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An Overview of A Formal Framework For Managing Mathematics
 Annals of Mathematics and Artificial Intelligence
, 2003
"... Mathematics is a process of creating, exploring, and connecting mathematical models. This paper presents an overview of a formal framework for managing the mathematics process as well as the mathematical knowledge produced by the process. The central idea of the framework is the notion of a biform t ..."
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Cited by 12 (6 self)
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Mathematics is a process of creating, exploring, and connecting mathematical models. This paper presents an overview of a formal framework for managing the mathematics process as well as the mathematical knowledge produced by the process. The central idea of the framework is the notion of a biform theory which is simultaneously an axiomatic theory and an algorithmic theory. Representing a collection of mathematical models, a biform theory provides a formal context for both deduction and computation. The framework includes facilities for deriving theorems via a mixture of deduction and computation, constructing sound deduction and computation rules, and developing networks of biform theories linked by interpretations. The framework is not tied to a specific underlying logic; indeed, it is intended to be used with several background logics simultaneously. Many of the ideas and mechanisms used in the framework are inspired by the imps Interactive Mathematical Proof System and the Axiom computer algebra system.
Classification of Communication and Cooperation Mechanisms for Logical and Symbolic Computation Systems
, 1996
"... . The combination of logical and symbolic computation systems has recently emerged from prototype extensions of standalone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service ..."
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Cited by 10 (4 self)
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. The combination of logical and symbolic computation systems has recently emerged from prototype extensions of standalone systems to the study of environments allowing interaction among several systems. Communication and cooperation mechanisms of systems performing any kind of mathematical service enable to study and solve new classes of problems and to perform efficient computation by distributed specialized packages. The classification of communication and cooperation methods for logical and symbolic computation systems given in this paper provides and surveys different methodologies for combining mathematical services and their characteristics, capabilities, requirements, and differences. The methods are illustrated by recent wellknown examples. We separate the classification into communication and cooperation methods. The former includes all aspects of the physical connection, the flow of mathematical information, the communication language(s) and its encoding, encryption, and ...
Automated Theorem Proving in Support of Computer Algebra: Symbolic Definite Integration as a Case Study
"... We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integrat ..."
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Cited by 10 (5 self)
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We assess the current state of research in the application of computer aided formal reasoning to computer algebra, and argue that embedded verification support allows users to enjoy its benefits without wrestling with technicalities. We illustrate this claim by considering symbolic definite integration, and present a verifiable symbolic definite integral table look up: a system which matches a query comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of lemmas about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman's webbased table by including parametric limits of integration and queries w...
The Constraint Solver Collaboration Language of BALI
 In Proceedings of the International Workshop Frontiers of Combining Systems, FroCoS'98
, 1998
"... In order to deal with constraint solvers integration, reusability, and cooperation, we have designed a domain independent environment for constraint solver collaboration (i.e., solver cooperation and solver combination) called BALI. This system allows one designing and implementing solver colla ..."
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Cited by 10 (6 self)
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In order to deal with constraint solvers integration, reusability, and cooperation, we have designed a domain independent environment for constraint solver collaboration (i.e., solver cooperation and solver combination) called BALI. This system allows one designing and implementing solver collaborations with a highlevel language to compose solvers using collaboration primitives (such as sequentiality, concurrency and parallelism) and control primitives (such as iterator, fixedpoint and conditional). In this paper, we present the solver collaboration language of BALI, its operational semantics, some enrichments of the framework, an overview of the implementation, and some applications as well. 1 Introduction The need for solver collaboration, i.e., that is solver combination and cooperation, has been by now well recognized: several solvers collaborate to process constraints that cannot be solved (or efficiently solved) by a single solver. Informally, combination [ Nelson a...
An Environment for Designing/Executing Constraint Solver Collaborations
 ENTCS, ELSEVIER SCIENCE PUBLISHERS
, 1998
"... Constraint programming is a paradigm based on the notion of constraints and mechanisms for their resolution. Thus the key point of this class of languages is not only to offer a wide class of constraints for declarativity reasons, but also to treat them efficiently. For this purpose, the need for ..."
