## A Linear Metalanguage for Concurrency (1998)

Venue: | Handbook of Logic in Computer Science |

Citations: | 11 - 4 self |

### BibTeX

@INPROCEEDINGS{Winskel98alinear,

author = {Glynn Winskel and Glynn Winskel},

title = {A Linear Metalanguage for Concurrency},

booktitle = {Handbook of Logic in Computer Science},

year = {1998},

pages = {1--148},

publisher = {Oxford University Press}

}

### OpenURL

### Abstract

A metalanguage for concurrent process languages is introduced.

### Citations

3605 | Communicating sequential processes
- Hoare
- 1978
(Show Context)
Citation Context ...y associated to the comonad (−)⊥ on Doms and a reflective subcategory of Doms. 6s[10,9]). An object P is to be thought of as consisting of finite computation paths (each one a “trace” in the sense of =-=[11]-=-), for example the finite string of actions that a CCS or CSP process might perform. The partial order p ≤ p ′ on P is thought of as saying that the computation path p can be extended to the computati... |

3384 | Communication and Concurrency - Milner - 1989 |

287 | A computational interpretation of linear logic
- Abramsky
- 1993
(Show Context)
Citation Context ... | (Injections and tests for lifted sums) (t, u) | [t >(x, −) ⇒ u] | [t >(−,x)⇒u] | (Pairing and tests for products) t ⊗ u | [t >x⊗y⇒u] (Tensor operation and tests) The language is similar to that in =-=[1]-=-, being based on a form of pattern matching. In particular [t >Inj(x) ⇒ u] “tests”or matches t denoting an element of a lifted sum against the pattern Inj(x) and passes the results of successful match... |

267 |
Event structures
- Winskel
- 1986
(Show Context)
Citation Context ...think of the union operation as being a form of nondeterministic sum. It’s worth remarking that the domains obtained in this way are precisely the infinitely-distributive algebraic lattices (see e.g. =-=[18,19]-=-) and that these are just the same as the prime algebraic lattices of [17], and free join completions of partial orders. There are several choices about what to take as maps between nondeterministic d... |

152 | Calculi for interaction
- Milner
- 1996
(Show Context)
Citation Context ...pecific category, can help provide a “presheaf model” of a higher-order Pi-Calculus to accompany [5]. This would be a good basis from which to compare and relate with the project of action structures =-=[16]-=-. The metalanguage here cries out for extensions in two directions, one to cope with name generation as in the Pi-Calculus, the other to go beyond linearity. The exponential ! of [20,5] seems appropri... |

130 | Proving in zero-knowledge that a number is the product of two safe primes - Camenisch, Michels - 1999 |

122 | Bisimulation from open maps
- Joyal, Nielsen, et al.
- 1996
(Show Context)
Citation Context ...tani and I have worked on presheaf models for interacting processes, culminating in Cattani’s forthcoming PhD thesis [3]. The work started from the general definition of bisimulation via open maps in =-=[13]-=- which suggested examining a broad class of models for concurrency—presheaf categories. Later we realised that presheaf models can themselves be usefully assembled together in a category in which the ... |

94 | Full abstraction for a simple parallel programming language
- Hennessy, Plotkin
- 1979
(Show Context)
Citation Context ...o we can identify � P with the partial order of downwards-closed subsets of P, ordered by inclusion. Thought of in this way it is sensible to think of � P as a nondeterministic domain in the sense of =-=[10,9]-=-; the order � P has joins got simply via unions so it is certainly a cpo, with least element ∅, and we can think of the union operation as being a form of nondeterministic sum. It’s worth remarking th... |

66 |
G.: Petri nets, event structures and domains, part I
- Nielsen, Plotkin, et al.
- 1981
(Show Context)
Citation Context ...rth remarking that the domains obtained in this way are precisely the infinitely-distributive algebraic lattices (see e.g. [18,19]) and that these are just the same as the prime algebraic lattices of =-=[17]-=-, and free join completions of partial orders. There are several choices about what to take as maps between nondeterministic domains. If we eschew “fairness”, the most generous we seem to have call fo... |

57 |
Using information systems to solve recursive domain equations
- Larsen, Winskel
- 1991
(Show Context)
Citation Context ... language, one where the input process can be run at most once to yield a single (computation) path. Fortunately the simple technique for solving recursive domain equations via information systems in =-=[14]-=- suffices to solve such equations. A path order P can be regarded as an information system in which every finite subset of P is consistent and in which the entailment relation is given by the partial ... |

45 | Presheaf models for concurrency
- Cattani, Winskel
- 1996
(Show Context)
Citation Context ...the maps are colimit-preserving functors. There are two main benefits: one is a general result stating that colimit-preserving functors between presheaf categories preserve open maps and bisimulation =-=[6]-=-; the other that the category of the presheaf models is a form of domain theory for concurrency, with a compositional account of bisimulation, though at the cost that domains are categories rather tha... |

