## Models for Name-Passing Processes: Interleaving and Causal (2000)

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Venue: | In Proceedings of LICS 2000: the 15th IEEE Symposium on Logic in Computer Science (Santa Barbara |

Citations: | 24 - 3 self |

### BibTeX

@INPROCEEDINGS{Cattani00modelsfor,

author = {Gian Luca Cattani and Peter Sewell},

title = {Models for Name-Passing Processes: Interleaving and Causal},

booktitle = {In Proceedings of LICS 2000: the 15th IEEE Symposium on Logic in Computer Science (Santa Barbara},

year = {2000},

pages = {322--333},

publisher = {IEEE Computer Society Press}

}

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### Abstract

We study syntax-free models for name-passing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual pi-calculus operations, defining Indexed Labelled Transition Systems. For noninterleaving causal semantics we define Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi. In each case we relate a denotational semantics to an operational view, for bisimulation and causal bisimulation respectively. We establish completeness properties of, and adjunctions between, categories of the two models. Alternative indexing structures and possible applications are also discussed. These are first steps towards a uniform understanding of the semantics and operations of name-passing calculi.

### Citations

3387 |
Communication and Concurrency
- Milner
- 1989
(Show Context)
Citation Context ...uniform behaviour of input transitions, can be argued to be unnecessary from the model-theoretic point of view (just as their analogues are neglected in the reduction of value-passing CCS to pure CCS =-=[3-=-9]). When 2a and 2b are omitted, 3b becomes essential. For illustrative purposes we list now a few simple consequences of Denition 3.4. Analogous properties of -terms are often established as lemmas, ... |

1057 | A calculus of mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...ure of process terms and equip it with an operational semantics dening behaviour (e.g. transition relations) over those terms. This has been followed for almost all work on -calculi, beginning with [40], in which an operational semantics denes transition relations with particular labels over -terms. By contrast, in this paper we study purely model-theoretic notions of behaviour for -calculi, with... |

818 | A calculus for cryptographic protocols: the spi calculus
- Abadi, Gordon
- 1999
(Show Context)
Citation Context ... the set of all traces). These can then be composed by parallel and restriction operators. One may thereby obtain a tight connection between this work and process-calculus modeling of protocols, e.g. =-=-=-[2]. 32 Out A ` C : xv xv ! C 0 In A ` xp:P xv ! C C f v = p gP Par A ` P ` ! C P 0 A ` P j Q ` ! C P 0 j Q Comm A ` P xv ! C P 0 A ` Q xv ! C Q 0 A ` P j Q ! ; (fvg n A)(P 0 j Q 0 ) Res A; x ` P ` !... |

430 | The Inductive Approach to Verifying Cryptographic Protocols
- Paulson
- 1998
(Show Context)
Citation Context ...t are less dependent on the precise expressiveness of the calculus used. Secondly, the model allows alternative styles of denition of system behaviours. For example, in the work of Paulson (see e.g. [=-=44]-=-) systems are described by disjunctions of predicates specifying when a given trace can be extended by a particular label. One can characterise the well-formed such predicates (loosely, those that are... |

374 | An Object Calculus for Asynchronous Communication
- Honda, Tokoro
- 1991
(Show Context)
Citation Context ...By contrast here we take a more concrete approach, with several advantages. Firstly, it is easy to conceive of minor modications to our denitions to suit calculi such as the asynchronous -calculus [7,=-= 28-=-]. In particular it should be quite straightforward to adapt the axioms of [50] to our models. It should also be easy to address the I-calculus [48], in which only new names are communicated (though t... |

284 | Mobile Values, New Names, and Secure Communication
- Abadi, Fournet
- 2001
(Show Context)
Citation Context ...ish to exclude equations that discard variables, to obtain an unambiguous notion of the new names in a value). An operational development with equational datatypes has been given by Abadi and Fournet =-=[1-=-]. Synchronisation Algebras More speculatively, one can ask whether synchronisation algebras [58] can be generalised to cover a useful variety of name-passing calculi, thereby supporting uniform denit... |

