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A Formal Verification of the Alternating Bit Protocol in the Calculus of Constructions
 Utrecht University
, 1993
"... We report on a formal verification of the Alternating Bit Protocol (ABP) in the Calculus of Constructions. We outline a semiformal correctness proof of the ABP with sufficient detail to be formalised. Thereafter we show by examples how the formalised proof has been verified by the automated proof c ..."
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Cited by 13 (3 self)
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We report on a formal verification of the Alternating Bit Protocol (ABP) in the Calculus of Constructions. We outline a semiformal correctness proof of the ABP with sufficient detail to be formalised. Thereafter we show by examples how the formalised proof has been verified by the automated proof checker Coq. This is part of an ongoing project aiming at the mechanisation of reasoning in (extensions of) process algebra, which we think important for the fruitful application of process algebra to concurrent systems. Key Words & Phrases: protocol verification, process algebra, typed lambda calculi. 1985 Mathematics Subject Classification: 68B10. 1987 CR Categories: D.2.4, D.4.5, F.3.1. 1 Introduction We report on a formal verification of the Alternating Bit Protocol [4] in the Calculus of Constructions, as part of an ongoing project aiming at the mechanisation of reasoning in (extensions of) process algebra. Formal verification distinguishes itself from verification in the usual sense...
Towards a formal mathematical vernacular
 Utrecht University
, 1992
"... Contemporary proof veri cators often use a command language to construct proofs. These commands are often called tactics. This new generation of theorem provers is a substantial improvement over earlier ones such asAUTOMATH. Based on experience with these new provers we feel the need to study these ..."
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Cited by 2 (0 self)
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Contemporary proof veri cators often use a command language to construct proofs. These commands are often called tactics. This new generation of theorem provers is a substantial improvement over earlier ones such asAUTOMATH. Based on experience with these new provers we feel the need to study these languages further, especially, because we think that these may be improved in their adequateness to express proofs closer to the established mathematical vernacular. We also feel that a systematic treatment of these vernaculars may lead to an improvement towards the automatic inference of trivial proof steps. In any case a systematic treatment will lead to a better understanding of the command languages. This exercise is carried out in the setting of Pure Type Systems (PTSs) in which a whole range of logics can be embedded. We rstidentify a subclass of PTSs, called the PTSs for logic. For this class we de ne a formal mathematical vernacular and we prove elementary sound and completeness. Via an elaborate example we try to assess how easy proofs in mathematics can be written down in our vernacular along the lines of the original proofs. 1
Impredicative Representations of Categorical Datatypes
, 1994
"... this document that certain implications are not based on a well stated formal theory but require a certain amount of handwaving. ..."
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this document that certain implications are not based on a well stated formal theory but require a certain amount of handwaving.
DomainTheoretic Methods for Program Synthesis
"... formal proofs. A recent outcome of this analysis is the development of computer systems for automated or interactive theorem proving that can for instance be used for computer aided program verication. An example of such a system is the interactive theorem prover Minlog developed by the logic group ..."
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formal proofs. A recent outcome of this analysis is the development of computer systems for automated or interactive theorem proving that can for instance be used for computer aided program verication. An example of such a system is the interactive theorem prover Minlog developed by the logic group at the University of Munich (7). As a former member of this group I was mainly involved in the theoretical background steering the implementation of the system. The system also exploits the socalled proofsasprograms paradigm as a logical approach to correct software development: from a formal proof that a certain specication has a solution one fully automatically extracts a program that provably meets the specication. We carried out a number of extended case studies extracting programs from proofs in areas such as arithmetic (6), graph theory (7), innitary combinatorics (7), and lambda calculus (1,2). Special emphasis has been put on an ecient implemen