## A game semantics of the asynchronous π-calculus (2005)

Venue: | In Proceedings of 16th CONCUR |

Citations: | 6 - 0 self |

### BibTeX

@INPROCEEDINGS{Laird05agame,

author = {J. Laird},

title = {A game semantics of the asynchronous π-calculus},

booktitle = {In Proceedings of 16th CONCUR},

year = {2005},

pages = {51--65}

}

### OpenURL

### Abstract

Abstract. This paper studies the denotational semantics of the typed asynchronous π-calculus. We describe a simple game semantics of this language, placing it within a rich hierarchy of games models for programming languages, A key element of our account is the identification of suitable categorical structures for describing the interpretation of types and terms at an abstract level. It is based on the notion of closed Freyd category, establishing a connection between our semantics, and that of the λ-calculus. This structure is also used to define a trace operator, with which name binding is interpreted. We then show that our categorical characterization is sufficient to prove a weak soundness result. Another theme of the paper is the correspondence between justified sequences, on which our model is based, and traces in a labelled transition system in which only bound names are passed. We show that the denotations of processes are equivalent, via this correspondence, to their sets of traces. These results are used to show that the games model is fully abstract with respect to may-equivalence. 1

### Citations

361 | An object calculus for asynchronous communication
- Honda, Tokoro
- 1991
(Show Context)
Citation Context ...ion of PCF into this fragment is fully abstract. This research has many parallels with the work described here. 2 A Simply-Typed Asynchronous π-calculus We recall the polyadic asynchronous π-calculus =-=[10, 5]-=-, of which the key operations are the asynchronous output x〈y〉 of the tuple of names y on channel x, and bound input x(y).P — reception of a tuple of names on channel x which are then substituted for ... |

258 |
Expressing Mobility in Process Algebras: First-Order and Higher-Order Paradigms
- Sangiorgi
- 1992
(Show Context)
Citation Context ...rms to their 10sdenotations as strategies. Rather than the standard LTS for the π-calculus, we use one in which only bound names may be passed. This corresponds to labelled transition systems for HOπ =-=[25, 13]-=-, in which messages are fresh names used as “triggers”. Actions α are either silent (τ) or take the form x〈k, l〉 (input) or x〈k, l〉 (the complementary output) where k, l are distinct names such that i... |

209 | Games and full completeness for multiplicative linear logic
- Abramsky, Jagadeesan
- 1992
(Show Context)
Citation Context ...ategies on the “function-space” A ⊥ ⊙ B, where ⊙ is the disjoint union of forests: A ⊙ B = 〈MA + MB, [λA, λB], [⊢A, ⊢B]〉 Composition of σ : A → B and τ : B → C is by “parallel composition plus hiding”=-=[1]-=-: σ; τ = {s ∈ J A ⊥ ⊙C | ∃t ∈ JA⊙B⊙C.t↾A ⊥ , B ∈ σ ∧ t↾B ⊥ , C ∈ τ ∧ t↾A ⊥ , C = s} (where t↾A ⊥ , B means t restricted to moves from A and B, with the former relabelled by swapping Player and Opponen... |

197 |
On full abstraction for PCF
- Hyland, Ong
(Show Context)
Citation Context ...articular form, described via their traces. Moreover, π-calculus terms have already been proposed as an elegant formalism for describing strategies in games models of functional languages such as PCF =-=[11, 3]-=-. One of the objectives of this paper is to clarify and generalize this relationship between games and the π-calculus (by showing that justified sequences of moves in the former correspond to traces i... |

192 | Full abstraction for pcf
- Abramsky, Jagadeesan, et al.
- 2000
(Show Context)
Citation Context ...e sequences which “copycat” between the two components: idA = � {s ∈ J A ⊥ ⊙A | ∀t ⊑ even .t↾A ⊥ = (t↾A) ⊥ } We show that P is a well-defined category following proofs for similar categories of games =-=[2, 11, 16]-=-. We observe that ⊙ acts as a symmetric monoidal product 3 on P with the empty arena I as its identity element, and an action on functions taking σ : A → C and τ : B → D to: σ ⊙ τ = {s ∈ A ⊥ ⊙ B ⊥ ⊙ C... |

175 | The polyadic π-calculus: A tutorial
- Milner
- 1992
(Show Context)
Citation Context ... are equivalent, via this correspondence, to their sets of traces. These results are used to show that the games model is fully abstract with respect to may-equivalence. 1 Introduction The π-calculus =-=[23]-=- is an elegant and powerful formalism offering a flexible description of name mobility; it can be used to give detailed descriptions of concurrent systems, whilst its conceptual and formal simplicity ... |