270 | Models for concurrency
- Winskel, Nielsen
- 1995
(Show Context)
Citation Context ...sal semantics, we dene Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi [=-=3, 55, 58-=-]. In each case we give a denotational semantics of a -calculus; we prove that the operational early and causal bisimulations [47, 6] coincide with model-theoretic notions. We also establish completen... |

267 |
Expressing mobility in process algebras: first-order and higher-order paradigms
- Sangiorgi
- 1992
(Show Context)
Citation Context ...ard Asynchronous Transition Systems model for CCS-like calculi [3, 55, 58]. In each case we give a denotational semantics of a -calculus; we prove that the operational early and causal bisimulations [=-=47, 6]-=- coincide with model-theoretic notions. We also establish completeness properties of and adjunctions between categories of the two models, assrst steps towards a uniform understanding of the semantics... |

230 |
Categories for the working mathematician, volume 5 of Graduate Texts in Mathematics
- Lane
- 1998
(Show Context)
Citation Context ... N-LTSs with initial name-set I and these morphisms. Theorem 3.13 For every name-set I, the category N -LTS I is complete and cocomplete. Proof: Completeness By a well-known result of category theory =-=-=-[36], it suces to show that N -LTS I has equalisers and small products. Equalisers: If T 1 T 2 are two morphisms in N -LTS I , dene T 0 = hS 0 ; ! 0 ; i 1 i ands: T 0 ,! T 1 as follows: S 0 S 1 S 2... |

198 |
Sheaves in geometry and logic. A first introduction to topos theory. Universitext
- Lane, Moerdijk
- 1994
(Show Context)
Citation Context ...sis a morphism in N -LTS I . The universal property follows from that of S 1 S 2 S 0 . Coproducts: The initial object is 0 I = hN (I ; ); ;; hI ; 1 I ii, where N (I ; ) is the representable functor [=-=37]-=-, N (I ; )(A) def = N (I ; A) = ff j f : I !Ag, N (I ; )(g)(f) def = N (I ; g)(f) = gf , for any g : A!B and f : I !A in N . Observe in fact that for any functor S : N ! Set and element i 2 S(I), ther... |

153 | A new approach to abstract syntax involving binders
- Gabbay, Pitts
- 1999
(Show Context)
Citation Context ...checking, via notions ofsnitely-generable N-LTS and N-LATS { the former of which may have interesting relationships with the HD-automata of [43], and wonder what the relationships are with the recent =-=[22, 21, 26-=-], where similar indexing structure is used in a -calculus setting. Finally, notice that in this paper we introduce transition systems with indexed sets of states, but not indexed sets of transitions.... |

148 |
Abstract syntax and variable binding
- Fiore, Plotkin, et al.
- 1999
(Show Context)
Citation Context ...checking, via notions ofsnitely-generable N-LTS and N-LATS { the former of which may have interesting relationships with the HD-automata of [43], and wonder what the relationships are with the recent =-=[22, 21, 26-=-], where similar indexing structure is used in a -calculus setting. Finally, notice that in this paper we introduce transition systems with indexed sets of states, but not indexed sets of transitions.... |

122 | Bisimulation from open maps
- Joyal, Nielsen, et al.
- 1996
(Show Context)
Citation Context ...nctions [49]. Moreover, the categorical study of process calculi gives the possibility of obtaining general congruence results: in [58] categorical models of CCS-like processes are axiomatised and in =-=[31]-=- an abstract model-theoretic notion of bisimulation is introduced (via open maps); in [13, 14] these two are combined to give abstract congruence results for strong bisimulation over a wide range of m... |

