## Verifying process algebra proofs in type theory (1993)

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Citations: | 16 - 1 self |

### BibTeX

@TECHREPORT{Sellink93verifyingprocess,

author = {M. P. A. Sellink},

title = {Verifying process algebra proofs in type theory},

institution = {},

year = {1993}

}

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### Abstract

In this paper we study automatic veri cation of proofs in process algebra. Formulas of process algebra are represented by types in typed-calculus. Inhabitants (terms) of these types represent proofs. The speci c typed-calculus we use is the Calculus of Inductive Constructions as implemented in the interactive proof construction program COQ.

### Citations

518 | Lambda calculi with types
- Barendregt
- 1992
(Show Context)
Citation Context ...es. `x is of type A' isdenotedasx : A. In Subsection 1.2 we treat type forming connectives more extensively. For the moment we just mention that A ! B is a type if A and B are types. In the -calculus =-=[1]-=- types are used to restrict application: a term F may only be applied to a term x if the types of F and x satisfy some restriction. More speci cally, Fx : B if F : A ! B and x : A. (This is formalized... |

471 |
The calculus of constructions
- Coquand, Huet
- 1988
(Show Context)
Citation Context ...T : T j V:T : T� and the context does not contain illegal types, will be denotated by usas LC. (L stands for Logic.) When p and s are identi ed in LC then we obtain the Calculus of Constructions ( C) =-=[6]-=-. 1.3 The calculus of inductive constructions The Calculus of Inductive Constructions ( IC) is an extension of LC. The main di erence between IC and LC is the presence of so called inductive types in ... |

163 | Inductive definitions in the system coq: Rules and properties - Paulin-Mohring - 1993 |

129 | A guide to LP, the Larch prover
- Garland, Guttag
- 1991
(Show Context)
Citation Context ... cation of concurrent systems. They started from the Temporal Logic of Actions (TLA) which is a logic for specifying and reasoning about concurrent systems. They made use of the veri cation system LP =-=[8]-=-. In order to avoid errors in the encoding of TLA-expressions into LP, a translator from TLA to LP is written. We adopt the algebraic approach of Jan Bergstra and Jan Willem Klop [2]. This approachisk... |

97 |
The syntax and semantics of CRL
- Groote, Ponse
- 1994
(Show Context)
Citation Context ...We adopt the algebraic approach of Jan Bergstra and Jan Willem Klop [2]. This approachisknown as Algebra of Communicating Processes (ACP). Jan Friso Groote and Alban Ponse developed a formal language =-=[10]-=- and an accompagnying proof theory [11] for ACP (+ data). The formal language is called CRL. This paper builds upon the proof theory for CRL, which was designed to facilitate automatic proof veri cati... |

60 | The algebra of recursively defined processes and the algebra of regular processes - Bergstra, Klop - 1984 |

33 |
A Calculus of Communicating Systems. Volume 92
- Milner
- 1980
(Show Context)
Citation Context ... attempt of automatic veri cation of propositions of process theory is from Rance Cleaveland and Prakash Panangaden [4], who gave an implementation of Milner's Calculus of Communicating Systems (CCS) =-=[13]-=- in NuPrl [5]. They constucted a model of CCS in non-well-founded set theory ZFC ; + AFA (ZFC where the foundation-axiom is replaced by theanti-foundation-axiom AFA) and then implemented ZFC ; + AFA i... |

18 | A computer-checked verification of Milner's scheduler - Korver, Springintveld - 1994 |

16 |
Proof theory for CRL
- Groote, Ponse
- 1991
(Show Context)
Citation Context ...Bergstra and Jan Willem Klop [2]. This approachisknown as Algebra of Communicating Processes (ACP). Jan Friso Groote and Alban Ponse developed a formal language [10] and an accompagnying proof theory =-=[11]-=- for ACP (+ data). The formal language is called CRL. This paper builds upon the proof theory for CRL, which was designed to facilitate automatic proof veri cation. We indicate how CRL properties can ... |