165 |
Traced monoidal categories
- Joyal, Street, et al.
- 1996
(Show Context)
Citation Context ...n pointers from the initial moves in C. In any distributive-closed Freyd category, including P, we may define a trace operator Tr B A,C : P(A ⊙ B, C ⊙ B) → P(B, C) making P a traced monoidal category =-=[15]-=-. This provides a natural notion of “feedback” connecting input to output, with which we interpret new-name binding. We define the trace of f : A ⊙ B → C ⊙ B: Tr B A,C(f) =!Λ(f; θB,C); ϱB,B,C; θB,B⇀C;... |

32 | A fully abstract game semantics for finite nondeterminism
- Harmer, Mccusker
- 1999
(Show Context)
Citation Context ...ly suitable only for characterizing testing equivalences. A natural extension of the current research would be to construct a model of must-testing, by recording traces resulting in divergence, as in =-=[8, 16]-=- and deadlock. However, there are many technical complications. We have also sketched “true concurrency” and “abstract interpretation” examples of our categorical semantics which require further inves... |

29 | Sequentiality and the π-calculus
- Berger, Honda, et al.
(Show Context)
Citation Context ...articular form, described via their traces. Moreover, π-calculus terms have already been proposed as an elegant formalism for describing strategies in games models of functional languages such as PCF =-=[11, 3]-=-. One of the objectives of this paper is to clarify and generalize this relationship between games and the π-calculus (by showing that justified sequences of moves in the former correspond to traces i... |

28 | Trace and testing equivalence on asynchronous processes
- Boreale, Nicola, et al.
(Show Context)
Citation Context ... equivalence for the asynchronous π-calculus obtained via interpretatation in the fully abstract model is essentially as described (for a somewhat different LTS) by Boreale, de Nicola and Pugliese in =-=[19]-=-. Connections between Hyland-Ong games and the π-calculus were initially investigated by Hyland and Ong themselves, who described a translation of PCF into the π-calculus derived from the representati... |

26 | Angelic semantics of fine-grained concurrency
- Ghica, Murawski
- 2004
(Show Context)
Citation Context ...regard games as an abstract and mathematically precise representation of trace semantics, this is already a useful development; for example, abstract interpretation [21] and model-checking techniques =-=[6, 7]-=- based on HO game semantics are available. Moreover, since our games model is constructed in a purely compositional way, it can be generalized to more “truly concurrent” representations of interaction... |

25 | Asynchrony and the Pi-calculus
- Boudol
- 1992
(Show Context)
Citation Context ...ion of PCF into this fragment is fully abstract. This research has many parallels with the work described here. 2 A Simply-Typed Asynchronous π-calculus We recall the polyadic asynchronous π-calculus =-=[10, 5]-=-, of which the key operations are the asynchronous output x〈y〉 of the tuple of names y on channel x, and bound input x(y).P — reception of a tuple of names on channel x which are then substituted for ... |

22 |
Contextual equivalence for higherorder pi-calculus revisited
- Jeffrey, Rathke
(Show Context)
Citation Context ...rms to their 10sdenotations as strategies. Rather than the standard LTS for the π-calculus, we use one in which only bound names may be passed. This corresponds to labelled transition systems for HOπ =-=[25, 13]-=-, in which messages are fresh names used as “triggers”. Actions α are either silent (τ) or take the form x〈k, l〉 (input) or x〈k, l〉 (the complementary output) where k, l are distinct names such that i... |

22 |
A fully abstract domain model for the π-calculus
- Stark
- 1996
(Show Context)
Citation Context ...in” of input and output. More generally, our account is part of an investigation of the logical structure of higher-order imperative/concurrent computation [17]. 1.1 Related Work Hennessey [9], Stark =-=[26]-=- and Fiore, Moggi and Sangiorgi [20] have described domain-theoretic models of the π-calculus, which are fully abstract with respect to various notions of process equivalence. These works differ from ... |

21 |
and full abstraction for a functional metalanguage with recursive types
- Games
- 1996
(Show Context)
Citation Context ...e)monoidal functor from the latter to the former. The closure property operates via this functor. We define a category of values or abstractions using the notion of well-opened strategy, adapted from =-=[22]-=-. Definition 4. A legal sequence on a justified arena A is well-opened if it is empty, or contains precisely one initial O-move, which is the first move. 3 For the sake of simplicity, we shall not hen... |

20 | The regular-language semantics of second-order idealized ALGOL
- Ghica, McCusker
(Show Context)
Citation Context ...regard games as an abstract and mathematically precise representation of trace semantics, this is already a useful development; for example, abstract interpretation [21] and model-checking techniques =-=[6, 7]-=- based on HO game semantics are available. Moreover, since our games model is constructed in a purely compositional way, it can be generalized to more “truly concurrent” representations of interaction... |