110 | Modal logic for mobile processes
- Milner, Parrow, et al.
- 1992
(Show Context)
Citation Context ...P ::= 0 ad:P bc:P P j Q (c)P Dening the behaviour of bc:P involves substitution. For example, the communication of a free name ad:P j ac:Q ! P j f d = c gQ is inferred in the `early' semantics of [41=-=, 4-=-7] with the rules below. Out ad:P ad ! P In ac:Q ad ! f d = c gQ Com P ad ! P 0 Q ad ! Q 0 P j Q ! P 0 j Q 0 Note that d might or might not be in the free names of Q. Moreover, unlike in CCS, -calcul... |

99 | Semantical analysis of higher-order abstract syntax
- Hofmann
- 1999
(Show Context)
Citation Context ...checking, via notions ofsnitely-generable N-LTS and N-LATS { the former of which may have interesting relationships with the HD-automata of [43], and wonder what the relationships are with the recent =-=[22, 21, 26-=-], where similar indexing structure is used in a -calculus setting. Finally, notice that in this paper we introduce transition systems with indexed sets of states, but not indexed sets of transitions.... |

91 |
Catégories of Asynchronous Systems
- Bednarczyk
- 1988
(Show Context)
Citation Context ...sal semantics, we dene Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi [=-=3, 55, 58-=-]. In each case we give a denotational semantics of a -calculus; we prove that the operational early and causal bisimulations [47, 6] coincide with model-theoretic notions. We also establish completen... |

84 | pi-calculus, internal mobility and agent passing calculi - Sangiorgi - 1996 |

72 |
Equivalence Notions for Concurrent Systems and Refinement of Actions
- Glabbeek, Goltz
- 1989
(Show Context)
Citation Context ...bove, while � ρ transitive closure of � ρ ID Ai-dependent on ℓi, where si = (Ai, si). is the ID which is defined as i �ρ ID j if i ≤ j and either not eiIej or ℓj is 23sHistory preserving bisimulation =-=[46, 23, 17]-=- is a bisimulation between runs of processes which accounts for causality by requiring related runs to originate isomorphic partial orders of transitions: Definition 5.4 If T is an N -LATS, define Run... |

70 |
Causal trees
- Darondeau, Degano
- 1989
(Show Context)
Citation Context ...terms of causality or locality. Here again there are model-theoretic and syntactic approaches { thesrst is surveyed in [58]; the second is represented by various annotated operational semantics, e.g. =-=[16, 8, 15, 32, 58]-=-. The two seem to have been carried out almost independently { to our knowledge, the only works to make precise connections are [16, 8, 58]. Moreover, only the syntactic approach has been developed to... |

66 | Testing equivalence for mobile processes
- Boreale, Nicola
- 1995
(Show Context)
Citation Context ...rong bisimulation), we focus on intensional models, over which a number of equivalences can be dened (though we give results only for bisimulation). The literature contains also testing-based models [=-=24, -=-4]. The precise relationships with these and other models dened in the literature, e.g. [42, 9, 30] requires further work. More speculatively, we believe our structures may form a useful basis for -ca... |

54 |
Permutations of transitions: an event structure semantics for CCS and SCCS
- Boudol, Castellani
- 1989
(Show Context)
Citation Context ...terms of causality or locality. Here again there are model-theoretic and syntactic approaches { thesrst is surveyed in [58]; the second is represented by various annotated operational semantics, e.g. =-=[16, 8, 15, 32, 58]-=-. The two seem to have been carried out almost independently { to our knowledge, the only works to make precise connections are [16, 8, 58]. Moreover, only the syntactic approach has been developed to... |

47 | Asynchrony and the -calculus - Boudol - 1992 |

47 | Asynchrony and the π-calculus - Boudol - 1991 |

46 |
Concurrent Machines
- Shields
- 1985
(Show Context)
Citation Context ...sal semantics, we dene Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCS-like calculi [=-=3, 55, 58-=-]. In each case we give a denotational semantics of a -calculus; we prove that the operational early and causal bisimulations [47, 6] coincide with model-theoretic notions. We also establish completen... |

