Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy write by Klaus Mainzer. This book was released on 2018-05-30. Proof And Computation: Digitization In Mathematics, Computer Science And Philosophy available in PDF, EPUB and Kindle. This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes Predicative Foundations, Constructive Mathematics and Type Theory, Computation in Higher Types, Extraction of Programs from Proofs, and Algorithmic Aspects in Financial Mathematics. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
Proofs and Computations
Proofs and Computations - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proofs and Computations write by Helmut Schwichtenberg. This book was released on 2011-12-15. Proofs and Computations available in PDF, EPUB and Kindle. Driven by the question, 'What is the computational content of a (formal) proof?', this book studies fundamental interactions between proof theory and computability. It provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science. Part I covers basic proof theory, computability and Gödel's theorems. Part II studies and classifies provable recursion in classical systems, from fragments of Peano arithmetic up to Π11–CA0. Ordinal analysis and the (Schwichtenberg–Wainer) subrecursive hierarchies play a central role and are used in proving the 'modified finite Ramsey' and 'extended Kruskal' independence results for PA and Π11–CA0. Part III develops the theoretical underpinnings of the first author's proof assistant MINLOG. Three chapters cover higher-type computability via information systems, a constructive theory TCF of computable functionals, realizability, Dialectica interpretation, computationally significant quantifiers and connectives and polytime complexity in a two-sorted, higher-type arithmetic with linear logic.
Computation, Proof, Machine
Computation, Proof, Machine - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computation, Proof, Machine write by Gilles Dowek. This book was released on 2015-05-05. Computation, Proof, Machine available in PDF, EPUB and Kindle. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation.
Proof and Computation
Proof and Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof and Computation write by Helmut Schwichtenberg. This book was released on 2011-12-22. Proof and Computation available in PDF, EPUB and Kindle. Logical concepts and methods are of growing importance in many areas of computer science. The proofs-as-programs paradigm and the wide acceptance of Prolog show this clearly. The logical notion of a formal proof in various constructive systems can be viewed as a very explicit way to describe a computation procedure. Also conversely, the development of logical systems has been influenced by accumulating knowledge on rewriting and unification techniques. This volume contains a series of lectures by leading researchers giving a presentation of new ideas on the impact of the concept of a formal proof on computation theory. The subjects covered are: specification and abstract data types, proving techniques, constructive methods, linear logic, and concurrency and logic.
Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification
Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification write by Klaus Mainzer. This book was released on 2021-07-27. Proof And Computation Ii: From Proof Theory And Univalent Mathematics To Program Extraction And Verification available in PDF, EPUB and Kindle. This book is for graduate students and researchers, introducing modern foundational research in mathematics, computer science, and philosophy from an interdisciplinary point of view. Its scope includes proof theory, constructive mathematics and type theory, univalent mathematics and point-free approaches to topology, extraction of certified programs from proofs, automated proofs in the automotive industry, as well as the philosophical and historical background of proof theory. By filling the gap between (under-)graduate level textbooks and advanced research papers, the book gives a scholarly account of recent developments and emerging branches of the aforementioned fields.