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Cited by 7 (7 self)
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Constraint programming is a paradigm based on the notion of constraints and mechanisms for their resolution. Thus the key point of this class of languages is not only to offer a wide class of constraints for declarativity reasons, but also to treat them efficiently. For this purpose, the need for collaboration i.e. combination and cooperation of solvers is widely recognized. This new concept enables to solve problems that cannot be tackled or efficiently solved with a single solver. Furthermore the demand for integrating symbolic mathematical tools into automated deduction system has significantly increased. In order to meet these motivations we propose BALI, an environment for designing/executing solver collaborations. BALI is a heterogeneous distributed collaborative problem solving system. It consists of a solver collaboration language and a host language. By providing several construction primitives (as concurrency, parallelism and sequentiality) and several combinators f...
SoleX: a DomainIndependent Scheme for Constraint Solver Extension
 In 4 th Intl. Conf. on Arti Intelligence and Symbolic Computation (AISC'98
, 1998
"... . In declarative programming languages based on the constraint programming paradigm, computations can be viewed as deductions and are enhanced with the use of constraint solvers. However, admissible constraints are restricted to formulae handled by solvers and thus, declarativity may be jeopardi ..."
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Cited by 5 (1 self)
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. In declarative programming languages based on the constraint programming paradigm, computations can be viewed as deductions and are enhanced with the use of constraint solvers. However, admissible constraints are restricted to formulae handled by solvers and thus, declarativity may be jeopardized. We present a domainindependent scheme for extending constraint solvers with new function symbols. This mechanism, called SoleX, consists of a collaboration of elementary solvers. They add and deduce information related to constraints involving new functions, complete the computation domain and purify constraints. Some extensions of computation domains have already been studied to demonstrate the broad scope of SoleX potential applications. 1 Introduction In the last decade constraint programming (CP) [8] emerged as a new programming paradigm. The basic notion of this framework is the separation between (1) a programming language to specify requirements (the constraints) on obje...
Handling ELAN rewrite programs via an exchange format
 Kirchner (Eds.), Proceedings Second International Workshop on Rewriting Logic and its Applications, ENTCS
, 1998
"... Designing a programming environment raises difficult implementation problems since such software is not just one piece of code able to execute programs expressed in a given programming language, but consists generally of several heterogeneous tools. The idea behind a data exchange format is to provi ..."
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Cited by 3 (1 self)
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Designing a programming environment raises difficult implementation problems since such software is not just one piece of code able to execute programs expressed in a given programming language, but consists generally of several heterogeneous tools. The idea behind a data exchange format is to provide a common representation for the interconnection of these different tools. Moreover, an exchange format is a way to handle programs like any kind of objects in the programming language, and so it is useful for instance in the context of the reflection problem. In this paper, we report our experiments with the current exchange format created and used by the actual implementation of the rulebased programming language ELAN. 1
System Description: Interface between Theorema And External Automated Deduction Systems
 In Linton and Sebastiani [175
, 2001
"... The interface between the Theorema system and external automated deduction systems is described. It provides a tool to access external provers within a Theorema session in the same way as \internal" Theorema provers. Currently 11 external systems are supported. The design of the interface allows ..."
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Cited by 3 (0 self)
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The interface between the Theorema system and external automated deduction systems is described. It provides a tool to access external provers within a Theorema session in the same way as \internal" Theorema provers. Currently 11 external systems are supported. The design of the interface allows combining external systems with each other as well as with \internal" Theorema provers.
Modeling Inheritance as Coercion in the Kenzo System
"... Abstract: In this paper the analysis of the data structures used in a symbolic computation system, called Kenzo, is undertaken. We deal with the specification of the inheritance relationship since Kenzo is an objectoriented system, written in CLOS, the Common Lisp Object System. We show how the ord ..."
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Cited by 3 (3 self)
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Abstract: In this paper the analysis of the data structures used in a symbolic computation system, called Kenzo, is undertaken. We deal with the specification of the inheritance relationship since Kenzo is an objectoriented system, written in CLOS, the Common Lisp Object System. We show how the ordersorted algebraic specification formalism can be adapted, through the “inheritance as coercion ” metaphor, in order to model the simple inheritance between structures in Kenzo.
VSDITLU: a verifiable symbolic definite integral table lookup
, 1999
"... We present a verifiable symbolic de nite integral table lookup: a system which matches a query, comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the tra ..."
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Cited by 2 (1 self)
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We present a verifiable symbolic de nite integral table lookup: a system which matches a query, comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. Our system is able to obtain correct answers in cases where standard techniques implemented in computer algebra systems fail. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman's webbased table by including parametric limits of integration and queries with side conditions.