17 | A game semantics of local names and good variables
- Laird
(Show Context)
Citation Context ...ructs, or the association of input and output capabilities to a single name. 13sWe could, however introduce the capacity to represent names explicitly into our model using the techniques described in =-=[18]-=- based on a category of games acted on by the group of natural number permutations. The representation of processes via their traces, is probably suitable only for characterizing testing equivalences.... |

17 |
Generalised flowcharts and games
- Malacaria, Hankin
- 1998
(Show Context)
Citation Context ...he π-calculus itself? If we simply regard games as an abstract and mathematically precise representation of trace semantics, this is already a useful development; for example, abstract interpretation =-=[21]-=- and model-checking techniques [6, 7] based on HO game semantics are available. Moreover, since our games model is constructed in a purely compositional way, it can be generalized to more “truly concu... |

14 |
D.: A fully abstract model for the π-calculus
- Fiore, Moggi, et al.
- 2002
(Show Context)
Citation Context ...lly, our account is part of an investigation of the logical structure of higher-order imperative/concurrent computation [17]. 1.1 Related Work Hennessey [9], Stark [26] and Fiore, Moggi and Sangiorgi =-=[20]-=- have described domain-theoretic models of the π-calculus, which are fully abstract with respect to various notions of process equivalence. These works differ from the semantics described here in aspe... |

12 | Causality and true concurrency: A data-flow analysis of the pi-calculus
- Jagadeesan, Jagadeesan
- 1995
(Show Context)
Citation Context ...ks it down into a smaller atoms. (Giving an equally natural characterization of agent mobility.) A closer parallel is with the data-flow semantics of the π-calculus given by Jagadeesan and Jagadeesan =-=[12]-=-, in which dynamic binding is described using 2snotions from the Geometry of Interaction, analogous to our use of the trace operator. Viewed in the light of the correspondence between game semantics a... |

11 |
A fully abstract denotational semantics for the π-calculus
- Hennessy
(Show Context)
Citation Context ... “plugging in” of input and output. More generally, our account is part of an investigation of the logical structure of higher-order imperative/concurrent computation [17]. 1.1 Related Work Hennessey =-=[9]-=-, Stark [26] and Fiore, Moggi and Sangiorgi [20] have described domain-theoretic models of the π-calculus, which are fully abstract with respect to various notions of process equivalence. These works ... |

10 |
A categorical semantics of higher-order store
- Laird
- 2002
(Show Context)
Citation Context ...uition that this corresponds to a “plugging in” of input and output. More generally, our account is part of an investigation of the logical structure of higher-order imperative/concurrent computation =-=[17]-=-. 1.1 Related Work Hennessey [9], Stark [26] and Fiore, Moggi and Sangiorgi [20] have described domain-theoretic models of the π-calculus, which are fully abstract with respect to various notions of p... |

6 |
A game semantics of ICSP
- Laird
- 2001
(Show Context)
Citation Context ... responds to a sequence of actions by the environment (O-moves), then it must make at least the same response to any sequence with more or earlier O-moves. The preorder is based on that introduced in =-=[16]-=-, but similar relations are well-established in concurrency theory, in particular we note their use in a LTS characterisation of may-equivalence for the π-calculus [19]. Definition 2. Let � be the lea... |

4 |
Environments in Freyd categories and κ-categories
- Power, Thielecke
- 1999
(Show Context)
Citation Context ...allowing us to identify a deeper “logical structure” within it. It is this structure which we aim to describe using categorical notions. In particular, our account is based on closed Freyd categories =-=[24]-=- which are categorical models of the computational λcalculus, making a semantic connection between the π-calculus and higher-order functional computation (which is implicit in existing translations of... |

2 |
A fully abstract may-testing semantics for concurrent objects
- Jeffrey, Rathke
- 2002
(Show Context)
Citation Context ...ht of the correspondence between game semantics and the labelled transition system described in Section 4, our work is also related to Jeffrey and Rathke’s may-testing semantics of concurrent objects =-=[14]-=-. The characterization of may-testing equivalence for the asynchronous π-calculus obtained via interpretatation in the fully abstract model is essentially as described (for a somewhat different LTS) b... |

1 |
Strong normalization in the π-calculus
- Berger, Honda, et al.
- 2001
(Show Context)
Citation Context ...Ong themselves, who described a translation of PCF into the π-calculus derived from the representation of innocent strategies as π-calculus terms. This work was developed by Honda, Berger and Yoshida =-=[3, 4]-=-, who developed a typing system for the π-calculus identifying sequential processes, and showed that the translation of PCF into this fragment is fully abstract. This research has many parallels with ... |