The Seventeen Provers of the World: Foreword by Dana S. Scott (Lecture Notes in Computer Science)

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. Informal / Henk Barendregt -- Hol / John Harrison, Konrad Slind, Rob Arthan -- Mizar / Andrzej Trybulec -- Pvs / Bart Jacobs, John Rushby -- Coq / Laurent Théry, Pierre Letouzey, Georges Gonthier -- Otter/ivy / Michael Beeson, William Mccune -- Isabelle/isar / Markus Wenzel, Larry Paulson -- Alfa/agda / Thierry Coquand -- Acl2 / Ruben Gamboa -- Phox / Christophe Raffalli, Paul Rozière -- Imps / William Farmer -- Metamath / Norman Megill -- Theorema / Wolfgang Windsteiger, Bruno Buchberger, Markus Rosenkranz -- Lego / Conor Mcbride -- Nupri / Paul Jackson -- Omega / Christoph Benzmüller [and Others] -- B Method / Dominique Cansell -- Minlog / Helmut Schwichtenberg. Freek Wiedijk (ed.) ; Foreword By Dana S. Scott. Includes Bibliographical References And Index. Also Issued Online. Front Matter....Pages - Introduction....Pages 1-9 Informal....Pages 10-10 HOL....Pages 11-19 Mizar....Pages 20-23 PVS....Pages 24-27 Coq....Pages 28-35 Otter/Ivy....Pages 36-40 Isabelle/Isar....Pages 41-49 Alfa/Agda....Pages 50-54 ACL2....Pages 55-66 PhoX....Pages 67-71 IMPS....Pages 72-87 Metamath....Pages 88-95 Theorema....Pages 96-107 Lego....Pages 108-115 Nuprl....Pages 116-126 Ωmega....Pages 127-141 B Method....Pages 142-150 Minlog....Pages 151-157 Back Matter....Pages - "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."--Jacket