45 | Presheaf models for concurrency
- Cattani, Winskel
- 1996
(Show Context)
Citation Context ...ition system, and because we have found the early style suits work on concurrent language semantics and on secure encapsulation [51, 53, 54, 52]. Presheaf models exist for both early and late notions =-=[10-=-]. Moreover we should add that, in contrast to [56, 20] (which have full-abstraction results wrt. strong bisimulation), we focus on intensional models, over which a number of equivalences can be dened... |

45 |
A theory of bisimulation for the -calculus
- Sangiorgi
- 1996
(Show Context)
Citation Context ...even more, notice that if a bisimulation is further required to be a relation between S 1 and S 2 in the categorical sense, i.e. a subobject of the product S 1 S 2 , one obtains an open bisimulation [=-=San96-=-b]. Compositional semantics to -terms is given using the operations dened above in the obvious way. For a process term P , with free names in I , we write [[P ]] I for the corresponding N -LTS. We con... |

41 | C.: Non-interleaving semantics for mobile processes
- Degano, Priami
- 1999
(Show Context)
Citation Context ... to our knowledge, the only works to make precise connections are [16, 8, 58]. Moreover, only the syntactic approach has been developed to address name-passing, in the annotated operational models of =-=[6, 18]-=-. There is also work that does notst this categorisation, having both syntactic and model-theoretic aspects, with Petri nets and graph rewriting [9, 42]. Our goal in the second half of this paper is t... |

38 | Secure composition of untrusted code: Wrappers and causality types
- Sewell, Vitek
- 2000
(Show Context)
Citation Context ...s of (Par) and (Comm) are elided. Figure 4: Coloured operational semantics Relating to Coloured Semantics Lastly, we observe that the model-theoretic view would enhance work on secure encapsulation [=-=53, 54]-=-. As above, quantifying over elements of the model, rather than over syntactic processes, would allow stronger security properties to be stated. Further, that work introduced an adhocscoloured operati... |

35 |
Categorical Logic and Type Theory. Number 141
- Jacobs
- 1999
(Show Context)
Citation Context ...ollows: for every name-set A, R(A) = N -LTSA , while for every function f : A!B, R(f) is the functor R(f)(hS; !; ii) = hS; !; f ii R(f)() = : This allows us to employ the Grothendieck construction [29] to produce a category N -LTS cobred over N . In more concrete terms we have the following: Denition 3.15 Dene N -LTS to be the following category: Objects: N-LTSs Arrows: h; fi :hS; !; hA; iii !h... |

34 | Secure composition of insecure components
- Sewell, Vitek
- 1999
(Show Context)
Citation Context ... for the two models, related by the results presented in Section 6. One could then use these results to address the problem of giving causal semantics to variants of the -calculus, e.g. the box- of [5=-=3, 54]-=-, for which an approximate notion of causality is used to state security properties. Preliminary discussion of this, and of other future directions, can be found in Section 8. Among earlier models of ... |

32 | History Dependent Automata - Pistore - 1999 |

30 |
Structured coalgebras and minimal hdautomata for the i-calculus
- Montanari, Pistore
- 2005
(Show Context)
Citation Context ...l basis for -calculus interleaving and partial-order model checking, via notions ofsnitely-generable N-LTS and N-LATS { the former of which may have interesting relationships with the HD-automata of [=-=43-=-], and wonder what the relationships are with the recent [22, 21, 26], where similar indexing structure is used in a -calculus setting. Finally, notice that in this paper we introduce transition syste... |

26 |
Partial orderings descriptions and observations of nondeterministic concurrent processes
- Degano, Nicola, et al.
- 1989
(Show Context)
Citation Context ... ID is the transitive closure of ID which is dened as i ID j if i j and either not e i Ie j or ` j is A i -dependent on ` i , where s i = (A i ; s i ). 23 History preserving bisimulation [46, 23=-=, 1-=-7] is a bisimulation between runs of processes which accounts for causality by requiring related runs to originate isomorphic partial orders of transitions: Denition 5.4 If T is an N-LATS, dene Run(T ... |

