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## Algebraic Theories for Name-Passing Calculi (1996)

Citations: | 52 - 11 self |

### Citations

4100 | Communicating Sequential Processes
- Hoare
- 1985
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Citation Context ...ed as data objects 2 turns out to be non-essential for our purposes. Our algebraic characterisations are thus also relevant for more limited versions of value-passing calculi such as CCS [Mil89], CSP =-=[Hoa85]-=- and ACP [BK85]; moreover the axiomatisation of the subcalculus without nondeterminism is in some respects similar to axiomatisations of functional programs. An extended discussion of related work on ... |

3886 |
Communication and Concurrency
- Milner
- 1989
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Citation Context ...n be considered as data objects 2 turns out to be non-essential for our purposes. Our algebraic characterisations are thus also relevant for more limited versions of value-passing calculi such as CCS =-=[Mil89]-=-, CSP [Hoa85] and ACP [BK85]; moreover the axiomatisation of the subcalculus without nondeterminism is in some respects similar to axiomatisations of functional programs. An extended discussion of rel... |

1577 |
A calculus of communicating systems
- Milner
- 1980
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Citation Context ...d CC laws, although the underlying formalism is quite different. In the setting of process algebra, value-passing and conditional constructs have been present since Milner's first presentation of CCS =-=[Mil80]-=-. Many of the now well-known axioms are given there but there are no completeness results, and the only laws for 45 conditionals are counterparts of our C1 and C2. In later publications, notably [Mil8... |

367 | Functions as processes - MILNER - 1990 |

289 |
Expressing Mobility in Process Algebras: First-Order and HigherOrder Paradigms
- Sangiorgi
- 1992
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Citation Context ...h each other for such events. The early bisimulation is also the one which naturally arises from a reduction semantics on the lines of Berry and Boudol's Chemical Abstract Machine [BB90], as shown in =-=[San92]-=- using the notion of barbed bisimulation. The late bisimulation equivalence builds on a more refined operational intuition: an agent can decide to receive input on a port, and by doing so it becomes a... |

262 |
Algebra of communicating processes with abstraction
- Bergstra, Klop
- 1985
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Citation Context ...ts 2 turns out to be non-essential for our purposes. Our algebraic characterisations are thus also relevant for more limited versions of value-passing calculi such as CCS [Mil89], CSP [Hoa85] and ACP =-=[BK85]-=-; moreover the axiomatisation of the subcalculus without nondeterminism is in some respects similar to axiomatisations of functional programs. An extended discussion of related work on axiomatisations... |

253 | Barbed bisimulation - Milner, Sangiorgi - 1992 |

236 | A basis for a mathematical theory of computation
- McCarthy
- 1963
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Citation Context ...nary conditionals (if : : : then : : : ). The completeness proof must consequently take a new direction. The resulting axiom system is reminiscent of basic theories of conditionals such as McCarthy's =-=[McC63]-=-, and a comparison with the system for the full calculus reveals that the laws for conditional and summation are structurally similar. The use of binary conditionals also indicates that our choice of ... |

181 |
A Calculus of Mobile
- Milner, Parrow, et al.
- 1992
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Citation Context ...onment and between components; however, the programs may not perform any computation directly on the values apart from testing equality. The inspiration for our formalisation comes from the -calculus =-=[MPW92]-=-, where it has been demonstrated that such a language can encode computations over arbitrary data domains. For example P1 and P2 above would be written P1 : i(x): [x=3]ox P2 : i(x): [x=3]o3 Here i(x) ... |

173 |
Symbolic bisimulations
- Hennessy, Lin
- 1995
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Citation Context ...set of free names of the agents, but equivalent agents might have different sets of free names. The algorithmic aspects of equality in value-passing languages are largely unexplored. Hennessy and Lin =-=[HL92]-=- provide an algorithm, based on symbolic execution, for some interesting subclasses of the language of [HL93]. Our completeness result implies an algorithm, but because of the saturation in the normal... |

129 | Modal logics for mobile processes
- Milner, Parrow, et al.
- 1993
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Citation Context ...atched. Thus late equivalence is strictly finer than early (but for deterministic agents both early and late coincide with trace equivalence) . Further discussion of the early vs. late question is in =-=[MPW91]-=-, where the equivalences are given modal logic characterisations. Late bisimulation equivalence was axiomatised in the original paper on the -calculus [MPW92] but no axiomatisation of early equivalenc... |

