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Five axioms of alphaconversion
 Ninth international Conference on Theorem Proving in Higher Order Logics TPHOL
, 1996
"... Abstract. We present five axioms of namecarrying lambdaterms identified up to alphaconversion—that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambdaabstraction. Other constants represent a function Fv that returns the set of free variab ..."
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Abstract. We present five axioms of namecarrying lambdaterms identified up to alphaconversion—that is, up to renaming of bound variables. We assume constructors for constants, variables, application and lambdaabstraction. Other constants represent a function Fv that returns the set of free variables in a term and a function that substitutes a term for a variable free in another term. Our axioms are (1) equations relating Fv and each constructor, (2) equations relating substitution and each constructor, (3) alphaconversion itself, (4) unique existence of functions on lambdaterms defined by structural iteration, and (5) construction of lambdaabstractions given certain functions from variables to terms. By building a model from de Bruijn’s nameless lambdaterms, we show that our five axioms are a conservative extension of HOL. Theorems provable from the axioms include distinctness, injectivity and an exhaustion principle for the constructors, principles of structural induction and primitive recursion on lambdaterms, Hindley and Seldin’s substitution lemmas and
A Full Formalisation of πCalculus Theory in the Calculus of Constructions
, 1997
"... A formalisation of picalculus in the Coq system is presented. Based on a de Bruijn notation for names, our... ..."
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A formalisation of picalculus in the Coq system is presented. Based on a de Bruijn notation for names, our...
A Framework for High Assurance Security of Distributed Objects
 IN DATABASE SECURITY, X: STATUS AND PROSPECTS
, 1997
"... High assurance security is difficult to achieve in distributed computer systems and databases because of their complexity, nondeterminism and inherent heterogeneity. The practical application of formal methods is the key to high assurance security in open, distributed environments. This paper pro ..."
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High assurance security is difficult to achieve in distributed computer systems and databases because of their complexity, nondeterminism and inherent heterogeneity. The practical application of formal methods is the key to high assurance security in open, distributed environments. This paper proposes the use of formal methods and a special layered architecture to achieve secure interoperation of heterogeneous distributed objects. The foundation is provided by ROC, a process calculus tailored for concurrent objects. Lying aboveROC in the layered architecture is a metaobject model for creating object models with various programming constructs, megaprogramming facilities and securitymechanisms. Successive layers of the architecture represent more sophisticated toolkits for modeling distributed objects. Since eachlayer inherits ROC's formal foundation, it automatically has an unambiguous semantics and supports verification.
A Formalization of the Process Algebra CCS in Higher Order Logic
, 1992
"... : This paper describes a mechanization in higher order logic of the theory for a subset of Milner's ccs. The aim is to build a sound and effective tool to support verification and reasoning about process algebra specifications. To achieve this goal, the formal theory for pure ccs (no value pass ..."
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: This paper describes a mechanization in higher order logic of the theory for a subset of Milner's ccs. The aim is to build a sound and effective tool to support verification and reasoning about process algebra specifications. To achieve this goal, the formal theory for pure ccs (no value passing) is defined in the interactive theorem prover hol, and a set of proof tools, based on the algebraic presentation of ccs, is provided. y Research supported by Consiglio Nazionale delle Ricerche (C.N.R.), Italy. Contents 1 Introduction 2 2 The HOL System 3 3 CCS 4 3.1 Syntax and Operational Semantics : : : : : : : : : : : : : : : : : : : : : : : 4 3.2 Observational Semantics : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 5 3.3 Axiomatic Characterization of Observational Congruence : : : : : : : : : : 6 3.4 A Modal Logic : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 7 4 Mechanization of CCS in HOL 8 4.1 The Syntax : : : : : : : : : : : : : : : : : : : : : ...
Process Algebra in PVS
 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
, 1999
"... 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 ..."
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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 ACPstyle process algebras [2, 3]. In this framework, processes are represented by terms constructed from atoms (denoting atomic actions) and operators such as choice (nondeterminism), sequential composition, and para...
Analysis of a Guard Condition in Type Theory
, 1997
"... We present a realizability interpretation of coinductive types based on partial equivalence relations (per's). We extract from the per's interpretation sound rules to type recursive definitions. These recursive definitions are needed to introduce "infinite" and "total" ..."
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We present a realizability interpretation of coinductive types based on partial equivalence relations (per's). We extract from the per's interpretation sound rules to type recursive definitions. These recursive definitions are needed to introduce "infinite" and "total" objects of coinductive type such as an infinite stream or a nonterminating process. We show that the proposed type system enjoys the basic syntactic properties of subject reduction and strong normalization with respect to a confluent rewriting system first studied by Gimenez. We also compare the proposed type system with those studied by Coquand and Gimenez. In particular, we provide a semantic reconstruction of Gimenez's system which suggests a rule to type nested recursive definitions.
