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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.

Proof theory --- Algebra --- Algèbre --- Data processing. --- Computer programs. --- Logiciels --- Computer programs --- Computer Science --- Mechanical Engineering - General --- Engineering & Applied Sciences --- Mathematics --- Mechanical Engineering --- Physical Sciences & Mathematics --- Information Technology --- Artificial Intelligence --- Computer science. --- Software engineering. --- Mathematical logic. --- Artificial intelligence. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Software Engineering. --- Mathematical Logic and Formal Languages. --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Computer software engineering --- Engineering --- Informatics --- Science --- Artificial Intelligence. --- Proof theory - Data processing --- Algebra - Computer programs

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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.

Mathematical logic --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- wiskunde --- software engineering --- logica --- robots

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This Festschrift, dedicated to Herman Geuvers on the occasion of his 60th birthday, contains papers written by many of his closest collaborators. Herman Geuvers is a full professor at Radboud University Nijmegen and holds a part-time professorship at Eindhoven University of Technology. He received his PhD from Radboud University in 1993 and he was promoted to full professor in Computer Assisted Reasoning in 2006. Prof. Geuvers is an internationally renowned researcher in the field of proof assistants, logic in computer science, lambda calculus, and type theory. He has been a steering committee chair of the TYPES and FSCD conferences, chair of related EU Cost Action projects, and program chair or editor of related conferences and special issues in the area of computer science logic. He is a successful, generous and inspiring advisor and educator. He has been director of education and director of research of the Computer Science Institute at Radboud University Nijmegen, and he is currently chair of the examination board of computer science and chair of the board of the Institute for Programming Research and Algorithmics, a Dutch national inter-university research school. The contributions in this volume reflect Prof. Geuvers’ main research interests.

Computer science. --- Computer science --- Mathematics. --- Computer Science. --- Computer Science Logic and Foundations of Programming. --- Mathematical Applications in Computer Science. --- Applications of Mathematics. --- Mathematics of Computing. --- Computer logic. --- Lambda calculus. --- Type theory.

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This volume contains the proceedings of the Sixth Workshop on Hybrid Systems: Computation and Control (HSCC 2003), which was held in Prague, during April 3–5, 2003. The Hybrid Systems workshops attract researchers interested in the modeling, analysis, control, and implementation of systems which involve the interaction of both discrete and continuous state dynamics. The newest results and latest developments in hybrid system models, formal methods for analysis and control, computational tools, as well as new applications and examples are presented at these annual meetings. The Sixth Workshop continued the series of workshops held in Grenoble, France (HART’97), Berkeley, California, USA (HSCC’98), Nijmegen, The Neth- lands (HSCC’99), Pittsburgh, Pennsylvania, USA (HSCC 2000), Rome, Italy (HSCC 2001), and Stanford, California, USA (HSCC 2002). Proceedings of these workshops have been published by Springer-Verlag in the Lecture Notes in C- puter Science (LNCS) series. This year we assembled a technical program committee with a broad expertise in formal methods in computer science, control theory, applied mathematics, and arti?cial intelligence. We received a set of 75 high-quality submitted papers. After detailed review and discussion of these papers by the program committee, 36 papers were accepted for presentation at the workshop, and the ?nal versions of these papers appear in this volume.

Hybrid computers --- Calculateurs hybrides --- Congresses. --- Congrès --- Digital control systems --- Electrical Engineering --- Computer Science --- Electrical & Computer Engineering --- Engineering & Applied Sciences --- Congrès --- Computer science. --- Microprocessors. --- Special purpose computers. --- Software engineering. --- Computers. --- Computer logic. --- Computer Science. --- Theory of Computation. --- Special Purpose and Application-Based Systems. --- Processor Architectures. --- Software Engineering. --- Computation by Abstract Devices. --- Logics and Meanings of Programs. --- Computer science logic --- Logic, Symbolic and mathematical --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Computer software engineering --- Engineering --- Special purpose computers --- Computers --- Minicomputers --- Informatics --- Science --- Automatic control --- Electronic digital computers --- Information theory. --- Logic design. --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Switching theory --- Communication theory --- Communication --- Hybrid computers - Congresses. --- Digital control systems - Congresses.

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This book constitutes the refereed proceedings of the Second International Conference on Interactive Theorem proving, ITP 2011, held in Berg en Dal, The Netherlands, in August 2011. The 25 revised full papers presented were carefully reviewed and selected from 50 submissions. Among the topics covered are counterexample generation, verification, validation, term rewriting, theorem proving, computability theory, translations from one formalism to another, and cooperation between tools. Several verification case studies were presented, with applications to computational geometry, unification, real analysis, etc.

Mathematical logic --- Logic --- Computer science --- Programming --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- ontwerpen --- programmeren (informatica) --- programmeertalen --- wiskunde --- software engineering --- robots