116 | Laws of Programming. - Hoare - 1987 |

71 | Testing equivalence for mobile processes
- Boreale, Nicola
- 1995
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Citation Context ...re the equivalence and preorders are based on testing. The axiomatisation contains a counterpart to our law IP2; the only laws for conditionals are the counterparts of C1 and C2. Boreale and DeNicola =-=[BD92]-=- and Hennessy [He91] apply a similar system to an axiomatisation of testing equivalence in the -calculus. Hennessy explores an alternative proof system in [He91b]. This system explicitly represents as... |

55 |
A process specification formalism
- Mauw, Veltink
- 1990
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Citation Context ... top of ACP in a modular way; the system is akin to our axiomatisation of bisimilarity in that the laws for conditionals imply evaluation of the conditions. A similar language is investigated by Mauw =-=[Mauw91]-=-. 8.3 Further Work One idea for further work is to clarify the role of mismatching. In the original -calculus syntax this is absent; there is only the unary matching operator. There is a good reason f... |

51 |
Axioms for Concurrency
- MOLLER
- 1989
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Citation Context ... derivations and determining properties preserved by inference; we have not found any simpler argument in terms of counter models. A similar type of argument can be found in Faron Moller's PhD Thesis =-=[Mol89]-=- for demonstrating nonexistence of finite axiomatisations. Although we have proved that the existence of each of our axioms is necessary, some questions might remain on whether some axioms can be weak... |

48 |
A theory of bisimulation for the -calculus
- Sangiorgi
- 1996
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Citation Context ...(x): Q j Note that the premise may contain a free x which is bound in the conclusion; the premise thus has an implicitly universally quantified x. By the time this paper has been completed, one of us =-=[San93]-=- has studied and axiomatised a variant of late bisimilarity in which, intuitively, the instantiation of the parameter of an input happens only when the name is needed. An attractive feature of this bi... |

47 |
The chemical abstract machine, Theoretical Computer Science 96
- Berry, Boudol
- 1992
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Citation Context ...ilar agents can match each other for such events. The early bisimulation is also the one which naturally arises from a reduction semantics on the lines of Berry and Boudol's Chemical Abstract Machine =-=[BB90]-=-, as shown in [San92] using the notion of barbed bisimulation. The late bisimulation equivalence builds on a more refined operational intuition: an agent can decide to receive input on a port, and by ... |

43 | Deciding bisimulation equivalences for a class of nonfinite-state programs
- Jonsson, Parrow
- 1993
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Citation Context ...ting to see if this idea can be transferred to the -calculus. If recursion is added to our language with prefixing and sum, the equivalence problem is NP-hard even if no conditions at all are allowed =-=[JP89]. Finally -=-it should be possible to extend our results to other equivalences. A good first candidate is the weak bisimulation equivalence, or "observation" equivalence. As for strong bisimilarity this ... |

21 |
A theory of communicating processes with value-passing
- Hennessy, Ingólfsdóttir
- 1990
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Citation Context ...t the same case analyses may occur in a calculus where value variables are distinguished, at least if the proof system is defined for ground terms only (cf. the system by Hennessy and Ing'olfsd'ottir =-=[HI89]-=-). For to prove (3) in a calculus where x is a value variable, that equation must be established for all environments, i.e. all possible substitutions of values for x. In order to avoid the case analy... |

15 |
A proof system for communicating processes with value-passing
- Hennessy
- 1991
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Citation Context ...rts of C1 and C2. Boreale and DeNicola [BD92] and Hennessy [He91] apply a similar system to an axiomatisation of testing equivalence in the -calculus. Hennessy explores an alternative proof system in =-=[He91b]. This sys-=-tem explicitly represents assumptions about the values of free value variables, and there is a "cut" rule to split such assumptions (thus IP2 is not needed since the cut rule can accomplish ... |

8 |
A Model for the ~-Calculus
- Hennessy
- 1991
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Citation Context ...nd preorders are based on testing. The axiomatisation contains a counterpart to our law IP2; the only laws for conditionals are the counterparts of C1 and C2. Boreale and DeNicola [BD92] and Hennessy =-=[He91]-=- apply a similar system to an axiomatisation of testing equivalence in the -calculus. Hennessy explores an alternative proof system in [He91b]. This system explicitly represents assumptions about the ... |

