## Solo Diagrams (2001)

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Venue: | PROCEEDINGS OF TACS 2001 |

Citations: | 16 - 2 self |

### BibTeX

@INPROCEEDINGS{Laneve01solodiagrams,

author = {Cosimo Laneve and Joachim Parrow and Björn Victor},

title = {Solo Diagrams},

booktitle = {PROCEEDINGS OF TACS 2001},

year = {2001},

publisher = {Springer}

}

### Years of Citing Articles

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### Abstract

We address the problems of implementing the replication operator efficiently in the solos calculus---a calculus of mobile processes without prefix. This calculus is expressive enough to admit an encoding of the whole fusion calculus and thus the pi-calculus. We show that nested occurrences of replication can be avoided, that the size of replicated terms can be limited to three particles, and that the usual unfolding semantics of replication can be replaced by three simple reduction rules. To illustrate the results and show how the calculus can be efficiently implemented we present a graphic representation of agents in the solos calculus, adapting ideas from interaction diagrams and pi-nets.

### Citations

2334 | Statecharts: A Visual Formalism for Complex Systems - Harel - 1987 |

1064 | Bigraphs and mobile processes - Jensen, Milner - 2003 |

490 | The chemical abstract machine - Berry, Boudol - 1990 |

375 | An Object Calculus for Asynchronous Communications - Honda, Tokoro - 1991 |

335 |
Functions as Processes
- Milner
- 1992
(Show Context)
Citation Context ...ve "similarly", the only difference is the route into the replication box, which is one step shorter in NN. [The encoding of the -calculus into the ��-calculus was first studied in depth=-= by Milner in [Mil92]-=- and subsequently by Davide Sangiorgi in [San93], and the correctness criteria and proofs are nontrivial. In fact, as given here it correctly represents only the lazy reduction strategy of the -calcul... |

282 | The Polyadic -calculus: a Tutorial - Milner - 1993 |

272 |
Expressing Mobility in Process Algebras: First-order and Higher-order Paradigms
- Sangiorgi
- 1992
(Show Context)
Citation Context ... into the replication box, which is one step shorter in NN. [The encoding of the -calculus into the ��-calculus was first studied in depth by Milner in [Mil92] and subsequently by Davide Sangiorgi=-= in [San93]-=-, and the correctness criteria and proofs are nontrivial. In fact, as given here it correctly represents only the lazy reduction strategy of the -calculus, where a fi-reduction can only take place for... |

263 | Piet: A programming language based on the pi- calculus - Pierce, Turner - 1997 |

253 | The Reflexive Chemical Abstract Machine and the Join calculus - Fournet, Gonthier - 1996 |

233 | Barbed bisimulation - Milner, Sangiorgi - 1992 |

174 | Interaction nets - Lafont - 1990 |

165 |
A Calculus of Mobile
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...resentation to facilitate understanding. To stress this intent I use the term "diagram" rather than "graph". Among the related algebraic theories there are already several versions=-= of the ��-calculus [MPW92]-=-, and I hope that this paper also works partly as a tutorial, after which the reader can understand the formalistic presentations with more ease. These calculi focus interest on operators such as para... |

115 | The fusion calculus: Expressiveness and symmetry in mobile processes - Parrow, Victor - 1998 |

106 | The geometry of optimal lambda reductions - Gonthier, Abadi, et al. - 1992 |

92 | A calculus of mobile processes, part I/II - Milner, Parrow, et al. - 1992 |

86 | On the bisimulation proof method - Sangiorgi - 1994 |

78 | A sort inference algorithm for the polyadic -calculus - Gay - 1993 |

56 |
pi-calculus Semantics for Object-Oriented Programming Languages
- Walker
- 1991
(Show Context)
Citation Context ...ic interactions which only serve to enforce temporal precedence can be removed). But the basic principles are the same. A ��-calculus semantics of an object-oriented language is given by David Wal=-=ker [Wal91]-=-. It is interesting to see that we can achieve the same effect without explicit temporal sequencing.] 9 The -calculus As a final example we shall consider fi-reduction in the -calculus. This is a calc... |

42 | Asynchrony and the -calculus (note). Rapports de Recherche 1702, INRIA Soa-Antipolis - Boudol - 1992 |

41 | On the π-calculus and linear logic - Bellin, Scott - 1994 |

22 | Recommendation Z.100, Specification and Description Language SDL - CCITT - 1993 |

22 | A Proof Theoretical Approach to Communication - Fu - 1997 |

21 | Solos in concert - Laneve, Victor - 1999 |

19 | Graph notation for concurrent combinators - Yoshida |

13 | Trios in concert - Parrow - 2000 |

9 | Reaction Graph - Fu - 1998 |

7 |
Action structure for the -calculus
- Milner
- 1993
(Show Context)
Citation Context ...efore the action implied by a(x). Also, aP is a kind of agent for which no transitions are defined so there are no subjunctive reductions. Current research, notably Robin Milner's "action structu=-=res" [Mil93a]-=-, seems to indicate that these principles can be relaxed.] 4 Replication and Recursion The size of an interaction diagram (the number of nodes and arrows) is always reduced by a reduction. Consequentl... |

6 | G-LOTOS: A Graphical Language for Concurrent Systems, LOTOSphere: Software Development with LOTOS - Bolognesi, Najm, et al. - 1995 |

5 | Pi-nets: A graphical form of pi-calculus - Milner - 1994 |

4 | Pi-nets: A graphical form of -calculus - Milner - 1994 |

4 | Interaction diagrams. Nordic - Parrow - 1995 |

3 |
The polyadic -calculus: a tutorial, Research Report LFCS--91--180
- Milner
- 1991
(Show Context)
Citation Context ...th molecular interaction is written C = l(al:lv 1 :lv 2 ) S = !a(x):x(y):x(z) The transmission of tuples of names as a primitive construct is studied at depth in the polyadic versions of the calculus =-=[Mil91]. There, t-=-he same example would be written: C = ahv 1 v 2 i S =!a(yz)] 6 Finite Data Domains In the previous section we alluded to a Client emitting "values" to a Server, but we did not go into the na... |

3 | On the -calculus and linear logic. Theoretical Computer Science - Bellin, Scott - 1994 |

2 |
Notes on actions I: -nets with boxes and replication
- Milner
- 1993
(Show Context)
Citation Context ...depicting particular concurrent systems and in theory development by making the underlying intuitions visible. Hopefully interaction diagrams can contribute in the same way. Milner's recent "��=-=��-nets" [Mil93b]-=-, although developed independently as a formal model of an action structure, share many characteristics of interaction diagrams, notably the idea that a reduction coalesces two nodes. There is a super... |

1 | Typing and subtyping for mobile processes. Mathematical Structures in Computer Science, to appear. (A summary is - Pierce, Sangiorgi - 1995 |

1 | Notes on linear logic and ludics - Girard - 2000 |

1 | Sorts in the -calculus (extended abstract - Milner - 1991 |

1 | Solos in concert. Full version of [10], submitted for journal publication - Laneve, Victor - 2001 |