A FirstOrder Syntax for the piCalculus in Isabelle/HOL using Permutations
"... . A formalized theory of alphaconversion for the #calculus in ..."
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. A formalized theory of alphaconversion for the #calculus in
Up to context proofs for the calculus in the Coq system
, 1997
"... La formalisation dans le système Coq de la théorie des progressions de relations de Sangiorgi permet, dans son application au calcul, la vérication du théorème de preuve au contexte près. Ce résultat s'avère crucial dans le cadre d'une mécanisation du calcul, dans la mesure où il facilit ..."
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La formalisation dans le système Coq de la théorie des progressions de relations de Sangiorgi permet, dans son application au calcul, la vérication du théorème de preuve au contexte près. Ce résultat s'avère crucial dans le cadre d'une mécanisation du calcul, dans la mesure où il facilite considérablement les preuves de bisimulation, en les rendant plus compactes et plus lisibles. S'agissant de notre implémentation du calcul en Coq, basée sur une notation de De Bruijn pour l'ensemble des noms de canaux, cela permet de prouver un certain nombre de résultats classiques en théorie algébrique du calcul: nous présentons ici les preuves vériées des théorèmes d'équivalence structurelle, ainsi que l'unicité des solutions pour les équations. We present a formalisation of polyadic calculus in the Calculus of Inductive Constructions. Processes are implemented using a De Bruijn notation for names, and early transitions semantics is represented with an inductively dened relation. We mechanise some bisimulation proofs for the calculus using an upto context technique, which is proved correct within an implementation of Sangiorgi's theory of progressions [20]. This technique, which allows us to shorten the proofs by reducing the size of the relations one has to exhibit, is applied to prove structural equivalence laws, as well as uniqueness of solutions for equations. Possible applications of this work include the proof of other important theorems in calculus, as well as the design of a system to check bisimilarities for processes.
A Hybrid Model for Reasoning about Composed Hardware Systems
 Conference on ComputerAided Verification
, 1994
"... . To formally specify and reason about composed systems, a process algebra is developed that integrates an extended interpreter model. This approach utilizes the interpreter model for device decomposition, while also being able to reason about larger systems that require interdevice communication. B ..."
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. To formally specify and reason about composed systems, a process algebra is developed that integrates an extended interpreter model. This approach utilizes the interpreter model for device decomposition, while also being able to reason about larger systems that require interdevice communication. By combining these approaches, convenient notations are available to specify and verify both device independent properties (e.g., instruction sets) and device interdependent properties (e.g., communication protocols). 1 Introduction Previous approaches to system verification have decomposed systems into several hardware and software layers that may be independently verified [3, 9, 11, 17]. Each layer consists of an implementation description and a more abstract specification. The layers are joined, or "stacked", with each implementation description serving as the specification for the next lower layer. The hardware layers of these systems have been modeled as a microprocessor with memory. Th...
Bisimulation proofs for the calculus in the Calculus of Constructions
"... Nous présentons une implémentation dans le système Coq des techniques de preuves de bisimulation exposées par Davide Sangiorgi dans [San94]. Coq [CCF 96] est un logiciel d'aide à la preuve développé à l'INRIA et à l'École Normale Supérieure de Lyon. Nous décrivons la théorie des prog ..."
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Nous présentons une implémentation dans le système Coq des techniques de preuves de bisimulation exposées par Davide Sangiorgi dans [San94]. Coq [CCF 96] est un logiciel d'aide à la preuve développé à l'INRIA et à l'École Normale Supérieure de Lyon. Nous décrivons la théorie des progressions de relations sur un ensemble de processus quelconque, que nous appliquons ensuite à l'implantation d'un mini calcul polyadique ni; nous nous intéressons en particulier à la clôture d'une relation pour une famille de contextes. Les techniques implantées permettent de simplier les preuves de bisimulation entre termes. We present an implementation of the bisimulation proof techniques described by Davide Sangiorgi in [San94]. The system we use is the Coq Proof Assistant [CCF 96], a theorem prover developped at INRIA and at the École Normale Supérieure de Lyon. We rstly implement the theory about progressions of relations on a set of processes, and then specialise it with our implementation of a nite polyadic calculus; we consider in full detail the particular case of the closure under contexts of a relation. This gives a toolkit to make bisimulation proofs much shorter than the usual ones.