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E-raamat: Seventeen Provers of the World: Foreword by Dana S. Scott

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Commemorating the 50th anniversary of the first time a mathematical theorem was proven by a computer system, Freek Wiedijk initiated the present book in 2004 by inviting formalizations of a proof of the irrationality of the square root of two from scientists using various theorem proving systems.





The 17 systems included in this volume are among the most relevant ones for the formalization of mathematics. The systems are showcased by presentation of the formalized proof and a description in the form of answers to a standard questionnaire. The 17 systems presented are HOL, Mizar, PVS, Coq, Otter/Ivy, Isabelle/Isar, Alfa/Agda, ACL2, PhoX, IMPS, Metamath, Theorema, Leog, Nuprl, Omega, B method, and Minlog.

Arvustused

From the reviews:









"The central idea of the book is to provide a comparisonsomehow on the surfaceof different proof systems. the book is accessible to everybody with elementary school knowledge of mathematics. this book is a must for everybody developing a proof system. Everybody who uses (or like to use) a theorem prover will find it useful. it is essential to locate your prover in the world of theorem proving." (Reinhard Kahle, Studia Logica, Vol. 87, 2007)

Introduction 1(9)
Freek Wiedijk
Informal
10(1)
Henk Barendregt
Hol
11(9)
John Harrison
Konrad Slind
Rob Arthan
Mizar
20(4)
Andrzej Trybulec
PVS
24(4)
Bart Jacobs
John Rushby
Coq
28(8)
Laurent Thery
Pierre Letouzey
Georges Gonthier
Otter/Ivy
36(5)
Michael Beeson
William McCune
Isabelle/Isar
41(9)
Markus Wenzel
Larry Paulson
Alfa/Agda
50(5)
Thierry Coquand
ACL2
55(12)
Ruben Gamboa
PhoX
67(5)
Christophe Raffalli
Paul Roziere
IMPS
72(16)
William Farmer
Metamath
88(8)
Norman Megill
Theorema
96(12)
Wolfgang Windsteiger
Bruno Buchberger
Markus Rozenkranz
Lego
108(8)
Conor McBride
Nuprl
116(11)
Paul Jackson
Omega
127(15)
Christoph Benzmuller
Armin Fiedler
Andreas Meier
Martin Pollet
Jorg Siekmann
B Method
142(9)
Dominique Cansell
Minlog
151(8)
Helmut Schwichtenberg
Author Index 159