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A Formal Verification of the Alternating Bit Protocol in the Calculus of Constructions
"... 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 su cient detail to be formalised. Thereafter we show by examples how the formalised proof has been veri ed by the automated proof chec ..."
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Cited by 14 (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 su cient detail to be formalised. Thereafter we show by examples how the formalised proof has been veri ed 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.
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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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.
KORSO Reference Languages  Concepts and Application Domains
, 1994
"... This paper gives an overview of the three Korso reference languages Spectrum, Troll light, and Special, exposing their motivation and background, language concepts, and typical application domains. The presentation of the different languages is followed by a discussion to what extent these languages ..."
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This paper gives an overview of the three Korso reference languages Spectrum, Troll light, and Special, exposing their motivation and background, language concepts, and typical application domains. The presentation of the different languages is followed by a discussion to what extent these languages may complement each other in the software development process.
Program Derivation by Proof Transformation
, 1993
"... In the proofsasprograms methodology, verified programs are developed through theoremproving in a constructive logic. Under this approach, the theoremproving process can be regarded as a program derivation process. The merits of this approach to programming are twofold. First, working with proofs ..."
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In the proofsasprograms methodology, verified programs are developed through theoremproving in a constructive logic. Under this approach, the theoremproving process can be regarded as a program derivation process. The merits of this approach to programming are twofold. First, working with proofs instead of programs concentrates the developer's effort on the intellectually difficult part of the development process: understanding, solving, and explaining the solution to a mathematical problem. Second, the proof provides a formal and trustworthy basis for an explanation of the program. This thesis investigates the use of proof transformations as a way to address important concerns in program derivation that are not addressed by theoremproving alone. One difficulty with the proofsasprograms strategy arises from the conflict between elegance and efficiency. A simple, elegant proof may lead to an inefficient program. A more complex proof that corresponds to a more efficient program ma...
ProofChecking a Data Link Protocol
 Proceedings International Workshop TYPES'93
, 1994
"... A data link protocol developed and used by Philips Electronics is modeled and verified using I/O automata theory. Correctness is computerchecked with the Coq proof development system. AMS Subject Classification (1991): 03B15 [Mathematical logic and foundations]: Higherorder logic and type theor ..."
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A data link protocol developed and used by Philips Electronics is modeled and verified using I/O automata theory. Correctness is computerchecked with the Coq proof development system. AMS Subject Classification (1991): 03B15 [Mathematical logic and foundations]: Higherorder logic and type theory; 03B35 [Mathematical logic and foundations]: Mechanization of proofs and logical operations; 68Q22 [Computer science]: Parallel and distributed algorithms; 68Q60 [Computer science]: Specification and verification of programs. CR Subject Classification (1991): C.2.2 [Computer systems organization]: Network protocols  Protocol verification; F.3.1 [Theory of computation]: Specifying and verifying and reasoning about programs  Invariants, mechanical verification; F.4.1 [Theory of computation]: Mathematical logic  Lambda calculus and related systems, mechanical theorem proving. Keywords & Phrases: Communication protocols, protocol verification, I/O automata, proofchecking, type ...
Modularity in the LF Logical Framework
, 1991
"... this paper we make a concrete proposal for a module system for the Elf language which attempts to address those three central issues. Various approaches to the static and dynamic semantics of such a module calculus are possible, but beyond the scope of this paper. Here we provide only informal discu ..."
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this paper we make a concrete proposal for a module system for the Elf language which attempts to address those three central issues. Various approaches to the static and dynamic semantics of such a module calculus are possible, but beyond the scope of this paper. Here we provide only informal discussions of the meanings of various language constructs and properties. As an extended example throughout the paper we will use two formulations of minimal propositional calculus with implication and conjunction: an axiom system in the style of Hilbert and Gentzen's calculus of natural deduction. The problem of modularity in the presentation of theories and logical system has been addressed from the semantical [10, 9] and the typetheoretic [3, 4, 25] point of view. Our design has been guided by these ideas and the pragmatic principles of the ML module system [14, 17]. For further discussion of related work, the reader is referred to Section 7. Modularity in LF 2 The remainder of this paper is organized as follows. In Section 2 we review the LF Logical Framework as it is realized within the Elf programming language. As our approach to a module calculus is explicitly stratified (modules do not gain the status of objects, but exist in a different level of language), this core language is not modified in any essential way by the addition of modules. In Section 3 we present a calculus for signatures with three basic structuring mechanisms: inclusion, parametrization, and instantiation. As valid objects constructed over a given signatures represent objectlanguage expressions and deductions, this is the centerpiece and most important aspect of the module calculus. In Section 4 we move on to realizations which can express logic interpretations through which theorems can be transpor...
A Natural Deduction Style Proof System For Propositional µCalculus And Its Formalization In Inductive Type Theories
, 1998
"... this paper, we present a formalization of Kozen's propositional modal calculus, in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higherorder abstract syntax in inductive sets in presence of recursive constructors, the encoding of modal (&q ..."
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this paper, we present a formalization of Kozen's propositional modal calculus, in the Calculus of Inductive Constructions. We address several problematic issues, such as the use of higherorder abstract syntax in inductive sets in presence of recursive constructors, the encoding of modal ("proof") rules and of context sensitive grammars. The encoding can be used in the Coq system, providing an experimental computeraided proof environment for the interactive development of errorfree proofs in the calculus. The techniques we adopted can be readily ported to other languages and proof systems featuring similar problematic issues. Introduction In this paper, we present a formalization of Kozen's propositional modal  calculus 10 , often referred to as K, in the Coq proof assistant 4 . The calculus is a temporal logi