## Relationally Staged Computations in Calculi of Mobile Processes (2004)

Citations: | 10 - 2 self |

### BibTeX

@MISC{Ghani04relationallystaged,

author = {Neil Ghani and Kidane Yemane and Björn Victor},

title = {Relationally Staged Computations in Calculi of Mobile Processes},

year = {2004}

}

### Years of Citing Articles

### OpenURL

### Abstract

... syntax and functorial operational semantics to give a compositional and fully abstract semantics for the π-calculus equipped with open bisimulation. The key novelty in our work is the realisation that the sophistication of open bisimulation requires us to move from the usual semantic domain of presheaves over subcategories of Set to presheaves over subcategories of Rel. This extra structure is crucial in controlling the renaming of extruded names and in providing a variety of different dynamic allocation operators to model the different binders of the π-calculus.

### Citations

1329 | A calculus of communicating systems - Milner - 1980 |

434 |
The π-calculus: a Theory of Mobile Processes
- Sangiorgi, Walker
- 2001
(Show Context)
Citation Context ... is achieved by using abstract ideas such as coalgebra, naturality and indexing to avoid the various technical side conditions concerning free and bound names which appear in the standard definitions =-=[SW01]-=-. The sophistication of open bisimulation arises from its closure under varying classes of renamings. The novelty of our approach is that we capture this feature by moving from presheaves over a subca... |

134 | G.: Towards a mathematical operational semantics
- Turi, Plotkin
- 1997
(Show Context)
Citation Context ...rovided that the behaviour functor is finitary and preserves weak pullbacks. That such natural transformations give rise to a compositional and fully abstract semantics goes back to the seminal paper =-=[TP97]-=-. More recent work [LPW00,Pow03a] has recast the abstract theory more elegantly in terms of distributivity laws but, since our goal is to establish the existence of such distributivity laws, we stick ... |

108 | The fusion calculus: Expressiveness and symmetry in mobile processes. LICS’98
- Parrow, Victor
- 1998
(Show Context)
Citation Context ...directions we wish to take this research. Firstly relational presheaves seem to offer the extra structure required to model sophisticated bisimulations such as open bisimulations. The fusion calculus =-=[PV98]-=- is a variant of the π-calculus where the communication rule com u(x) P −−→ P ′ , Q uy −→ Q ′ , P | Q τ −→ P ′ {y/x} | Q ′ is replaced by the communication rule com ux P −→ P ′ , Q uy −→ Q ′ P | Q {x=... |

87 |
A calculus of mobile processes, part I/II
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...n operators to model the different binders of the π-calculus. Key words: Process Calculi, Abstract Syntax, Algebra, Coalgebra 1 Introduction The π-calculus was introduced by Milner, Parrow and Walker =-=[MPW92]-=- as an attempt to extend previous paradigms for distributed and concurrent computation with structure to reflect the locality of information. Thus, in addition to the usual combinators of process alge... |

82 |
A Calculus of Communicating Systems, volume 92 of LNCS
- Milner
- 1980
(Show Context)
Citation Context ...sses. One of the key advances of research in process algebra was the concept of bisimulation as a method of proving equivalences of processes. While this concept is fairly simple as introduced in CCS =-=[Mil80]-=-, the concept becomes more sophisticated in process algebra with variable binding as a variety of different possibilities exist. The simpler ones, such as early bisimulation and late bisimulation [MPW... |

65 |
A theory of bisimulation for the π-calculus
- Tiu, Sangiorgi, et al.
- 1996
(Show Context)
Citation Context ...ra with variable binding as a variety of different possibilities exist. The simpler ones, such as early bisimulation and late bisimulation [MPW92] suffer from not being congruences. Open bisimulation =-=[San96]-=- on the other hand is a congruence but is complicated since the bisimulation relation must be closed under not only transitions, but also certain substitutions and these substitutions vary from proces... |

56 |
Bigraphs and transitions
- Jensen, Milner
- 2003
(Show Context)
Citation Context ...er order process calculi and much of the semantic infrastructure already exists and is waiting to be used. We would also like to consider whether these techniques can be extended to Milner’s bigraphs =-=[JM03]-=- which is a formalism intended to abstract away from specific process calculi. Further, it would be interesting to test the applicability of Power’s recent work on computing with distributivity laws [... |

