P. Aczel and N. Mendler. A final coalgebra theorem. In D.H. Pitt et al., editors, Proc. category theory and computer science, volume 389 of LNCS, pages 357--365. Springer-Verlag, 1989. Home/Search Document Not in Database Summary Related Articles Check |
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Invariants, Bisimulations and the Correctness of Coalgebraic.. - Jacobs (1997) (Correct)
.... 0 (R = fhx 1 ; y 1 i j R (x 1 ; y 1 )g [ fh x 2 ; y 2 i j R hev ffi Theta id; ev ffi Theta idi = f(f 1 ; f 2 ) j 8a 2 A R (f 1 (a) f 2 (a) g: Bisimulations have received a lot of attention in process theory (see e.g. 22] but also in coalgebra, see e.g. [1, 26, 27]. The greatest bisimulation on two coalgebras is usually written as . It captures behavioural indistinguishability. A standard result is that elements of the state spaces of two arbitrary T coalgebras are bisimilar if and only if they are mapped to the same element of the terminal T coalgebra. ....
P. Aczel and N. Mendler. A final coalgebra theorem. In D.H. Pitt, A. Poign'e, and D.E. Rydeheard, editors, Category Theory and Computer Science, number 389 in Lect. Notes Comp. Sci., pages 357--
Generalised Coinduction - Bartels (2001) (9 citations) (Correct)
....principle which is given directly by finality. We call it coiteration here to distinguish it from The research reported here was part of the NWO project ProMACS. c #2001 Published by Elsevier Science B. V. derived variants. The main tool for proving states equal is that of an F bisimulation [AM89], a categorical generalisation of notions of bisimulation used for di#erent concrete systems. But these basic principles are often too rigid to nicely cover given examples. Many functions into the carrier of a final coalgebra can be shown not to be coiterative and many statements about behavioural ....
Peter Aczel and Nax Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, editors, Proceedings 3rd Conf. on Category Theory and Computer Science, CTCS'89, Manchester, UK, 5--8 Sept 1989, volume 389 of Lecture Notes in Computer Science, pages 357--365. Springer-Verlag, Berlin, 1989.
Observational Ultraproducts of Polynomial Coalgebras - Goldblatt (2002) (Correct)
....graph ( a,f(a) a A) is a bisimulation from a to [36, Theorem 2.5] a morphism is essentially a functional bisimulation. When Dom a C Dom , a is a subcoalgebra of iff the identity relation on Dom a is a bisimulation from a to . The above categorical definition of bisimulation appeared in [1]. It has a chaxacterisation [18, 19] in terms of liftings of relations R C A x B to relations R T C TAx TB. This in turn was transformed in [10] to another characterisation of bisimulations that uses the idea of paths between functors, an idea introduced in [24, Section 6] A path is a ....
....and blank assigns a truth value to a state according to whether or not the screen is clear in that state. These functions combine into a coalgebra A , C over ) x (A x true, false ) with play = r o a, next = r o (r2 o a) and blank = r2 o (r2 o a) Let = data, l, bool , with [data] C, [1] = over and [bool] true,false . Define the type r to be (data 1) x (St x bool) Then (A, a) above is a r coalgebra. Now for any ground r term M of type St, let play(M) be the term rtr(M) of type data 1. The denotation [play(M) is the function x play( M] x) In particular, play(s) ....
Peter Aczel and Nax Mendler. A final coalgebra theorem. In D. H. Pitt et al., editors, Category Theory and Computer Science. Proceedings 1989.
GSOS for Probabilistic Transition Systems - Bartels (2002) (2 citations) (Correct)
....of the type P , we see that LTS are coalgebras for the functor . In the same way we get that PTS are coalgebras for the functor . The notions of a nondeterministic and probabilistic bisimulation from Def. 3.4 and Def. 3.5 can be generalized to arbitrary B coalgebras. Definition 6. 4 (cf. [AM89]) A bisimulation between two B coalgebras relation R such that there exists a B coalgebra operation #R : R BR making the projections P and # 2 : R Q homomorphisms from respectively. # BP BR The greatest bisimulation between two coalgebras is denoted ....
