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MBase: Representing Knowledge and Context for the Integration of Mathematical Software Systems
, 2000
"... In this article we describe the data model of the MBase system, a webbased, ..."
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In this article we describe the data model of the MBase system, a webbased,
Models for Persistence in Lazy Functional Programming Systems
, 1993
"... Research into providing support for long term data in lazy functional programming systems is presented in this thesis. The motivation for this work has been to reap the benefits of integrating lazy functional programming languages and persistence. The benefits are . the programmer need not write cod ..."
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Cited by 9 (0 self)
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Research into providing support for long term data in lazy functional programming systems is presented in this thesis. The motivation for this work has been to reap the benefits of integrating lazy functional programming languages and persistence. The benefits are . the programmer need not write code to support long term data since this is provided as part of the programming system . persistent data can be used in a type safe way since the programming language type system applies to data with the whole range of persistence . the benefits of lazy evaluation are extended to the full lifetime of a data value. Whilst data is reachable, any evaluation performed on the data persists. A data value changes monotonically from an unevaluated state towards a completely evaluated state over time. . interactive data intensive applications such as functional databases can be developed. These benefits are realised by the development of models for persistence in lazy functional programming systems. Tw...
ΩMKRP: A Proof Development Environment
 PROCEEDINGS OF THE 12TH CADE
, 1994
"... In the following we describe the basic ideas underlying\Omega\Gamma mkrp, an interactive proof development environment [6]. The requirements for this system were derived from our experiences in proving an interrelated collection of theorems of a typical textbook on semigroups and automata [3] wi ..."
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In the following we describe the basic ideas underlying\Omega\Gamma mkrp, an interactive proof development environment [6]. The requirements for this system were derived from our experiences in proving an interrelated collection of theorems of a typical textbook on semigroups and automata [3] with the firstorder theorem prover mkrp [11]. An important finding was that although current automated theorem provers have evidently reached the power to solve nontrivial problems, they do not provide sufficient assistance for proving the theorems contained in such a textbook. On account of this, we believe that significantly more support for proof development can be provided by a system with the following two features:  The system must provide a comfortable humanoriented problemsolving environment. In particular, a human user should be able to specify the problem to be solved in a natural way and communicate on proof
Functional Programming in a Basic Database Course
, 1995
"... This paper describes why and how a functional programming language was used in an introductory database course. The purpose of the programming exercises in this course is to give students a better understanding of the internal structure and use of databases and database management systems. We used a ..."
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This paper describes why and how a functional programming language was used in an introductory database course. The purpose of the programming exercises in this course is to give students a better understanding of the internal structure and use of databases and database management systems. We used a functional language for its high level of abstraction and the automatic memory management which make writing a simple database management system considerably easier. Although the students had no previous knowledge of functional programming, they were capable to obtain useful experience in the database field. In order to enable students to concentrate on the database aspects of the exercises and to make rather elaborated systems in a limited amount of time, we supplied skeletons of the programs to make. Only the parts that are the core of the exercise had to be written by the students. The exercises appear to serve their purpose very well. The corresponding parts of the exams are made consid...
BERNAYS AND SET THEORY
"... Abstract. We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higherorder reflection principles. Paul Isaak Bernays (1888–1977) is an important figure in the development of mathematical logic, being the main bridge between Hilbert and Göd ..."
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Abstract. We discuss the work of Paul Bernays in set theory, mainly his axiomatization and his use of classes but also his higherorder reflection principles. Paul Isaak Bernays (1888–1977) is an important figure in the development of mathematical logic, being the main bridge between Hilbert and Gödel in the intermediate generation and making contributions in proof theory, set theory, and the philosophy of mathematics. Bernays is best known for the twovolume 1934,1939 Grundlagen der Mathematik [39, 40], written solely by him though Hilbert was retained as first author. Going into many reprintings and an eventual second edition thirty years later, this monumental work provided a magisterial exposition of the work of the Hilbert school in the formalization of firstorder logic and in proof theory and the work of Gödel on incompleteness and its surround, including the first complete proof of the Second Incompleteness Theorem. 1 Recent reevaluation of Bernays ’ role actually places him at the center of the development of mathematical logic and Hilbert’s program. 2 But starting in his forties, Bernays did his most individuated, distinctive mathematical work in set theory, providing a timely axiomatization and later applying higherorder reflection principles, and produced a stream of
On the Origins of Bisimulation and
"... Bisimulation and bisimilarity are coinductive notions, and as such are intimately related to fixed points, in particular greatest fixed points. Therefore also the appearance of coinduction and fixed points is discussed, though in this case only within Computer Science. The paper ends with some histo ..."
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Bisimulation and bisimilarity are coinductive notions, and as such are intimately related to fixed points, in particular greatest fixed points. Therefore also the appearance of coinduction and fixed points is discussed, though in this case only within Computer Science. The paper ends with some historical remarks on the main fixedpoint theorems (such as KnasterTarski) that underpin the fixedpoint theory presented.