## Typed event Structures and the π-calculus (2006)

Venue: | In Proc. MFPS’06 |

Citations: | 5 - 3 self |

### BibTeX

@INPROCEEDINGS{Varacca06typedevent,

author = {Daniele Varacca and Nobuko Yoshida},

title = {Typed event Structures and the π-calculus},

booktitle = {In Proc. MFPS’06},

year = {2006}

}

### OpenURL

### Abstract

Abstract. We propose a typing system for the true concurrent model of event structures that guarantees an interesting behavioural property known as confusion freeness. A system is confusion free if nondeterministic choices are localised and do not depend on the scheduling of independent components. It is a generalisation of confluence to systems that allow nondeterminism. Ours is the first typing system to control behaviour in a true concurrent model. To demonstrate its applicability, we show that typed event structures give a semantics of linearly typed version of the π-calculi with internal mobility. The semantics we provide is the first event structure semantics of the π-calculus and generalises Winskel’s original event structure semantics of CCS. 1

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Citation Context ...stances of such models are Petri nets [30], Mazurkiewicz traces [23] and event structures [28]. Interleaving models are very successful in defining observational equivalence, by means of bisimulation =-=[25]-=-. Although bisimulation can be defined for true concurrent models too [19], it has not been used to characterise interesting observational congruences. The reason lies in the fact that true concurrent... |

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Citation Context ...t freeness, which is, in a sense, the true concurrent version of confluence. The second contribution of this paper is to give the first sound event structure semantics of a fragment of the π-calculus =-=[26]-=-. Various causal semantics of the π-calculus exist [18, 8, 13, 5, 11, 9], but none is given in terms of event structures. The technical difficulty in extending CCS semantics to the π-calculus lies in ... |

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Citation Context ... order of E9 refines the causal order of E10. 3 Typed event structures In this section we present a notion of types for an event structure, which are inspired from the types for the linear π-calculus =-=[41, 3, 21]-=-. We will clearly see this connection later, when we devise a process calculus that makes use of these types. The event structure which interprets a type records the causality between the names contai... |

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Citation Context ...el of event structures [28, 36]. Event structures have been used to give semantics to concurrent process languages. Possibly the earliest and the most intuitive is Winskel’s semantics of Milner’s CCS =-=[35]-=-. The first contribution of this paper is to present a compositional typing system for event structures that ensures an important behavioural property: confusion freeness. This property was first iden... |

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Citation Context ...two papers [8, 13] present Petri nets semantics of the π-calculus. Since we can unfold Petri nets into event structures, these could indirectly provide event structure semantics of the π-calculus. In =-=[2]-=-, an event structure unfolding of double push-out rewriting systems is studied, and this also could indirectly provide an event structure semantics of the π-calculus via the double push-out semantics ... |

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Citation Context ... which is the main ingredient to represent dynamic creation of names. We are able to solve this problem for a restricted version of the π-calculus, a linearly typed version of Sangiorgi’s πI-calculus =-=[31, 41]-=-. This fragment is expressive enough to encode the typed λ-calculus (in fact, to encode it fully abstractly [41]). We argue that in this fragment, α-conversion need not be performed dynamically (at “r... |

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Citation Context ... order of E9 refines the causal order of E10. 3 Typed event structures In this section we present a notion of types for an event structure, which are inspired from the types for the linear π-calculus =-=[41, 3, 21]-=-. We will clearly see this connection later, when we devise a process calculus that makes use of these types. The event structure which interprets a type records the causality between the names contai... |

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Citation Context ... push-out rewriting systems is studied, and this also could indirectly provide an event structure semantics of the π-calculus via the double push-out semantics of the π-calculus presented in [27]. In =-=[6]-=-, Petri Nets are used to provide a type theory for the Join-calculus, a language with several features in common with the π-calculus. None of the above semantics directly uses event structures and no ... |

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Citation Context ...support recursion. Infinite parallel composition is similar to replication in that it provides infinite behaviour “in width” rather that “in depth”. Recent studies on recursion versus replication are =-=[7, 15]-=-. Future works include extending this approach to a probabilistic framework, for instance the probabilistic π-calculus [16], by using a typed version of probabilistic event structures [32]. The typed ... |

