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Inductive datatypes in HOL  lessons learned in FormalLogic Engineering
 Theorem Proving in Higher Order Logics: TPHOLs ’99, LNCS 1690
, 1999
"... Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also su ..."
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Cited by 42 (6 self)
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Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also support inverted datatype definitions for characterizing existing types as being inductive ones later. All our constructions are fully definitional according to established HOL tradition. Stepping back from the logical details, we also see this work as a typical example of what could be called "FormalLogic Engineering". We observe that building realistic theorem proving environments involves further issues rather than pure logic only. 1
The Impact of the Lambda Calculus in Logic and Computer Science
 Bulletin of Symbolic Logic
, 1997
"... One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the represent ..."
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Cited by 23 (0 self)
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One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand. Acknowledgement. The following persons provided help in various ways. Erik Barendsen, Jon Barwise, Johan van Benthem, Andreas Blass, Olivier Danvy, Wil Dekkers, Marko van Eekelen, Sol Feferman, Andrzej Filinski, Twan Laan, Jan Kuper, Pierre Lescanne, Hans Mooij, Robert Maron, Rinus Plasmeijer, Randy Pollack, Kristoffer Rose, Richard Shore, Rick Statman and Simon Thompson. Partial support came from the European HCM project Typed lambda calculus (CHRXCT920046), the Esprit Working Group Types (21900) and the Dutch NWO project WINST (612316607). 1. Introduction This paper is written to honor Church's gr...
ComputerAssisted Mathematics at Work  The HahnBanach Theorem in Isabelle/Isar
 TYPES FOR PROOFS AND PROGRAMS: TYPES’99, LNCS
, 2000
"... We present a complete formalization of the HahnBanach theorem in the simplytyped settheory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides ..."
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Cited by 7 (4 self)
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We present a complete formalization of the HahnBanach theorem in the simplytyped settheory of Isabelle/HOL, such that both the modeling of the underlying mathematical notions and the full proofs are intelligible to human readers. This is achieved by means of the Isar environment, which provides a framework for highlevel reasoning based on natural deduction. The final result is presented as a readable formal proof document, following usual presentations in mathematical textbooks quite closely. Our case study demonstrates that Isabelle/Isar is capable to support this kind of application of formal logic very well, while being open for an even larger scope.
Structure and Hierarchy in RealTime Systems
, 2002
"... The development of digital systems is particularly challenging, if their correctness depends on the right timing of operations. One approach to enhance the reliability of such systems is modelbased development. This allows for a formal analysis throughout all stages of design. Modelbased ..."
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Cited by 4 (0 self)
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The development of digital systems is particularly challenging, if their correctness depends on the right timing of operations. One approach to enhance the reliability of such systems is modelbased development. This allows for a formal analysis throughout all stages of design. Modelbased
Problems in type theory
 Computational Logic, Proceedings of the NATO Advanced Study Institute on Computational Logic, held in Marktoberdorf, 1997, volume 165 of Series F: ZF a hack? 19 Computer and Systems Sciences
, 1999
"... In this paper the reader will be introduced to type theories (predicative and impredicative, with and without inductive types) by ashort section giving theoretical background and by another section with exercises about thecalculusofconstructions and its ne structure the lambda cube. 1. Background Ma ..."
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Cited by 2 (0 self)
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In this paper the reader will be introduced to type theories (predicative and impredicative, with and without inductive types) by ashort section giving theoretical background and by another section with exercises about thecalculusofconstructions and its ne structure the lambda cube. 1. Background Mathematics consists of de ning, reasoning and computing. Type systems are designed to represent mathematics in such a way that it can be veri ed automatically whether the de nitions are wellformed, the derivations are correct and the computations are performed by a simple underlying reduction system. This veri cation method is expected to be useful for the development of mathematics and the teaching of it. Also for the veri cation of hardware and software systems. See Barendregt [1996] and [1997] for a discussion and more information. Type systems as presented are based on work of Russell and Whitehead
(CHRXCT920046), the Esprit Working Group Types (21900)and the DutchNWO
, 1997
"... One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the represent ..."
Abstract
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One of the most important contributions of A. Church to logic is his invention of the lambda calculus. We present the genesis of this theory and its two major areas of application: the representation of computations and the resulting functional programming languages on the one hand and the representation of reasoning and the resulting systems of computer mathematics on the other hand. Acknowledgement. The following persons provided help in various ways. Erik