## Circular Coinductive Rewriting (2000)

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Venue: | In Proceedings of Automated Software Engineering 2000 |

Citations: | 50 - 11 self |

### BibTeX

@INPROCEEDINGS{Goguen00circularcoinductive,

author = {Joseph Goguen and Kai Lin and Grigore Rosu},

title = {Circular Coinductive Rewriting},

booktitle = {In Proceedings of Automated Software Engineering 2000},

year = {2000},

pages = {123--131},

publisher = {IEEE}

}

### Years of Citing Articles

### OpenURL

### Abstract

Circular coinductive rewriting is a new method for proving behavioral properties, that combines behavioral rewriting with circular coinduction. This method is implemented in our new BOBJ behavioral specification and computation system, which is used in examples throughout this paper. These examples demonstrate the surprising power of circular coinductive rewriting. The paper also sketches the underlying hidden algebraic theory and briefly describes BOBJ and some of its algorithms.

### Citations

244 | A tutorial on (co)algebras and (co)induction
- Jacobs, Rutten
- 1996
(Show Context)
Citation Context ...ial cases include hidden algebra [7, 8, 10, 9], coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra =-=[16, 1]-=-. Because of space constraints, we omit all proofs and most definitions, instead giving explanations and examples. We assume the reader familiar with algebraic specification and theorem proving, espec... |

90 | Towards an algebraic semantics for the object paradigm
- Goguen, Diaconescu
- 1994
(Show Context)
Citation Context ...en visible and hidden sorts, with equality being strict on visible sorts and behavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidde=-=n algebra [7, 8, 10, 9]-=-, coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit... |

76 | Types as theories - Goguen - 1991 |

60 |
Vicious Circles: On the Mathematics of Non-Wellfounded Phenomena
- Barwise, Moss
- 1996
(Show Context)
Citation Context ...ial cases include hidden algebra [7, 8, 10, 9], coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra =-=[16, 1]-=-. Because of space constraints, we omit all proofs and most definitions, instead giving explanations and examples. We assume the reader familiar with algebraic specification and theorem proving, espec... |

55 |
Context induction: a proof principle for behavioral abstractions
- Hennicker
- 1991
(Show Context)
Citation Context ... = head(S) . eq tail(zip(S,S')) = zip(S',tail(S)) . end 2.2 Circular Coinductive Rewriting in BOBJ Few behavioral properties can be proved with just equational behavioral reasoning. Context induction =-=[14]-=- and coinduction are more powerful proof techniques, but unfortunately both need human intervention. Circular coinductive rewriting integrates behavioral rewriting [6, 17] with circular coinduction [1... |

55 | Observational logic
- Hennicker, Bidoit
- 1999
(Show Context)
Citation Context ...sorts and behavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidden algebra [7, 8, 10, 9], coherent hidden algebra [5, 6], observatio=-=nal logic [15, 2]-=-, and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit all proofs and most definitions, instead giving explanations... |

44 | Hiding more of hidden algebra
- Goguen, Roşu
- 1999
(Show Context)
Citation Context ...BOBJ and some of its algorithms. 1 Introduction Circular coinductive rewriting is an algorithm for proving behavioral equalities that integrates behavioral rewriting [6, 17] with circular coinduction =-=[19, 11, 12]-=-. We give examples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss and Rosu [3] shows that no such algorithm can be complete. Of course, incomplet... |

40 | Behavioral coherence in object-oriented algebraic specification
- Diaconescu, Futatsugi
(Show Context)
Citation Context ...ity being strict on visible sorts and behavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidden algebra [7, 8, 10, 9], coherent hidde=-=n algebra [5, 6]-=-, observational logic [15, 2], and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit all proofs and most definitions... |

36 | Observer complete definitions are behaviourally coherent
- Bidoit, Hennicker
- 1999
(Show Context)
Citation Context ...sorts and behavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidden algebra [7, 8, 10, 9], coherent hidden algebra [5, 6], observatio=-=nal logic [15, 2]-=-, and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit all proofs and most definitions, instead giving explanations... |

32 |
A hidden agenda. Theoretical Computer Science
- Goguen, Malcolm
- 1997
(Show Context)
Citation Context ...en visible and hidden sorts, with equality being strict on visible sorts and behavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidde=-=n algebra [7, 8, 10, 9]-=-, coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit... |

29 | Hidden congruent deduction
- Roşu, Goguen
- 2000
(Show Context)
Citation Context ...BOBJ and some of its algorithms. 1 Introduction Circular coinductive rewriting is an algorithm for proving behavioral equalities that integrates behavioral rewriting [6, 17] with circular coinduction =-=[19, 11, 12]-=-. We give examples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss and Rosu [3] shows that no such algorithm can be complete. Of course, incomplet... |

27 | Incompleteness of behavioral logics
- Buss, Roşu
- 2000
(Show Context)
Citation Context ...es behavioral rewriting [6, 17] with circular coinduction [19, 11, 12]. We give examples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss and Rosu =-=[3]-=- shows that no such algorithm can be complete. Of course, incompleteness is more the rule than the exception for non-trivial theorem proving problem classes. We work in a general framework for equatio... |

