebraic approach to coinduction is that, under suitable conditions, equivalences induced by coiterative morphisms can be characterized as greatest coalgebraic F bisimulations ([1,2,20]) The problem addressed in [13] and in this section, is that of extending this paradigm to generalized coiterative morphisms, thus providing coalgebraic coinduction principles for reasoning on them. Generalized coiterative morphisms arise from the generalized coiteration scheme, which we call ....

J. Rutten and D. Turi, Initial algebra and final coalgebra semantics for concurrency, Proc. REX workshop A Decade of Concurrency -- Reflections and Perspectives, Lecture Notes in Comp Science 803, J. de Bakker et al (eds.) Springer-Verlag (1994), 530--582

....approach, however, often appears quite ad hoc, just think, for example, of how one would prove set theoretically the existence of a coiterative function into streams. In recent years, a categorical explanation of coinduction has appeared, based on the notion of coalgebra, see e.g. [Acz88, AM89, Acz93, RT93, RT94, Tur96, TP97, Len98]) Work supported by Esprit Working Group Types , MURST 97 Cofin. Sistemi Formali. grant, TMR Linear FMRX CT98 0170. 1 we shall refer to it as coalgebraic coinduction. Coalgebraic coinduction has proved to be extremely fertile ( HL95, Jac96, Len96, Rut96, Jac97, RV97, HLMP98, Mos, Len99] ....

....Coinduction up to [ see Section 4. 2 for more details) 7 2 Coalgebraic Description of Coinduction and Coiterative Morphisms In this section, we present the categorical description of coinduction based on the notion of coalgebra, for capturing equivalences induced by coiterative morphisms ([Acz88, AM89, RT93, RT94, Rut96, Tur96, TP97, Len98]) In this setting, the categorical counterparts of set theoretic bisimulations are F bisimulations, i.e. spans of coalgebra morphisms ( TP97] One of the advantages of a categorical description is that we can deal uniformly with coinductively defined objects and coiterative morphisms. In fact, ....

J.J.M.M.Rutten, D.Turi. Initial algebra and final coalgebra semantics for concurrency: A Decade of Concurrency - Reflections and Perspectives, REX Conference Proceedings, J.de Bakker et al. eds., Springer LNCS 803, 1994, 530--582.

....version. The final version will be published in Electronic Notes in Theoretical Computer Science URL: www.elsevier.nl locate entcs Honsell, Lenisa Introduction In recent years, much effort has been devoted to developing adequate categorical foundations to coinduction, based on coalgebras, [Acz88,AM89,RT93,RT94], etc. This approach amounts, essentially, to viewing coinductive types as final coalgebras, and to construing coiterative functions in terms of coalgebras. This research enterprise has been very successful. It has provided a new approach to the semantics of programming languages and process ....

.... categories for Final Semantics are the categories of classes of hypersets, i.e. non wellfounded sets satisfying the Antifoundation Axiom X 1 of [FH83] called AFA in [Acz88] However, despite the vast amount of published literature on final semantics in categories of sets and hypersets, e.g. [Acz88,AM89,Bar93,Bar94,RT93,RT94] [BM96,MD96,Tur96,TR98] a definitive, final, picture is just only beginning to emerge [Moss00] Each paper utilizes its peculiar definition, and little attention has been given to comparing the various results or to achieving generality. In this paper, we try to give a general form of Aczel s ....

[Article contains additional citation context not shown here]

J.J.M.M.Rutten, D.Turi. Initial algebra and final coalgebra semantics for concurrency: A Decade of Concurrency - Reflections and Perspectives, REX Conference Proceedings, J.de Bakker et al. eds., Springer LNCS 803, 1994, 530--582.

....In fact, the pattern of recursion used to construct transition trees is precisely the pattern of recursion captured by unfold. Hence, an operational semantics can be characterised as a semantics defined by unfolding to transition trees. This connection has been developed using category theory [18, 21], but most functional programmers are not aware of this connection. In this paper we explain how recursion operators can be used to structure and reason about program semantics within the functional language Haskell [16] In particular, we show how fold can be used to structure denotational ....

Jan Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker et al., editor, Proc. A Decade of Concurrency --- Reflections and Perspectives, LNCS. SpringerVerlag, 1994.

.... a suitable foundation for the object paradigm [16, 22, 27] Bisimulation has played a central part in concurrency theory [30, 7] model theoretic logics [1] and game theory [9, 40] and is currently enjoying a wider interest, perhaps partly due to recent results linking it to coalgebraic semantics [2, 34, 5, 37, 25, 36, 23, 35]. Minimal realisation of machines, a subject with a long history, was one of the earliest topics in computer science to be treated in an elegant categorical manner [14, 13, 4, 3] The relationship between behavioural equivalence and bisimulation seems to have suddenly become known or at least ....