42 |
A completeness theorem for open maps
- Joyal, Moerdijk
- 1994
(Show Context)
Citation Context ... ′ -paths in X restrict to p-paths in X. In this way a presheaf can model the nondeterministic branching of a process. Bisimulation on presheaves is derived from notion of open map between presheaves =-=[12,13]-=-. Open maps are a generalisation of functional bisimulations, or zig-zag morphisms, known from transition systems [13]. Presheaves in � P are bisimilar iff there is a span of surjective (i.e., epi) op... |

33 | A Presheaf Semantics of Value-Passing Processes
- Winskel
- 1996
(Show Context)
Citation Context ...gory of the presheaf models is a form of domain theory for concurrency, with a compositional account of bisimulation, though at the cost that domains are categories rather than special partial orders =-=[20,4]-=-. ⋆ Invited paper AMAST ’98, Brazil ⋆⋆ Basic Research in CS, Centre of the Danish National Research Foundation.sWe originally concentrated on the category of presheaf categories with colimit-preservin... |

26 | An axiomatic approach to adequacy
- Braüner
- 1996
(Show Context)
Citation Context ...erm-formation rules are listed below alongside their interpretations as a constructors on morphisms, taking the morphisms denoted by the premises to that denoted by the conclusion (along the lines of =-=[2]-=-). We assume that the variables in any enviroment list which appears are distinct. Structural rules: x : P ⊢ x : P , interpreted as P 1P → P . ∆ ⊢ t : P , interpreted as Γ, ∆ ⊢ t : P ∆ t → P Γ ⊗ ∆ ∅⊗1... |

24 | A theory of recursive domains with application to concurrency
- Cattani, Fiore, et al.
- 1998
(Show Context)
Citation Context ...gory of the presheaf models is a form of domain theory for concurrency, with a compositional account of bisimulation, though at the cost that domains are categories rather than special partial orders =-=[20,4]-=-. ⋆ Invited paper AMAST ’98, Brazil ⋆⋆ Basic Research in CS, Centre of the Danish National Research Foundation.sWe originally concentrated on the category of presheaf categories with colimit-preservin... |

18 | A categorical axiomatics for bisimulation
- Cattani, Power, et al.
- 1998
(Show Context)
Citation Context ...ake better account of Con and the metalanguage. The range of interpretations for the metalanguage indicated in Section 5.2 is restrictive, for example, in requiring V to be cocomplete. As remarked in =-=[8]-=- there are sensible choices for V which are not cocomplete—the countable sets for instance, provided we also restrict the path orders to be countable. Perhaps instantiating V to some specific category... |

17 |
Presheaf models for the π-calculus
- Cattani, Stark, et al.
- 1997
(Show Context)
Citation Context ... instance, provided we also restrict the path orders to be countable. Perhaps instantiating V to some specific category, can help provide a “presheaf model” of a higher-order Pi-Calculus to accompany =-=[5]-=-. This would be a good basis from which to compare and relate with the project of action structures [16]. The metalanguage here cries out for extensions in two directions, one to cope with name genera... |

13 | Presheaf models for the #-calculus - Cattani, Stark, et al. - 1997 |

9 |
A fully abstract denotational semantics for the pi-calculus
- Hennessy
(Show Context)
Citation Context ...o we can identify � P with the partial order of downwards-closed subsets of P, ordered by inclusion. Thought of in this way it is sensible to think of � P as a nondeterministic domain in the sense of =-=[10,9]-=-; the order � P has joins got simply via unions so it is certainly a cpo, with least element ∅, and we can think of the union operation as being a form of nondeterministic sum. It’s worth remarking th... |

4 |
On bisimulation for higher order processes
- Cattani, Winskel
- 1998
(Show Context)
Citation Context ...connected colimits in each argument separately. However, the preservation of connected colimits is all we need of a functor between presheaf categories for it to preserve bisimulation. Proposition 1. =-=[7]-=- Let G : � P → � Q be any connected-colimit preserving functor between presheaf categories. Then G preserves surjective open maps and open-map bisimulation. Define Con to be the category consisting of... |

3 |
A representation of completely distributive algebraic lattices
- Winskel
- 1983
(Show Context)
Citation Context ...think of the union operation as being a form of nondeterministic sum. It’s worth remarking that the domains obtained in this way are precisely the infinitely-distributive algebraic lattices (see e.g. =-=[18,19]-=-) and that these are just the same as the prime algebraic lattices of [17], and free join completions of partial orders. There are several choices about what to take as maps between nondeterministic d... |

1 |
Forthcoming
- Cattani
(Show Context)
Citation Context ...ems and lines of future work. 1 Introduction Over the last few years, Gian Luca Cattani and I have worked on presheaf models for interacting processes, culminating in Cattani’s forthcoming PhD thesis =-=[3]-=-. The work started from the general definition of bisimulation via open maps in [13] which suggested examining a broad class of models for concurrency—presheaf categories. Later we realised that presh... |