## Process Algebra in PVS (1999)

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Venue: | Proc. of the International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS '99), volume 1579 of Lecture Notes in Computer Science |

Citations: | 9 - 0 self |

### BibTeX

@INPROCEEDINGS{Basten99processalgebra,

author = {Twan Basten and Jozef Hooman},

title = {Process Algebra in PVS},

booktitle = {Proc. of the International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS '99), volume 1579 of Lecture Notes in Computer Science},

year = {1999},

pages = {270--284},

publisher = {Springer-Verlag}

}

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### Abstract

The aim of this work is to investigate mechanical support for process algebra, both for concrete applications and theoretical properties. Two approaches are presented using the verification system PVS. One approach declares process terms as an uninterpreted type and specifies equality on terms by axioms. This is convenient for concrete applications where the rewrite mechanisms of PVS can be exploited. For the verification of theoretical results, often induction principles are needed. They are provided by the second approach where process terms are defined as an abstract datatype with a separate equivalence relation. 1 Introduction We investigate the possibilities of obtainingmechanical support for equational reasoning in process algebra. In particular, we consider ACP-style process algebras [2, 3]. In this framework, processes are represented by terms constructed from atoms (denoting atomic actions) and operators such as choice (non-determinism), sequential composition, and para...

### Citations

307 | Formal Verification for Fault-Tolerant Architectures: Prolegomena to the Design of PVS
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- 1995
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Citation Context ...cal results, we do not aim at completely automatic verification. In this paper, we investigate how process algebra can be incorporated in the framework of the tool PVS (Prototype Verification System) =-=[16]-=- (for more information, see also http://www.csl.sri.com/sri-csl-pvs.html). 1 Properties can be proved in PVS by means of an interactive proof checker. This means that the user applies proof commands t... |

203 |
Process Algebra
- Baeten, Weijland
- 1990
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Citation Context ...equivalence relation. 1 Introduction We investigate the possibilities of obtainingmechanical support for equational reasoning in process algebra. In particular, we consider ACP-style process algebras =-=[2, 3]-=-. In this framework, processes are represented by terms constructed from atoms (denoting atomic actions) and operators such as choice (non-determinism), sequential composition, and parallel compositio... |

138 |
Isabelle: A Generic Theorem
- Paulson
- 1994
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Citation Context ... the definition of several models (term model, projective limit model, process graphs) in PVS. As an alternative to PVS, it would be interesting to experiment with the generic theorem prover Isabelle =-=[17]-=-, since it allows the definition of user-defined congruence relations and ordered rewriting (allowing, e.g., rewriting using a commutativity axiom). Acknowledgments We would like to thank Jaco van de ... |

51 | Process algebra with iteration and nesting - Bergstra, Bethke, et al. - 1994 |

18 | Formalizing Process Algebraic Verifications in the Calculus of Constructions. Formal Aspects of Computing
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- 1997
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Citation Context ...d on the basis of HOL [6, 7, 15]. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus [14]. For CRL, an ACP-like language with data structures, both Coq =-=[5, 11]-=- and PVS [10] have been investigated. In [5] pure algebraic reasoning is used, whereas [10, 11] combine algebraic and assertional reasoning. Most of the research mentioned above aims at concrete appli... |

18 | The Concurrency Factory: practical tools for specification, simulation, verification and implementation of concurrent systems
- Cleaveland, Gada, et al.
- 1994
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Citation Context ...elated tool which provides flexible language support. Another class of dedicated tools aims at automatic verification, including bisimulation and model checkers. An example is the Concurrency Factory =-=[8]-=-. More related to our work is research on the use of general purpose proof checkers. E.g., tool support for CCS and CSP has been obtained on the basis of HOL [6, 7, 15]. This theorem prover has also b... |

17 | PAM: A Process Algebra Manipulator
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- 1995
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Citation Context ...devoted to the development of dedicated tools for process algebra. For PSF [13], an extension of ACP with abstract datatypes, tools are available that mainly support specification and simulation. PAM =-=[12]-=- is a related tool which provides flexible language support. Another class of dedicated tools aims at automatic verification, including bisimulation and model checkers. An example is the Concurrency F... |

17 |
A mechanized theory of -calculus in HOL
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- 1992
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Citation Context ...proof checkers. E.g., tool support for CCS and CSP has been obtained on the basis of HOL [6, 7, 15]. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus =-=[14]-=-. For CRL, an ACP-like language with data structures, both Coq [5, 11] and PVS [10] have been investigated. In [5] pure algebraic reasoning is used, whereas [10, 11] combine algebraic and assertional ... |