Jan J.M.J. Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proc. REX Symposium `A decade of Concurrency', pages 530--582. Springer-Verlag Lecture notes in Computer Science 803, 1994.

No context found.

J. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J. de Bakker et al., editors, Proc. of the REX workshop A Decade of Concurrency -- Reflections and Perspectives, volume 803 of LNCS, pages 530--582. Springer-Verlag, 1994.

No context found.

Jan Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. In Jaco de Bakker et al., editors, Proc. of the REX workshop A Decade of Concurrency -- Reflections and Perspectives, volume 803 of Lecture Notes in Computer Science, pages 530--582. Springer Verlag, 1994.

....as studied, e.g. by Jones and Plotkin [JP89] and by Edalat [Eda94] are twofold. Firstly, one can resort to the rich literature for standard measure theory on metric spaces. Secondly, we can apply the recently developed theory on coalgebraic bisimulation and final coalgebras in the metric setting [AM89,RT94]. Notably, we shall see that M 1 is locally contractive, from which it follows that it has a final coalgebra. Because of the coalgebraic definition of bisimulation, we thus obtain an internally fully abstract domain. Such a full abstractness result has been lacking so far in the literature. In ....

J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proc. REX School/Symposium `A Decade of Concurrency', pages 530--582. LNCS 803, 1994.

.... One of the advantages of the coalgebraic view on transition systems is the existence of a general definition of F bisimulation, for any functor F (cf. AM89] For instance, applying that definition to the functor L above yields the standard notion of strong bisimulation of [Mil80, Par81] cf. [RT94], see also Section 2) In general, the coalgebraic theory gives a generic approach to the definition and description of bisimulation: First define or characterize the transition systems one is interested in as coalgebras of a suitably chosen functor F . Then obtain a definition of bisimulation for ....

....such as [Jon89, JP89] and [Eda94, Eda95] are twofold. Firstly, one can resort to the rich literature for standard measure theory on metric spaces (see, e.g. KV84] Secondly, we can apply the recently developed theory on coalgebraic bisimulation and final coalgebras in the metric setting [AM89, RT94]. Notably, we shall see that M 1 is locally contractive, from which it follows that it has a final coalgebra. Because of the coalgebraic definition of bisimulation, we thus obtain an internally fully abstract domain. Such a full abstractness result has been lacking so far in the literature. 2 In ....

J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proc. REX School/Symposium `A Decade of Concurrency', pages 530--582. Lecture Notes in Computer Science 803, 1994.

....more standard use of ordered structures, such as [Jon89, JP89] and [Eda95a, Eda95b] are twofold. Firstly, one can resort to the rich literature on standard measure theory for metric spaces (see, e.g. KV84] Secondly, we can use the recently developed coalgebraic theory on metric spaces [AR89, RT94], which seems to be better suited to describe (both ordinary and probabilistic) bisimulation than the corresponding theory for ordered spaces (cf. RT94] We shall see that the functor involved is locally contractive, from which it follows that it has a final coalgebra. Because of the coalgebraic ....

.... measure theory for metric spaces (see, e.g. KV84] Secondly, we can use the recently developed coalgebraic theory on metric spaces [AR89, RT94] which seems to be better suited to describe (both ordinary and probabilistic) bisimulation than the corresponding theory for ordered spaces (cf. [RT94]) We shall see that the functor involved is locally contractive, from which it follows that it has a final coalgebra. Because of the coalgebraic definition of bisimulation, we thus obtain an internally fully abstract domain. Such a full abstractness result has been lacking so far in the ....

J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In J.W. de Bakker, W.-P. de Roever, and G. Rozenberg, editors, Proc. REX School/Symposium `A Decade of Concurrency', pages 530--582. Lecture Notes in Computer Science 803, 1994.

No context found.

Jan J.M.M. Rutten and Daniele Turi. Initial algebra and final coalgebra semantics for concurrency. Lecture Notes in Computer Science, 803:530-- 582, 1994.

No context found.

J.J.M.M. Rutten and D. Turi. Initial algebra and final coalgebra semantics for concurrency. In REX School/Symposium, pages 530--582. LNCS 666, 1993.

No context found.

J.J.M.Rutten and D.Turi. Initial algebra and final co--algebra semantics for concurrency. Technical Report CS-R9404, CWI Amsterdam, 1994.

No context found.

J. Rutten and D. Turi, Initial algebra and final coalgebra semantics for concurrency, Proc. of the REX workshop A Decade of Concurrency -- Reflections and Perspectives (J. de Bakker et al., eds.), LNCS, vol. 803, SpringerVerlag, 1994, pp. 530--582.

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