23 |
A fully abstract domain model for the π-calculus
- Stark
- 1996
(Show Context)
Citation Context ... the closest to our N -LTS, though they employ a slightly different indexing structure (cf. Section 7). In [12] the models are defined using domain theoretical techniques similar to those employed in =-=[56, 20]-=-, as the solutions to semantic equations. By contrast here we take a more concrete approach, with several advantages. Firstly, it is easy to conceive of minor modifications to our definitions to suit ... |

22 |
A fully abstract semantics for causality in the -calculus
- Boreale, Sangiorgi
- 1994
(Show Context)
Citation Context ...ard Asynchronous Transition Systems model for CCS-like calculi [3, 55, 58]. In each case we give a denotational semantics of a -calculus; we prove that the operational early and causal bisimulations [=-=47, 6]-=- coincide with model-theoretic notions. We also establish completeness properties of and adjunctions between categories of the two models, assrst steps towards a uniform understanding of the semantics... |

19 | On implementations and semantics of a concurrent programming language
- SEWELL
- 1997
(Show Context)
Citation Context ...cus here is on early semantics, both to obtain a simpler notion of transition system, and because we have found the early style suits work on concurrent language semantics and on secure encapsulation =-=[51, 53, 54, 52]-=-. Presheaf models exist for both early and late notions [10]. Moreover we should add that, in contrast to [56, 20] (which have full-abstraction results wrt. strong bisimulation), we focus on intension... |

17 |
Concurrent semantics for the -calculus
- Montanari, Pistore
- 1995
(Show Context)
Citation Context ...passing, in the annotated operational models of [6, 18]. There is also work that does notst this categorisation, having both syntactic and model-theoretic aspects, with Petri nets and graph rewriting =-=[9, 42]-=-. Our goal in the second half of this paper is to develop the model-theoretic approach, and to make precise connections to the annotated operational notions. We develop a simple syntax-free non-interl... |

17 |
A fully abstract domain model for the -calculus
- Stark
- 1996
(Show Context)
Citation Context ...are the closest to our N-LTS, though they employ a slightly dierent indexing structure (cf. Section 7). In [12] the models are dened using domain theoretical techniques similar to those employed in [5=-=6, 2-=-0], as the solutions to semantic equations. By contrast here we take a more concrete approach, with several advantages. Firstly, it is easy to conceive of minor modications to our denitions to suit ca... |

17 |
A symbolic semantics for the π-calculus
- Boreale, Nicola
- 1996
(Show Context)
Citation Context ...cesses it is often intuitively clear that only a finite number of transitions are ‘important’. Several authors have worked on finitary characterisations using a refined symbolic operational semantics =-=[35, 45, 5]-=-. It may be fruitful to consider the alternative approach of model-checking algorithms that work directly over finite presentations, thereby again decoupling the algorithm design from the exact choice... |

17 |
A fully abstract semantics for causality in the π-calculus
- Boreale, Sangiorgi
- 1994
(Show Context)
Citation Context ...ard Asynchronous Transition Systems model for CCS-like calculi [3, 55, 58]. In each case we give a denotational semantics of a π-calculus; we prove that the operational early and causal bisimulations =-=[47, 6]-=- coincide with model-theoretic notions. We also establish completeness properties of and adjunctions between categories of the two models, as first steps towards a uniform understanding of the semanti... |

17 |
Presheaf models for the π-calculus
- Cattani, Stark, et al.
- 1997
(Show Context)
Citation Context ...rties. Preliminary discussion of this, and of other future directions, can be found in Section 8. Among earlier models of π-processes, the name passing synchronisation trees of [27] and presheaves of =-=[12]-=- are the closest to our N -LTS, though they employ a slightly different indexing structure (cf. Section 7). In [12] the models are defined using domain theoretical techniques similar to those employed... |