3 |
Conditional expressions with equality tests
- Sethi
- 1978
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Citation Context ...of course NP-hard to determine if even a simple equation such as 'P = / P holds, but if (as in the -calculus) only elementary conditionals are allowed more efficient algorithms may be possible. Sethi =-=[Set78]-=- gives a polynomial algorithm to determine if nested elementary conditional forms are semantically equal and it would be interesting to see if this idea can be transferred to the -calculus. If recursi... |

2 |
On the axiomatization of "if-then-else
- Guessarian, Meseguer
- 1987
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Citation Context ... consensus on a more compact notation. McCarthy [McC63] and others write ' ! P; Q; Hoare [Hoa85, H+87] and others write P \Delta 'sQ; Bloom and Tindell [BT83] write ('; P; Q); Guessarian and Meseguer =-=[GM87]-=- write ['; P; Q]; Manes [Man85] writes If ' (P; Q). Our own ' P Q works well for the purposes of this paper, and its brevity hopefully conveys an impartiality about notational conventions. Axiomatic t... |

1 |
Varieties of "if-then-else
- Bloom, Tindell
- 1983
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Citation Context ...y nested conditionals. Unfortunately there is no consensus on a more compact notation. McCarthy [McC63] and others write ' ! P; Q; Hoare [Hoa85, H+87] and others write P \Delta 'sQ; Bloom and Tindell =-=[BT83]-=- write ('; P; Q); Guessarian and Meseguer [GM87] write ['; P; Q]; Manes [Man85] writes If ' (P; Q). Our own ' P Q works well for the purposes of this paper, and its brevity hopefully conveys an impart... |

1 |
Process algebra with guards. CWI technical report CS-R9069
- Groote, Ponse
- 1990
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Citation Context ... the generalisation of the theory to a calculus with mismatching is not obvious. Other efforts in process algebra are more remotely related to the present work. We would here mention Groote and Ponse =-=[GP90] who introduce "-=-;guards" as a primitive conditional construct. The setting is different since they do not consider value-passing, but they formulate a law (their "G4") remarkably similar to our SP. A l... |

1 |
Proof Theory for CRL. CWI technical report CS-R9138
- Groote, Ponse
- 1991
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Citation Context ...rimitive conditional construct. The setting is different since they do not consider value-passing, but they formulate a law (their "G4") remarkably similar to our SP. A later work by the sam=-=e authors [GP91]-=- defines a specification language with value-passing and conditionals built on top of ACP in a modular way; the system is akin to our axiomatisation of bisimilarity in that the laws for conditionals i... |

1 |
Proof systems for message-passing algebras
- Hennessy, Lin
- 1993
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Citation Context ... about the values of free value variables, and there is a "cut" rule to split such assumptions (thus IP2 is not needed since the cut rule can accomplish any necessary case analysis). Henness=-=y and Lin [HL93]-=- adapt this system to late and early bisimulation semantics. The resulting systems are more complex and more powerful than our LB and EB, since they incorporate arbitrary tests (not only matching) and... |

1 |
Guard modules. Algebra Universalis 21:103--110
- Manes
- 1985
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Citation Context ...otation. McCarthy [McC63] and others write ' ! P; Q; Hoare [Hoa85, H+87] and others write P \Delta 'sQ; Bloom and Tindell [BT83] write ('; P; Q); Guessarian and Meseguer [GM87] write ['; P; Q]; Manes =-=[Man85]-=- writes If ' (P; Q). Our own ' P Q works well for the purposes of this paper, and its brevity hopefully conveys an impartiality about notational conventions. Axiomatic treatments of the conditional da... |

1 |
Mismatching' and early equivalence (-calculus note JP13
- Parrow
- 1990
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Citation Context ...interaction between the components. So the addition of matching causes no dramatic change of the theory; in fact most occurrences of matching can be encoded by parallel composition. As pointed out in =-=[Par90]-=-, where mismatching in the -calculus and the law SP were first considered, the addition of mismatching preserves the theory of the calculus with the minor exception of the following monotonicity prope... |