## A Coinductive Calculus of Component Connectors (2002)

Citations: | 58 - 25 self |

### BibTeX

@INPROCEEDINGS{Arbab02acoinductive,

author = {F. Arbab and J. J. M. M. Rutten},

title = {A Coinductive Calculus of Component Connectors},

booktitle = {},

year = {2002},

pages = {35--56},

publisher = {Springer-Verlag}

}

### Years of Citing Articles

### OpenURL

### Abstract

Reo is a recently introduced channel-based coordination model, wherein complex coordinators, called connectors, are compositionally built out of simpler ones. Using a more liberal notion of a channel, Reo generalises existing dataflow networks. In this paper, we present a simple and transparent semantical model for Reo, in which connectors are relations on timed data streams. Timed data streams constitute a characteristic of our model and consist of twin pairs of separate data and time streams. Furthermore, coinduction is our main reasoning principle and we use it to prove properties such as connector equivalence.

### Citations

1332 | A Calculus of Communicating Systems - Milner - 1980 |

298 | Universal coalgebra: a theory of systems - Rutten |

228 | A tutorial on (co)algebras and (co)induction - Jacobs, Rutten - 1997 |

146 | Reo: A channel-based coordination model for component composition - Arbab |

96 |
K.: Specification and Development of Interactive Systems
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(Show Context)
Citation Context ... much more general notion of channels. 3. The model of Reo is based on a clear separation of data and time. 4. Coinduction is the main reasoning principle. Of all related work, Broy and Stlen's book [=-=BS01]-=- deserves special mention, since it is also based on (timed) data streams. However, the points mentioned above distinguish our model also from theirs. In particular, the separation of data and time, i... |

77 |
A Really Abstract Concurrent Model and its Temporal Logic
- Barringer, Kuiper, et al.
- 1986
(Show Context)
Citation Context ...er, is more abstract than the model with `discrete time' would be, in the sense that more connector equivalences can be proved. (In the world of temporal logic, this observation goes back to at least =-=[BRP8-=-6].) An example is the equivalence of asfo 2 buer (with capacity 2) with the composition of twosfo 1 buers in Section 7. Finally, it is often useful to require time streams a to be not only increasing... |

36 | Concurrency and automata on in sequences - Park - 1981 |

33 |
A xedpoint theorem and its applications
- Tarski
- 1955
(Show Context)
Citation Context ... ! is itself a (bisimulation and thus a) post-xed point, it is in fact the greatestsxed point of . Therefore the above equality is an instance of the following well-known greatestsxed point theorem [T=-=-=-ar55]. Let X be any set and let P(X) = fV j V Xg be the set of all its subsets. Ifs: P(X) ! P(X) is a monotone operator, that is, R S impliess(R) s(S) for all R X and S X, thenshas a greatestsxed ... |

20 | Coordination through channel composition - Arbab, Mavaddat |

19 |
Elements of stream calculus (an extensive exercise in coinduction
- Rutten
- 2001
(Show Context)
Citation Context ...perations of initial value and stream derivative: A ! ! A A ! ; 7! h(0); 0 i See [JR97, Rut00] for general references on coalgebra. For a detailed treatment of thesnal coalgebra of streams, see [Rut=-=01-=-]. The latter paper contains in particular detailed results about behavioural dierential equations (for streams over the set A = IR of real numbers). 3 Coinduction and greatestsxed points There is yet... |

16 |
Components as Coalgebras
- Barbosa
- 2001
(Show Context)
Citation Context ...of coinduction, leads to simpler specications (denitions) and proofs. See Section 9 for a concrete example. Finally, coalgebra and coinduction have been used in models of component-based systems in [B=-=ar01-=-] and [Dob02]. Also these models are distinguished from ours by the (rst three) points above. Moreover, our model is far more concrete, and therefore allows actual equivalence proofs. 2 Streams and co... |

1 |
and modelling a software architecture through relations
- Pipes
- 2002
(Show Context)
Citation Context ...on, leads to simpler specications (denitions) and proofs. See Section 9 for a concrete example. Finally, coalgebra and coinduction have been used in models of component-based systems in [Bar01] and [D=-=ob02-=-]. Also these models are distinguished from ours by the (rst three) points above. Moreover, our model is far more concrete, and therefore allows actual equivalence proofs. 2 Streams and coinduction Le... |