16 |
Models for concurrency: Towards a classification. Theoretical Computer Science
- Sassone, Nielsen, et al.
- 1996
(Show Context)
Citation Context ...uages. 5sFurther Motivation, Future Directions and Related Work Viewing models categorically has proven useful in study of the interleaving/non-interleaving and linear-time/branchingtime distinctions =-=[49]-=-. Moreover, the categorical study of process calculi gives the possibility of obtaining general congruence results: in [58] categorical models of CCS-like processes are axiomatised and in [31] an abst... |

15 |
A Petri net semantics for -calculus
- Busi, Gorrieri
- 1995
(Show Context)
Citation Context ...passing, in the annotated operational models of [6, 18]. There is also work that does notst this categorisation, having both syntactic and model-theoretic aspects, with Petri nets and graph rewriting =-=[9, 42]-=-. Our goal in the second half of this paper is to develop the model-theoretic approach, and to make precise connections to the annotated operational notions. We develop a simple syntax-free non-interl... |

13 |
Presheaf models for the #-calculus
- Cattani, Stark, et al.
- 1997
(Show Context)
Citation Context ...rties. Preliminary discussion of this, and of other future directions, can be found in Section 8. Among earlier models of -processes, the name passing synchronisation trees of [27] and presheaves of [=-=1-=-2] are the closest to our N-LTS, though they employ a slightly dierent indexing structure (cf. Section 7). In [12] the models are dened using domain theoretical techniques similar to those employed in... |

13 | U.: On the consistency of “truly concurrent” operational and denotational semantics - Degano, Nicola, et al. - 1988 |

13 | R.: Causality and true concurrency: A data-flow analysis of the pi-calculus
- Jagadeesan, Jagadeesan
- 1995
(Show Context)
Citation Context ...efined (though we give results only for bisimulation). The literature contains also testing-based models [24, 4]. The precise relationships with these and other models defined in the literature, e.g. =-=[42, 9, 30]-=- requires further work. More speculatively, we believe our structures may form a useful basis for π-calculus interleaving and partial-order model checking, via notions of finitely-generable N -LTS and... |

11 |
Equivalence notions for concurrent systems and re of actions (Extended abstract
- Glabbeek, Goltz
- 1989
(Show Context)
Citation Context ... ID is the transitive closure of ID which is dened as i ID j if i j and either not e i Ie j or ` j is A i -dependent on ` i , where s i = (A i ; s i ). 23 History preserving bisimulation [46, 23=-=, 1-=-7] is a bisimulation between runs of processes which accounts for causality by requiring related runs to originate isomorphic partial orders of transitions: Denition 5.4 If T is an N-LATS, dene Run(T ... |

11 |
A Petri net semantics for π-calculus, in
- Busi, Gorrieri
- 1995
(Show Context)
Citation Context ...ssing, in the annotated operational models of [6, 18]. There is also work that does not fit this categorisation, having both syntactic and model-theoretic aspects, with Petri nets and graph rewriting =-=[9, 42]-=-. Our goal in the second half of this paper is to develop the model-theoretic approach, and to make precise connections to the annotated operational notions. We develop a simple syntax-free non-interl... |

11 |
A fully abstract denotational semantics for the π-calculus
- Hennessy
(Show Context)
Citation Context ...ong bisimulation), we focus on intensional models, over which a number of equivalences can be defined (though we give results only for bisimulation). The literature contains also testing-based models =-=[24, 4]-=-. The precise relationships with these and other models defined in the literature, e.g. [42, 9, 30] requires further work. More speculatively, we believe our structures may form a useful basis for π-c... |

11 |
Concurent semantics for the π-calculus
- Montanari, Pistore
- 1995
(Show Context)
Citation Context ...ssing, in the annotated operational models of [6, 18]. There is also work that does not fit this categorisation, having both syntactic and model-theoretic aspects, with Petri nets and graph rewriting =-=[9, 42]-=-. Our goal in the second half of this paper is to develop the model-theoretic approach, and to make precise connections to the annotated operational notions. We develop a simple syntax-free non-interl... |