The Seventeen Provers of the World

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.

• Coq
• Isabelle
• computer algebra systems
• formal methods
• formal reasoning systems
• formal verification
• formalization
• mathematical formalizations
• mathematical proof assistants
• mathematics
• provers
• proving
• theorem proving
• theorem proving systems

From the reviews:

"The central idea of the book is to provide a comparison–somehow on the surface–of 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)

• Institute for Computing and Information Sciences, Radboud University Nijmegen, Nijmegen, The Netherlands

  Freek Wiedijk