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45
OMDoc: Towards an Internet Standard for the Administration, Distribution and Teaching of mathematical Knowledge
 IN PROCEEDINGS AISC'2000
, 2000
"... In this paper we present an extension OMDoc to the OpenMath standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematic ..."
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Cited by 43 (5 self)
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In this paper we present an extension OMDoc to the OpenMath standard that allows to represent the semantics and structure of various kinds of mathematical documents, including articles, textbooks, interactive books, courses. It can serve as the content language for agent communication of mathematical services on a mathematical software bus.
Modular Data Structure Verification
 EECS DEPARTMENT, MASSACHUSETTS INSTITUTE OF TECHNOLOGY
, 2007
"... This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java ..."
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Cited by 38 (21 self)
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This dissertation describes an approach for automatically verifying data structures, focusing on techniques for automatically proving formulas that arise in such verification. I have implemented this approach with my colleagues in a verification system called Jahob. Jahob verifies properties of Java programs with dynamically allocated data structures. Developers write Jahob specifications in classical higherorder logic (HOL); Jahob reduces the verification problem to deciding the validity of HOL formulas. I present a new method for proving HOL formulas by combining automated reasoning techniques. My method consists of 1) splitting formulas into individual HOL conjuncts, 2) soundly approximating each HOL conjunct with a formula in a more tractable fragment and 3) proving the resulting approximation using a decision procedure or a theorem prover. I present three concrete logics; for each logic I show how to use it to approximate HOL formulas, and how to decide the validity of formulas in this logic. First, I present an approximation of HOL based on a translation to firstorder logic, which enables the use of existing resolutionbased theorem provers. Second, I present an approximation of HOL based on field constraint analysis, a new technique that enables
The Heterogeneous Tool Set
 of Lecture Notes in Computer Science
, 2007
"... Abstract. Heterogeneous specification becomes more and more important because complex systems are often specified using multiple viewpoints, involving multiple formalisms. Moreover, a formal software development process may lead to a change of formalism during the development. However, current resea ..."
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Cited by 36 (21 self)
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Abstract. Heterogeneous specification becomes more and more important because complex systems are often specified using multiple viewpoints, involving multiple formalisms. Moreover, a formal software development process may lead to a change of formalism during the development. However, current research in integrated formal methods only deals with adhoc integrations of different formalisms. The heterogeneous tool set (Hets) is a parsing, static analysis and proof management tool combining various such tools for individual specification languages, thus providing a tool for heterogeneous multilogic specification. Hets is based on a graph of logics and languages (formalized as socalled institutions), their tools, and their translations. This provides a clean semantics of heterogeneous specification, as well as a corresponding proof calculus. For proof management, the calculus of development graphs (known from other largescale proof management systems) has been adapted to heterogeneous specification. Development graphs provide an overview of the (heterogeneous) specification module hierarchy and the current proof state, and thus may be used for monitoring the overall correctness of a heterogeneous development. 1
Computer algebra meets automated theorem proving: Integrating Maple and pvs
 Theorem Proving in Higher Order Logics (TPHOLs 2001), volume 2152 of LNCS
, 2001
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Integrating HolCasl into the Development Graph Manager
 In A. Armando (Ed.) Frontiers of Combining Systems (FroCoS '02), Santa Margherita Ligure, Italy, Springer LNAI
"... For the recently developed specification language Casl, there exist two different kinds of proof support: while HOLCasl has its strength in proofs about specifications inthesmall, Maya has been designed for management of proofs in (Casl) specifications inthelarge, within an evolutionary formal ..."
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Cited by 18 (14 self)
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For the recently developed specification language Casl, there exist two different kinds of proof support: while HOLCasl has its strength in proofs about specifications inthesmall, Maya has been designed for management of proofs in (Casl) specifications inthelarge, within an evolutionary formal software development process involving changes of specifications. In this work, we discuss our integration of HOLCasl and Maya into a powerful system providing tool support for Casl, which will also serve as a basis for the integration of further proof tools.
Executing the formal semantics of the Accellera Property Specification Language by mechanised theorem proving
 Proc. 12 th Advanced Research Working Conference on Correct Hardware Design and Verification Methods (CHARME 2003), Lecture
, 2003
"... The Accellera Property Specification Language (PSL) is designed for the formal specification of hardware. The Reference Manual contains a formal semantics, which we previously encoded in a machine readable version of higher order logic. In this paper we describe how to `execute' the formal ..."