11 |
A computer checked algebraic verification of a distributed summation algorithm
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Citation Context ...f HOL [6, 7, 15]. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus [14]. For CRL, an ACP-like language with data structures, both Coq [5, 11] and PVS =-=[10]-=- have been investigated. In [5] pure algebraic reasoning is used, whereas [10, 11] combine algebraic and assertional reasoning. Most of the research mentioned above aims at concrete applications. The ... |

9 |
Term rewriting analysis in process algebra
- Akkerman, Baeten
- 1991
(Show Context)
Citation Context ...ms (the number of symbols) are not correct, since we have to show, for example, that pa2b(lmrg(y, z)) + pa2b(lmrg(z, y)) != y // z. The solution is based on a weight function on PA terms mentioned in =-=[1]-=-. It uses the exponentiation function expt, which is already available in PVS. weight(x): RECURSIVE --n: nat --- n ?= 2 = CASES x OF atm(a) : 2, o(y, z) : weight(y) * weight(z) + weight(y), +(y, z) : ... |

7 |
A higher order logic mechanization of the CSP failure-divergence semantics
- Camilleri
- 1991
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Citation Context ... An example is the Concurrency Factory [8]. More related to our work is research on the use of general purpose proof checkers. E.g., tool support for CCS and CSP has been obtained on the basis of HOL =-=[6, 7, 15]-=-. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus [14]. For CRL, an ACP-like language with data structures, both Coq [5, 11] and PVS [10] have been i... |

6 |
Combining Interaction and Automation in Process Algebra Verification
- Camilleri, Inverardi, et al.
- 1991
(Show Context)
Citation Context ... An example is the Concurrency Factory [8]. More related to our work is research on the use of general purpose proof checkers. E.g., tool support for CCS and CSP has been obtained on the basis of HOL =-=[6, 7, 15]-=-. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus [14]. For CRL, an ACP-like language with data structures, both Coq [5, 11] and PVS [10] have been i... |

6 | On automating process algebra proofs,” in
- Korver, Sellink
- 1996
(Show Context)
Citation Context ...d on the basis of HOL [6, 7, 15]. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus [14]. For CRL, an ACP-like language with data structures, both Coq =-=[5, 11]-=- and PVS [10] have been investigated. In [5] pure algebraic reasoning is used, whereas [10, 11] combine algebraic and assertional reasoning. Most of the research mentioned above aims at concrete appli... |

6 |
A Mechanized Theory of the π-calculus in HOL
- Melham
- 1994
(Show Context)
Citation Context ...al purpose proof checkers. E.g., tool support for CCS and CSP has been obtained using HOL [6, 7, 15]. This theorem prover has also been used to get mechanized support for reasoning with the πcalculus =-=[14]-=-. For µCRL, an ACP-like language with data structures, both Coq [5, 11] and PVS [10] have been investigated. In [5] pure algebraic reasoning is used, whereas the work described in [10, 11] combines al... |

4 |
A proof assistant for PSF
- Mauw, Veltink
- 1991
(Show Context)
Citation Context ...ork in PVS that allows experiments with tool support for customized process algebras. Related Work. A lot of effort has been devoted to the development of dedicated tools for process algebra. For PSF =-=[13]-=-, an extension of ACP with abstract datatypes, tools are available that mainly support specification and simulation. PAM [12] is a related tool which provides flexible language support. Another class ... |

3 |
Value-passing CCS in HOL
- Nesi
- 1993
(Show Context)
Citation Context ... An example is the Concurrency Factory [8]. More related to our work is research on the use of general purpose proof checkers. E.g., tool support for CCS and CSP has been obtained on the basis of HOL =-=[6, 7, 15]-=-. This theorem prover has also been used to get mechanized support for reasoning with the #-calculus [14]. For CRL, an ACP-like language with data structures, both Coq [5, 11] and PVS [10] have been i... |

2 | Algebraic proof assistants in HOL
- Groenboom, Hendriks, et al.
- 1995
(Show Context)
Citation Context ...an be made when incorporating process algebra in a general purpose proof checker. In that respect, our work is probably most related to research on tool support for a CSP-like algebra by means of HOL =-=[9]-=-. In fact, they investigate similar approaches as we do, although they only consider small concrete examples. New in our paper is, besides the verification of non-trivial examples, that we additionall... |