Formalization Of Complex Analysis And Matrix Theory
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Formalization of Complex Analysis and Matrix Theory
This book discusses the formalization of mathematical theories centering on complex analysis and matrix theory, covering topics such as algebraic systems, complex numbers, gauge integration, the Fourier transformation and its discrete counterpart, matrices and their transformation, inner product spaces, and function matrices. The formalization is performed using the interactive theorem prover HOL4, chiefly developed at the University of Cambridge. Many of the developments presented are now integral parts of the library of this prover. As mathematical developments continue to gain in complexity, sometimes demanding proofs of enormous sizes, formalization has proven to be invaluable in terms of obtaining real confidence in their correctness. This book provides a basis for the computer-aided verification of engineering systems constructed using the principles of complex analysis and matrix theory, as well as building blocks for the formalization of more involved mathematical theories.
Formal Methods for Industrial Critical Systems
This book constitutes the proceedings of the 19th International Conference on Formal Methods for Industrial Critical Systems, FMICS 2014, held in Florence, Italy, in September 2014. The 13 papers presented in this volume were carefully reviewed and selected from 26 submissions. They are organized in topical sections named: cyber-physical systems; computer networks; railway control systems; verification methods; and hardware and software testing.
Theorem Proving in Higher Order Logics
Author: Joe Hurd
language: en
Publisher: Springer Science & Business Media
Release Date: 2005-08-08
This book constitutes the refereed proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, held in Oxford, UK, in August 2005. The 20 revised full papers presented together with 2 invited papers and 4 proof pearls (concise and elegant presentations of interesting examples) were carefully reviewed and selected from 49 submissions. All current issues in HOL theorem proving and formal verification of software and hardware systems are addressed. Among the topics of this volume are theorem proving, verification, recursion and induction, mechanized proofs, mathematical logic, proof theory, type systems, program verification, and proving systems like HOL, Coq, ACL2, Isabelle/HOL and Isabelle/HOLCF.