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Exceptions in the rewriting calculus
 PART I AND II. LOGIC JOURNAL OF THE INTEREST GROUP IN PURE AND APPLIED LOGICS
, 2001
"... In the context of the rewriting calculus, we introduce and study an exception mechanism that allows us to express in a simple way rewriting strategies and that is therefore also useful for expressing theorem proving tactics. This gives us the ability to simply express the semantics of the first tact ..."
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Cited by 77 (29 self)
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In the context of the rewriting calculus, we introduce and study an exception mechanism that allows us to express in a simple way rewriting strategies and that is therefore also useful for expressing theorem proving tactics. This gives us the ability to simply express the semantics of the first tactical and to describe in full details the expression of conditional rewriting.
Generating Proofs from a Decision Procedure
 Proceedings of the FLoC Workshop on RunTime Result Verification
, 1999
"... Fully automatic decision procedures are used to improve performance in many different applications of formal verification. In most cases, the decision procedures are treated as trusted components of the verification system. Because the decision procedures may be experimental and highly complex to ..."
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Cited by 17 (0 self)
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Fully automatic decision procedures are used to improve performance in many different applications of formal verification. In most cases, the decision procedures are treated as trusted components of the verification system. Because the decision procedures may be experimental and highly complex tools, it is desirable to have a way of independently confirming their results.
Translating Specifications in VDMSL to PVS
 Theorem Proving in Higher Order Logics: 9th International Conference, TPHOLs '96, volume 1125 of Lecture Notes in Computer Science
, 1996
"... . This paper presents a method for translating a subset of VDMSL to higher order logic, more specifically the PVS specification language. This method has been used in an experiment where we have taken three existing, relatively large specifications written in VDMSL, handtranslated these to PVS an ..."
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. This paper presents a method for translating a subset of VDMSL to higher order logic, more specifically the PVS specification language. This method has been used in an experiment where we have taken three existing, relatively large specifications written in VDMSL, handtranslated these to PVS and then tried to type check the results. This is not as simple as it may sound since the specifications make extensive use of subtypes, via type invariants and pre and postconditions, and therefore type checking necessarily involves some theorem proving. In trying to prove some of these type checking conditions, a worrying number of errors were identified in the specifications. 1 Introduction In a research project entitled "Towards industrially applicable proof support for VDMSL", we aim at developing tool support for proving theorems about specifications written in the VDM Specification Language (VDMSL) [6]. We would like to base our work on available theorem proving technology. The goal...
Embedding Display Calculi into Logical Frameworks: Comparing Twelf and Isabelle
 ENTCS
, 2001
"... Logical frameworks are computer systems which allow a user to formalise mathematics using specially designed languages based upon mathematical logic and Church's theory of types. They can be used to derive programs from logical specifications, thereby guaranteeing the correctness of the resulti ..."
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Logical frameworks are computer systems which allow a user to formalise mathematics using specially designed languages based upon mathematical logic and Church's theory of types. They can be used to derive programs from logical specifications, thereby guaranteeing the correctness of the resulting programs. They can also be used to formalise rigorous proofs about logical systems. We compare several methods of implementing the display (sequent) calculus #RA for relation algebra in the logical frameworks Isabelle and Twelf. We aim for an implementation enabling us to formalise, within the logical framework, prooftheoretic results such as the cutelimination theorem for #RA and any associated increase in proof length. We discuss issues arising from this requirement. Key words: logical frameworks, higherorder logics, proof systems for relation algebra, nonclassical logics, automated deduction, display logic. 1 Supported by an Australian Research Council Small Research Grant. 2 Sup...
A Survey on Embedding Programming Logics in a Theorem Prover
 Institute of Information and Computing Sciences Utrecht University
, 2002
"... Theorem provers were also called 'proof checkers' because that is what they were in the beginning. They have grown powerful, however, capable in many cases to automatically produce complicated proofs. In particular, higher order logic based theorem provers such as HOL and PVS became popula ..."
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Theorem provers were also called 'proof checkers' because that is what they were in the beginning. They have grown powerful, however, capable in many cases to automatically produce complicated proofs. In particular, higher order logic based theorem provers such as HOL and PVS became popular because the logic is well known and very expressive. They are generally considered to be potential platforms to embed a programming logic for the purpose of formal verification. In this paper we investigate a number of most commonly used methods of embedding programming logics in such theorem provers and expose problems we discover. We will also propose an alternative approach: hybrid embedding.