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Cited by 17 (2 self)
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The Accellera Property Specification Language (PSL) is designed for the formal specification of hardware. The Reference Manual contains a formal semantics, which we previously encoded in a machine readable version of higher order logic. In this paper we describe how to `execute' the formal semantics using proof scripts coded in the HOL theorem prover's metalanguage ML. The goal is to see if it is feasible to implement useful tools that work directly from the o#cial semantics by mechanised proof. Such tools will have a high assurance of conforming to the standard. We have implemented two experimental tools: an interpreter that evaluates whether a finite trace w, which may be generated by a simulator, satisfies a PSL formula f (i.e. w f ), and a compiler that converts PSL formulas to checkers in an intermediate format suitable for translation to HDL for inclusion in simulation testbenches. Although our tools use logical deduction and are thus slower than handcrafted implementations, they may be speedy enough for some applications. They can also provide a reference for more e#cient implementations.
OMDoc: An infrastructure for openmath content dictionary information
 BULLETIN OF THE ACM SPECIAL INTEREST GROUP ON SYMBOLIC AND AUTOMATED MATHEMATICS (SIGSAM
, 2000
"... The OpenMath framework for transmitting mathematical objects over the Internet relies on the concept of Content Dictionaries (CDs) to define the semantics of mathematical objects. This is an essential measure for establishing a meaningful communication amongst mathematical software systems (and huma ..."
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Cited by 13 (3 self)
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The OpenMath framework for transmitting mathematical objects over the Internet relies on the concept of Content Dictionaries (CDs) to define the semantics of mathematical objects. This is an essential measure for establishing a meaningful communication amongst mathematical software systems (and humans). Currently, the infrastructure for conceiving, administering, viewing CDs is limited to a filebased almost flat repository. In this paper, we propose to use the OMDoc extension of the OpenMath Xml encoding as an infrastructure to express and manipulate content dictionary information. OMDoc extends OpenMath by adding support for document markup (making the CDs more readable to the human user) and structured specification (making them more explicit, formal, and allow the user to reuse, and inherit CD information in a flexible, but welldefined way).
Verication of clock synchronization algorithms: Experiments on a combination of deductive tools
 In Proceedings of AVOCS 2005, volume 145 of ENTCS
, 2005
"... We report on an experiment in combining the theorem prover Isabelle with automatic firstorder arithmetic provers to increase automation on the verification of distributed protocols. As a case study for the experiment we verify several averaging clock synchronization algorithms. We present a formal ..."
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We report on an experiment in combining the theorem prover Isabelle with automatic firstorder arithmetic provers to increase automation on the verification of distributed protocols. As a case study for the experiment we verify several averaging clock synchronization algorithms. We present a formalization of Schneider’s generalized clock synchronization protocol [15] in Isabelle/HOL. Then, we verify that the convergence functions used in two clock synchronization algorithms, namely, the Interactive Convergence Algorithm (ICA) of Lamport and MelliarSmith [10] and the Faulttolerant Midpoint algorithm of LundeliusLynch [11], satisfy Schneider’s general conditions for correctness. The proofs are completely formalized in Isabelle/HOL. We identify the parts of the proofs which are not fully automatically proven by Isabelle builtin tactics and show that these proofs can be handled by automatic firstorder provers with support for arithmetic like ICS and CVC Lite. Key words: Theorem proving, verification, clock synchronization. 1
On Linear Arithmetic with Stars
"... Abstract. We consider an extension of integer linear arithmetic with a star operator that takes closure under vector addition of the set of solutions of linear arithmetic subformula. We show that the satisfiability problem for this language is in NP (and therefore NPcomplete). Our proof uses a gene ..."
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Abstract. We consider an extension of integer linear arithmetic with a star operator that takes closure under vector addition of the set of solutions of linear arithmetic subformula. We show that the satisfiability problem for this language is in NP (and therefore NPcomplete). Our proof uses a generalization of a recent result on sparse solutions of integer linear programming problems. We present two consequences of our result. The first one is an optimal decision procedure for a logic of sets, multisets, and cardinalities that has applications in verification, interactive theorem proving, and description logics. The second is NPcompleteness of the reachability problem for a class of “homogeneous ” transition systems whose transitions are defined using integer linear arithmetic formulas. 1