Peter Aczel and Nax Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, editors, Proc. 3 rd CTCS, volume 389 of Lecture Notes in Computer Science, pages 357--365. Springer-Verlag, Berlin, 1989.
Equational Logic of Polynomial Coalgebras - Goldblatt (2001) (Correct)
....that achieved this. Observational equivalence was defined as the relation which is in fact the largest bisimulation between processes. Equivalent processes were later dubbed bisimilar. A category theoretic definition of bisimulation relations between T co algebras (A,r) and (B, was given in [1]: a relation R C A x B is a bisimulation if there is a transition structure p: lrl Tlrl such that the projections A x B A and A x B B are coalgebraic morphisms from p to r and (see Section 5) Bisimilarity is the largest such relation, which always exists because the union of any ....
....iff its graph (a, f(a) a A is a bisimulation from c to [32, Theorem 2.5] a morphism is essentially a functional bisimulation. When Dom c C Dom, c is a subcoalgebra of iff the identity relation on Dom c is a bisimulation from to. The above categorical definition of bisimulation appeared in [1]. It has a characterisation in terms of liftings of relations [14, 15] For R C A x B, define a relation R T C TAx TB by induction on the formation of the polynomial functor T: R D = idD R Id = R R rXr2 = x,y) xRry and 2xr22y = x, y) xy U (2x, xry Rr = f,g) Vd D, ....
Peter Aczel and Nax Mendler. A final coalgebra theorem. In D. H. Pitt et al., editors, Category Theory and Computer Science. Proceedings 1989.
GSOS for probabilistic transition systems (Extended Abstract) - Bartels (2002) (Correct)
.... as independent concepts [JLY01] De Vink and Rutten [dVR99] argue that probabilistic transition systems are B coalgebras for a suitable functor B which further exhibits probabilistic bisimulations according to the famous definition by Larsen and Skou as B bisimulations in the categorical sense [AM89]. Moreover they show that the functor under consideration is well behaved in that it weakly preserves pullbacks and possesses a final system, two important properties for the structure theory of coalgebras. Some authors have specified basic composition operators for probabilistic transition ....
....desirable properties. To express them, we recall the following definitions: Definition 3.3 (initial final algebra (coalgebra, # bialgebra) An initial (final) object in Alg (Coalg B , # Bialg) is called an initial (final) # algebra (B coalgebra, # bialgebra) Definition 3. 4 (bisimulation [AM89]) A bisimulation between two B co algebras is a triple consisting of a set R, and two functions r 1 : R P and r 2 : R Q such that there exists a B coalgebra operation # : R BR making r 1 and r 2 homomorphisms from ## to respectively. When talking about a ....
Peter Aczel and Nax Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, editors, Proc. 3 rd CTCS, volume 389 of Lecture Notes in Computer Science, pages 357--365. Springer-Verlag, Berlin, 1989.
Towards a Mathematical Operational Semantics - Turi, Plotkin (1997) (53 citations) (Correct)
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P. Aczel and N. Mendler. A final coalgebra theorem. In D.H. Pitt et al., editors, Proc. category theory and computer science, volume 389 of LNCS, pages 357--365. Springer-Verlag, 1989.
A Logic for Parametric Polymorphism - Plotkin, Abadi (1993) (47 citations) (Correct)
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Peter Aczel and Nax Mendler. A final co-algebra theorem. In D. H. Pitt et al., editors, Category Theory and Computer Science Lecture Notes in Computer Science, 389:357--365 Berlin, 1989. Springer-Verlag.
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Peter Aczel and Max Mendler. A Final Coalgebra Theorem. In Category Theory and Computer Science, Lecture Notes in Computer Science 389, eds. D. H. Pitt, D. E. Rydeheard, P. Dybjer, A. M. Pitts, and A. Poign'e, pages 357--365. September 1989. 32
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P. Aczel and N. Mendler. A final coalgebra theorem. In Proc. CTCS'89, LNCS 389, pages 357--365, Berlin, 1989. Springer-Verlag.
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Peter Aczel and N. Mendler. A Final Coalgebra Theorem. In D. Pitt and D. Ryeheard and P. Dybjer and A. Pitts and A. Poigne, editor, Proceedings Category Theory and Computer Science, volume 389 of LNCS, pages 357--365. Springer, 1989.