HOL Light Tutorial (for version 2.20)
, 2007
"... The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, ..."
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The HOL Light theorem prover can be difficult to get started with. While the manual is fairly detailed and comprehensive, the large amount of background information that has to be absorbed before the user can do anything interesting is intimidating. Here we give an alternative ‘quick start ’ guide, aimed at teaching basic use of the system quickly by means of a graded set of examples. Some readers may find it easier to absorb; those who do not are referred after all to the standard manual. “Shouldn’t we read the instructions?”
A metamodelbased approach for analyzing securitydesign models
 In models 2007, volume 4735 of lncs
, 2007
"... Abstract We have previously proposed an expressive UMLbased language for constructing and transforming securitydesign models, which are models that combine design specifications for distributed systems with specifications of their security policies. Here we show how the same framework can be used ..."
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Abstract We have previously proposed an expressive UMLbased language for constructing and transforming securitydesign models, which are models that combine design specifications for distributed systems with specifications of their security policies. Here we show how the same framework can be used to analyze these models: queries about properties of the security policy modeled are expressed as formulas in UML’s Object Constraint Language and evaluated over the metamodel of the securitydesign language. We show how this can be done in a semantically precise and meaningful way and demonstrate, through examples, that this approach can be used to formalize and check nontrivial security properties of securitydesign models. The approach and examples presented have all been implemented and checked in the SecureMOVA tool. 1
Using Theory Morphisms for Implementing Formal Methods Tools
, 2003
"... Tools for a specification language can be implemented directly (by building a special purpose theorem prover) or by a conservative embedding into a typed metalogic, which allows their safe and logically consistent implementation and the reuse of existing theorem prover engines. ..."
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Cited by 6 (5 self)
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Tools for a specification language can be implemented directly (by building a special purpose theorem prover) or by a conservative embedding into a typed metalogic, which allows their safe and logically consistent implementation and the reuse of existing theorem prover engines.
Formal modelling, analysis and verification of hybrid systems
 In Unifying Theories of Programming and Formal Engineering Methods, volume 8050 of LNCS
, 2013
"... Abstract. Hybrid systems is a mathematical model of embedded systems, and has been widely used in the design of complex embedded systems. In this chapter, we will introduce our systematic approach to formal modelling, analysis and verification of hybrid systems. In our framework, a hybrid system i ..."
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Abstract. Hybrid systems is a mathematical model of embedded systems, and has been widely used in the design of complex embedded systems. In this chapter, we will introduce our systematic approach to formal modelling, analysis and verification of hybrid systems. In our framework, a hybrid system is modelled using Hybird CSP (HCSP), and specified and reasoned about by Hybrid Hoare Logic (HHL), which is an extension of Hoare logic to hybrid systems. For deductive verification of hybrid systems, a complete approach to generating polynomial invariants for polynomial hybrid systems is proposed; meanwhile, a theorem prover for HHL that can provide tool support for the verification has been implemented. We give some case studies from realtime world, for instance, Chinese HighSpeed Train Control System at Level 3 (CTCS3). In addition, based on our invariant generation approach, we consider how to synthesize a switching logic for a considered hybrid system by reduction to constraint solving, to meet a given safety, liveness, optimality requirement, or any of their combinations. We also discuss other issues of hybrid systems, e.g., stability analysis.
Semantics, calculi, and analysis for objectoriented specifications
, 2009
"... We present a formal semantics for an objectoriented specification language. The formal semantics is presented as a conservative shallow embedding in Isabelle/HOL and the language is oriented towards OCL formulae in the context of UML class diagrams. On this basis, we formally derive several equatio ..."
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Cited by 5 (4 self)
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We present a formal semantics for an objectoriented specification language. The formal semantics is presented as a conservative shallow embedding in Isabelle/HOL and the language is oriented towards OCL formulae in the context of UML class diagrams. On this basis, we formally derive several equational and tableaux calculi, which form the basis of an integrated proof environment including automatic proof support and support for the analysis of this type of specifications. We show applications of our proof environment to data refinement based on an adapted standard refinement notion. Thus, we provide an integrated formal method for refinementbased objectoriented development.