13 | A formal verification of the alternating bit protocol in the calculus of constructions - Bezem, Groote - 1993 |

13 |
The Coq proof assistant version 5.6 user's guide
- Dowek, Felty, et al.
- 1991
(Show Context)
Citation Context ...enerated inhabitants of the di erent induction principles (bool ind in this example) are not exposed. (b). When we run COQ we mayomit the declaration of the booleans because it is already done in the =-=[7]-=- which is automatically loaded in the initial state of the system. le prelude.v 4.2 The declaration of the functions and constants A function- or constant declaration in E has the following form: func... |

12 |
Inductive de nitions in the system Coq - rules and properties
- Paulin-Mohring
- 1993
(Show Context)
Citation Context ...d(V : T)fT j j Tg j Constr(N� T) j Elim(T� T)fT j j Tg Note that IC consists of extra rules de ning which Ind-types, which Constr-types and which Elim-types are legal. All these rules can be found in =-=[14]-=-. We do not expose them here. Types of the form Ind(V : T)fT j j Tg are called inductive types. For instance Ind(X : s )fX j X ! Xg is an inductive type. X is a bound variable in this type. This induc... |

7 |
Type theory and concurrency
- Cleaveland, Panangaden
- 1988
(Show Context)
Citation Context ...el of correctness of proofs for programs and protocols of realistic size. An earlier attempt of automatic veri cation of propositions of process theory is from Rance Cleaveland and Prakash Panangaden =-=[4]-=-, who gave an implementation of Milner's Calculus of Communicating Systems (CCS) [13] in NuPrl [5]. They constucted a model of CCS in non-well-founded set theory ZFC ; + AFA (ZFC where the foundation-... |

5 |
The algebra of recursively de ned processes and the algebra of regular processes
- Bergstra, Klop
- 1984
(Show Context)
Citation Context ... cation system LP [8]. In order to avoid errors in the encoding of TLA-expressions into LP, a translator from TLA to LP is written. We adopt the algebraic approach of Jan Bergstra and Jan Willem Klop =-=[2]-=-. This approachisknown as Algebra of Communicating Processes (ACP). Jan Friso Groote and Alban Ponse developed a formal language [10] and an accompagnying proof theory [11] for ACP (+ data). The forma... |

3 |
A formal veri cation of the alternating bit protocol in the calculus of constructions
- Bezem, Groote
- 1993
(Show Context)
Citation Context ...owisnotyet clear to us. This paper must be seen as a rst attempt. Proofs for Milner's Scheduler and the good old alternating bit protocol are computer-checked using the representation introduced here =-=[12,3]-=-. Recently, Jacovan de Pol checked a CRL proof of the Bounded Retransmission Protocol (BRP). Di erent from [12] and [3] the BRP proof was checked by building large tacticals that automatically rewrite... |

3 |
A computer-checked veri cation of Milner's scheduler
- Korver, Springintveld
(Show Context)
Citation Context ...owisnotyet clear to us. This paper must be seen as a rst attempt. Proofs for Milner's Scheduler and the good old alternating bit protocol are computer-checked using the representation introduced here =-=[12,3]-=-. Recently, Jacovan de Pol checked a CRL proof of the Bounded Retransmission Protocol (BRP). Di erent from [12] and [3] the BRP proof was checked by building large tacticals that automatically rewrite... |

2 | Towards a formal mathematical vernacular
- Groote
- 1992
(Show Context)
Citation Context ...is applied. (In this paper we always start on a new line when a subgoal is proved, but not vice versa). A solution for the denotational problem could be the use of proof constellations as proposed in =-=[9]-=-. The proof of 6.4.1 can be found using the following tactics: (i): Elim b. (ii): Elim b. Elim COND1 � Elim A3 � Auto. Intro � Elim COND1 � Elim COND1 � Auto. Elim COND2 � Elim A6 � Auto. Intro � Elim... |