| 书目名称 | Theorem Proving with the Real Numbers |
| 编辑 | John Harrison |
| 视频video | |
| 概述 | Formal development of classical mathematics using a computer * Combines traditional lines of research in theorem proving and computer algebra * Shows usefulness of real numbers in verification |
| 丛书名称 | Distinguished Dissertations |
| 图书封面 |  |
| 描述 | This book discusses the use of the real numbers in theorem proving. Typ ically, theorem provers only support a few ‘discrete‘ datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of float ing point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We de scribe the rigorous definitional construction of the real numbers, using a new version of Cantor‘s method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the ‘Tarski subset‘ of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning. Finally, we consider in more detail two interesting application areas. We discuss the desirability of combining the rigour of theorem provers with the power and convenience of computer algebra systems, and |
| 出版日期 | Book 1998 |
| 关键词 | algebra; algorithms; calculus; computer science; interactive theorem proving; logic; mathematics; proving; t |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-1-4471-1591-5 |
| isbn_softcover | 978-1-4471-1593-9 |
| isbn_ebook | 978-1-4471-1591-5 |
| copyright | Springer-Verlag London Limited 1998 |
发表于 2025-3-21 19:34:46