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P. Aczel and P. F. Mendler. A final coalgebra theorem. In D. H. Pitt, D. E. Rydeheard, P. Dybjer, A. M. Pitts, and A. Poign e, editors, Proc. Category Theory and Computer Science, volume 389 of LNCS, pages 357--365. SpringerVerlag, 1989.
Generalised Coinduction - Bartels (2000) (9 citations) (Correct)
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Peter Aczel and Nax Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, editors, Proceedings 3rd Conf. on Category Theory and Computer Science, CTCS'89, Manchester, UK, 5--8 Sept 1989, volume 389 of Lecture Notes in Computer Science, pages 357--365. Springer-Verlag, Berlin, 1989.
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P. Aczel and N. Mendler. A final coalgebra theorem. In D. H. Pitt et al, editor, Category Theory and Computer Science, volume 389 of LNCS, pages 357--365, Berlin, 1989. Springer.
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P. Aczel and N. Mendler. A final coalgebra theorem. In Proc. CTCS'89, LNCS 389, pages 357--365, 1989. Springer-Verlag.
Modular Construction of Modal Logics - Corina Crstea And (Correct)
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P. Aczel and N. Mendler. A final coalgebra theorem. In D. H. Pitt et al, editor, Category Theory and Computer Science, volume 389 of LNCS, pages 357--365, Berlin, 1989. Springer.
Unknown - (Correct)
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P. Aczel and N. Mendler, A final coalgebra theorem, Proceedings category theory and computer science (D.H. Pitt et al., eds.), Lecture Notes in Computer Science, Springer, 1989, pp. 357--365.
A Hierarchy of Probabilistic System Types - Falk Bartels Ana (2003) (4 citations) (Correct)
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Peter Aczel and Nax Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, editors, Proc. 3 rd CTCS, volume 389 of LNCS, pages 357--365. Springer, 1989. 22
An Application Of Coinductive Stream Calculus To Signal Flow Graphs - Rutten (2003) (1 citation) (Correct)
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P. Aczel and N. Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Ryeheard, P. Dybjer, A. M. Pitts, and A. Poigne, editors, Proceedings category theory and computer science, number 389 in Lecture Notes in Computer Science, pages 357--365. Springer-Verlag, 1989.
Translating Logics for Coalgebras - Pattinson (2002) (Correct)
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P. Aczel and N. Mendler. A Final Coalgebra Theorem. In D. H. Pitt et al, editor, Category Theory and Computer Science, volume 389 of Lect. Notes in Comp. Sci., pages 357365. Springer, 1989.
On Generalised Coinduction and Probabilistic Specification.. - Bartels (2004) (3 citations) (Correct)
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Peter Aczel and Nax Mendler. A final coalgebra theorem. In D.H. Pitt, D.E. Rydeheard, P. Dybjer, A.M. Pitts, and A. Poigne, editors, Proc. 3 rd CTCS, volume 389 of Lecture Notes in Computer Science, pages 357--365. Springer Verlag, 1989.
Modular Construction of Modal Logics - Crstea, Pattinson (2004) (Correct)
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P. Aczel and N. Mendler. A final coalgebra theorem. In D. H. Pitt et al, editor, Category Theory and Computer Science, volume 389 of LNCS. Springer, 1989.
Proof Principles for Datatypes with Iterated Recursion - Hensel, Jacobs (1997) (10 citations) (Correct)
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P. Aczel and N. Mendler. A final coalgebra theorem. In D.H. Pitt, A. Poign'e, and D.E. Rydeheard, editors, Category Theory and Computer Science, number 389 in Lect. Notes Comp. Sci., pages 357--
Coalgebraic Semantics of an Imperative Class Based Language - Honsell, Lenisa (Correct)
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P.Aczel, N.Mendler. A Final Coalgebra Theorem, in Category Theory and Computer Science, D.H.Pitt et al. eds., Springer LNCS 389, 1989, 357--365.
Modeling Fresh Names in the π-calculus Using.. - Bruni, Honsell, Lenisa.. (Correct)
No context found.
P. Aczel and N. Mendler. A final coalgebra theorem. In Proc. CTCS'89, LNCS 389, pages 357--365, Berlin, 1989. Springer-Verlag.
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