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Using Axiomatic Type Classes in Isabelle
, 2000
"... Isabelle o#ers ordersorted type classes on top of the simple types of plain HigherOrder Logic. The resulting type system is similar to that of the programming language Haskell. Its interpretation within the logic enables further application, though, apart from restricting polymorphism syntacticall ..."
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Cited by 4 (0 self)
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syntactically. In particular, the concept of Axiomatic Type Classes provides a useful lightweight mechanism for hierarchicallystructured abstract theories. Subsequently, we demonstrate typical uses of Isabelle's axiomatic type classes to model basic algebraic structures. This document describes axiomatic
Organizing numerical theories using axiomatic type classes
 Journal of Automated Reasoning
, 2004
"... Mathematical reasoning may involve several arithmetic types, including those of the natural, integer, rational, real and complex numbers. These types satisfy many of the same algebraic laws. These laws need to be made available to users, uniformly and preferably without repetition, but with due acco ..."
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Cited by 9 (2 self)
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account for the peculiarities of each type. Subtyping, where a type inherits properties from a supertype, can eliminate repetition only for a fixed type hierarchy set up in advance by implementors. The approach recently adopted for Isabelle uses axiomatic type classes, an established approach
Molecular classification of cancer: class discovery and class prediction by gene expression monitoring
 Science
, 1999
"... Although cancer classification has improved over the past 30 years, there has been no general approach for identifying new cancer classes (class discovery) or for assigning tumors to known classes (class prediction). Here, a generic approach to cancer classification based on gene expression monitori ..."
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Cited by 1777 (19 self)
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derived class predictor was able to determine the class of new leukemia cases. The results demonstrate the feasibility of cancer classification based solely on gene expression monitoring and suggest a general strategy for discovering and predicting cancer classes for other types of cancer, independent
GromovWitten classes, quantum cohomology, and enumerative geometry
 Commun. Math. Phys
, 1994
"... The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological ..."
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Cited by 474 (3 self)
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The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov–Witten classes, and a discussion of their properties for Fano varieties. Cohomological
Algebraic laws for nondeterminism and concurrency
 Journal of the ACM
, 1985
"... Abstract. Since a nondeterministic and concurrent program may, in general, communicate repeatedly with its environment, its meaning cannot be presented naturally as an input/output function (as is often done in the denotational approach to semantics). In this paper, an alternative is put forth. Firs ..."
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Cited by 608 (13 self)
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observation congruence class. The paper demonstrates, for a sequence of simple languages expressing finite (terminating) behaviors, that in each case observation congruence can be axiomatized algebraically. Moreover, with the addition of recursion and another simple extension, the algebraic language described
A Survey of Image Registration Techniques
 ACM Computing Surveys
, 1992
"... Registration is a fundamental task in image processing used to match two or more pictures taken, for example, at different times, from different sensors or from different viewpoints. Over the years, a broad range of techniques have been developed for the various types of data and problems. These ..."
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Cited by 979 (2 self)
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of distortions are distinguished. The first type are those which are the source of misregistration, i.e., they are the cause of the misalignment between the two images. Distortions which are the source of misregistration determine the transformation class which will optimally align the two images
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a qanalogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order differenti ..."
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Cited by 577 (6 self)
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differential or difference equation, the forward and backward shift operator, the Rodriguestype formula and generating functions of all classes of orthogonal polynomials in this scheme. In chapter 2 we give the limit relations between different classes of orthogonal polynomials listed in the Askey
Featherweight Java: A Minimal Core Calculus for Java and GJ
 ACM Transactions on Programming Languages and Systems
, 1999
"... Several recent studies have introduced lightweight versions of Java: reduced languages in which complex features like threads and reflection are dropped to enable rigorous arguments about key properties such as type safety. We carry this process a step further, omitting almost all features of the fu ..."
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Cited by 659 (23 self)
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computational “feel, ” providing classes, methods, fields, inheritance, and dynamic typecasts with a semantics closely following Java’s. A proof of type safety for Featherweight Java thus illustrates many of the interesting features of a safety proof for the full language, while remaining pleasingly compact
Domain names  Implementation and Specification
 RFC883, USC/Information Sciences Institute
, 1983
"... This RFC describes the details of the domain system and protocol, and assumes that the reader is familiar with the concepts discussed in a companion RFC, "Domain Names Concepts and Facilities " [RFC1034]. The domain system is a mixture of functions and data types which are an official pr ..."
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Cited by 724 (9 self)
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This RFC describes the details of the domain system and protocol, and assumes that the reader is familiar with the concepts discussed in a companion RFC, "Domain Names Concepts and Facilities " [RFC1034]. The domain system is a mixture of functions and data types which are an official
No Free Lunch Theorems for Optimization
, 1997
"... A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset by performan ..."
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Cited by 961 (10 self)
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A framework is developed to explore the connection between effective optimization algorithms and the problems they are solving. A number of “no free lunch ” (NFL) theorems are presented which establish that for any algorithm, any elevated performance over one class of problems is offset
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