27 | Hidden coinduction: Behavioral correctness proofs for objects
- Goguen, Malcolm
- 1999
(Show Context)
Citation Context ...en visible and hidden sorts, with equality being strict on visible sorts and behavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidde=-=n algebra [7, 8, 10, 9]-=-, coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hidden algebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit... |

13 | Circular coinduction
- Roşu, Goguen
- 2001
(Show Context)
Citation Context ...specifications behaviorally equivalent, in the sense of having the same models with the same behavioral equivalences [19, 11], by proving all equalities in each spec from those in the other (see also =-=[18]-=-). We encourage 5 the reader investigate why the last equation in STREAM2 is needed (hint: without it there could be models of STREAM2 that are not models of STREAM1). There are reasons to consider th... |

11 | Using a generalisation critic to find bisimulations for coinductive proofs
- Dennis, Bundy, et al.
- 1997
(Show Context)
Citation Context ...mming Examples We give some simple examples from lazy functional programming. Many similar examples were done by Louise Dennis using a system called CoClam with a complex heuristic planning algorithm =-=[4]-=-; all her examples that we tried can be done algorithmically by CCRW without human intervention or machine heuristics. We thank Wolfram Schulte for suggesting this direction. Example 1 We define a fun... |

10 | A protocol for distributed cooperative work
- Goguen, Ro, et al.
- 1999
(Show Context)
Citation Context ...BOBJ and some of its algorithms. 1 Introduction Circular coinductive rewriting is an algorithm for proving behavioral equalities that integrates behavioral rewriting [6, 17] with circular coinduction =-=[19, 11, 12]-=-. We give examples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss and Rosu [3] shows that no such algorithm can be complete. Of course, incomplet... |

6 | Behavioral coinductive rewriting
- Rosu
- 1999
(Show Context)
Citation Context ...raic theory and briefly describes BOBJ and some of its algorithms. 1 Introduction Circular coinductive rewriting is an algorithm for proving behavioral equalities that integrates behavioral rewriting =-=[6, 17]-=- with circular coinduction [19, 11, 12]. We give examples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss and Rosu [3] shows that no such algorith... |

2 |
A protocol for distributedcooperative work
- Goguen, Ros, et al.
- 1999
(Show Context)
Citation Context ...OBJ and some of its algorithms. 1 Introduction Circular coinductive rewriting is an algorithm for prov-ing behavioral equalities that integrates behavioral rewriting [6, 17] with circular coinduction =-=[19, 11, 12]-=-. We giveexamples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss andRos,u [3] shows that no such algorithm can be complete. Of course, incomplete... |

2 |
A tutorial on (co)algebras and(co)induction. Bulletin of the European Association for Theoretical Computer Science
- Jacobs, Rutten
- 1997
(Show Context)
Citation Context ...ial cases include hidden al-gebra [7, 8, 10, 9], coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hiddenalgebra [19, 18]. A related approach is coalgebra =-=[16, 1]-=-. Because of space constraints, we omit all proofs and mostdefinitions, instead giving explanations and examples. We assume the reader familiar with algebraic specification andtheorem proving, especia... |

2 |
Hidden congruent deduction
- Ros, u, et al.
- 2000
(Show Context)
Citation Context ...OBJ and some of its algorithms. 1 Introduction Circular coinductive rewriting is an algorithm for prov-ing behavioral equalities that integrates behavioral rewriting [6, 17] with circular coinduction =-=[19, 11, 12]-=-. We giveexamples showing that this algorithm is surprisingly powerful in practice, even though a recent result of Buss andRos,u [3] shows that no such algorithm can be complete. Of course, incomplete... |

1 |
Vicious Circles: On theMathematics of Non-wellfounded Phenomena
- Barwise, Moss
- 1996
(Show Context)
Citation Context ...ial cases include hidden al-gebra [7, 8, 10, 9], coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hiddenalgebra [19, 18]. A related approach is coalgebra =-=[16, 1]-=-. Because of space constraints, we omit all proofs and mostdefinitions, instead giving explanations and examples. We assume the reader familiar with algebraic specification andtheorem proving, especia... |

1 |
Hidden coinduction:Behavioral correctness proofs for objects
- Goguen, Malcolm
- 1999
(Show Context)
Citation Context ...en visible and hidden sorts, with equality being strict on visible sorts andbehavioral on hidden sorts, in the sense of "indistinguishability under experiments;" special cases include hidden al-gebra =-=[7, 8, 10, 9]-=-, coherent hidden algebra [5, 6], observational logic [15, 2], and our recent generalizations of hiddenalgebra [19, 18]. A related approach is coalgebra [16, 1]. Because of space constraints, we omit ... |

1 |
Context induction: a proof principle forbehavioural abstractions. Formal Aspects of Computing
- Hennicker
- 1991
(Show Context)
Citation Context ... = head(S) . eq tail(zip(S,S')) = zip(S',tail(S)) .end 2.2 Circular Coinductive Rewriting in BOBJ Few behavioral properties can be proved with just equa-tional behavioral reasoning. Context induction =-=[14]-=- and coinduction are more powerful proof techniques, but unfor-tunately both need human intervention. Circular coinductive rewriting integrates behavioral rewriting [6, 17] withcircular coinduction [1... |