53 |
Functorial Operational Semantics and its Denotational Dual
- Turi
- 1996
(Show Context)
Citation Context ...es it an ideal case study for some exciting recent developments in program language semantics, in particular for higher order abstract syntax (HOAS) [FPT99] and functorial operational semantics (FOS) =-=[Tur96]-=-. HOAS aims to extend the highly successful paradigm of initial algebra semantics to languages involving variable binding while FOS seeks a uniform framework in which to reason about the relationship ... |

46 | Semantics of name and value passing
- Fiore, Turi
- 2001
(Show Context)
Citation Context ...of open bisimulation arises from its closure under varying classes of renamings. The novelty of our approach is that we capture this feature by moving from presheaves over a subcategory of Set (as in =-=[FT01]-=-) to presheaves over a subcategory of Rel which we call relational presheaves. In this paper Rel is taken to be the category with relations as objects and monotone functions as morphisms. These relati... |

43 | The mobility workbench - a tool for the π- calculus - Victor, Moeller - 1994 |

28 | Minimizing transition systems for name passing calculi: A co-algebraic formulation - Ferrari, Montanari, et al. - 2002 |

28 | History Dependent Automata
- Pistore
- 1999
(Show Context)
Citation Context ...be interesting to test the applicability of Power’s recent work on computing with distributivity laws [Pow03a] to this setting. A more practical direction to take this research is that of HD-automata =-=[MP98]-=-. HD-automata seek to give an operational model of History Dependent calculi by decorating the states of automata with relevant information (free names of a processes) and establishing the corresponde... |

24 | Distributivity for endofunctors, pointed and copointed endofunctors, monads and comonads - Lenisa, Power, et al. |

21 | Abstract syntax and variable binding (extended abstract
- Fiore, Plotkin, et al.
- 1999
(Show Context)
Citation Context ...variety of different bisimulations it supports, makes it an ideal case study for some exciting recent developments in program language semantics, in particular for higher order abstract syntax (HOAS) =-=[FPT99]-=- and functorial operational semantics (FOS) [Tur96]. HOAS aims to extend the highly successful paradigm of initial algebra semantics to languages involving variable binding while FOS seeks a uniform f... |

10 | Verifying mobile processes in the hal environment - Ferrari, Gnesi, et al. - 1998 |

9 | D.: A partition refinement algorithm for the π-calculus - Pistore, Sangiorgi - 2001 |

5 |
A fully-abstract model for the π-calculus (extended abstract
- Fiore, Moggi, et al.
- 1996
(Show Context)
Citation Context ...formation δ + (X × BX) → BT X is generated by δ + N × δ + N × δ + X ρ −→ Pf(N × N × T X + N × δ + T X) 12Ghani, Yemane, Victor The definition of ρ can be given using the internal language defined in =-=[FMS96]-=-. ⎧ (a ′ (), q ′ ), if a is old(a ′ ) and if b = new(b ′ ) ⎪⎨ ρ(a, b, q) = ⎪⎩ ∅ if a = new(a ′) (a ′ b ′ , (νz)q ′ ), if a is old(a ′ ) and b = old(b ′ ) Where old and new are the injections D ✲ δ + D... |

4 |
A unified category-theoretic approach to variable binding
- Power
- 2003
(Show Context)
Citation Context ...ly mature, more complex examples need to be treated. This is precisely what we have done. For example, we wonder whether the relational presheaves we consider here fit into Power’s axiomatics for FOS =-=[Pow03b]-=-. In addition, two of the present authors work in the area of concurrency and came to this subject as they were interested in the possibility of more abstract treatment of their subject. Given the pro... |

2 |
Towards a theory of mathematical operational semantics
- Power
- 2003
(Show Context)
Citation Context ...] which is a formalism intended to abstract away from specific process calculi. Further, it would be interesting to test the applicability of Power’s recent work on computing with distributivity laws =-=[Pow03a]-=- to this setting. A more practical direction to take this research is that of HD-automata [MP98]. HD-automata seek to give an operational model of History Dependent calculi by decorating the states of... |

1 | FPT99] [FT01] [JM03] [LPW00 - Fiore, Plotkin, et al. - 1996 |