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Citation Context ...ersion of confluence. The second contribution of this paper is to give the first sound event structure semantics of a fragment of the π-calculus [26]. Various causal semantics of the π-calculus exist =-=[18, 8, 13, 5, 11, 9]-=-, but none is given in terms of event structures. The technical difficulty in extending CCS semantics to the π-calculus lies in the handling of α-conversion, which is the main ingredient to represent ... |

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Citation Context ...s, that we want to study in details. Also the types of the λ-calculus are given an event structure semantics. We aim at comparing this “true concurrent” semantics of the λ-types with concurrent games =-=[24, 22]-=-, and with ludics nets [14]. An event structure terminates if all its maximal configurations are finite. It would be interesting to study a typing system of event structures that guarantees terminatio... |

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Citation Context ...a structures [4], and their domain-theoretic counterpart are the concrete domains [20]. Finally, confusion freeness has been recognised as an important property in the context of probabilistic models =-=[32, 1]-=-. To illustrate this important notion, let us suppose that a system is composed of two processes P and Q. Suppose the system can reach a state where P has a choice between two different actions a1,a2,... |

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Citation Context ...but not explicitly constructed. In order to carry out our proofs, we needed a more concrete representation of the product. We have devised such a representation, which is inspired by the one given in =-=[10]-=-, but which is more suitable to an inductive reasoning. Let E1 := 〈E1,≤1,⌣1〉 and E2 := 〈E2,≤2,⌣2〉 be two event structures. Let E ∗ i := Ei ⊎{∗}. Consider the set ˜E obtained as the initial solution of... |

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Citation Context ...of double push-out rewriting systems is studied, and this also could indirectly provide an event structure semantics of the π-calculus via the double push-out semantics of the π-calculus presented in =-=[27]-=-. In [6], Petri Nets are used to provide a type theory for the Join-calculus, a language with several features in common with the π-calculus. None of the above semantics directly uses event structures... |

9 | and Pierre-Louis Curien. Sequential algorithms on concrete data structures - Berry - 1982 |

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Citation Context ...ersion of confluence. The second contribution of this paper is to give the first sound event structure semantics of a fragment of the π-calculus [26]. Various causal semantics of the π-calculus exist =-=[18, 8, 13, 5, 11, 9]-=-, but none is given in terms of event structures. The technical difficulty in extending CCS semantics to the π-calculus lies in the handling of α-conversion, which is the main ingredient to represent ... |

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Citation Context ...The only difficult case is the parallel composition. 16s6 A linear version of the π-calculus This section briefly summarises an extension of linear version of the π-calculus in [3] to non-determinism =-=[40]-=-. Although this summary is technically self-contained, the reader may refer to [3, 40] for detailed illustration and more examples. 6.1 Syntax and reduction The following gives the reduction rule of t... |

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Citation Context ...s, that we want to study in details. Also the types of the λ-calculus are given an event structure semantics. We aim at comparing this “true concurrent” semantics of the λ-types with concurrent games =-=[24, 22]-=-, and with ludics nets [14]. An event structure terminates if all its maximal configurations are finite. It would be interesting to study a typing system of event structures that guarantees terminatio... |

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Citation Context ...fferent way to give semantics to a process language, a kind of value passing CCS. That technique does not apply yet to the πcalculus where we need to model creation of new names, although recent work =-=[37]-=- is moving in that direction. A syntactic condition that imposes a similar restriction to our typing system was first introduced by Milner, in his confluent CCS [25]. The typing system we introduce is... |

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Citation Context ...support recursion. Infinite parallel composition is similar to replication in that it provides infinite behaviour “in width” rather that “in depth”. Recent studies on recursion versus replication are =-=[7, 15]-=-. Future works include extending this approach to a probabilistic framework, for instance the probabilistic π-calculus [16], by using a typed version of probabilistic event structures [32]. The typed ... |