Authors:
- First book of its kind on Simple Type Theory
- Provides tools for building mathematics libraries
- Provides a practical logic
Part of the book series: Computer Science Foundations and Applied Logic (CSFAL)
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Table of contents (15 chapters)
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Front Matter
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Back Matter
About this book
The book is an introduction to simple type theory, a classical higher-order version of predicate logic that extends first-order logic. It presents a practice-oriented logic called Alonzo that is based on Alonzo Church's formulation of simple type theory known as Church's type theory. Unlike traditional predicate logics, Alonzo admits undefined expressions. The book illustrates, using Alonzo, how simple type theory is suited ideally for reasoning about mathematical structures and constructing libraries of mathematical knowledge.
Topics and features:
- Offers the first book-length introduction to simple type theory as a predicate logic
- Provides the reader with a logic that is close to mathematical practice
- Presents the tools needed to build libraries of mathematical knowledge
- Employs two semantics, one for mathematics and one for logic
- Emphasizes the model-theoretic view of predicate logic
- Includes several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks
Aimed at students of computing and mathematics at the graduate or upper-undergraduate level, this book is also well-suited for mathematicians, computing professionals, engineers, and scientists who need a practical logic for expressing and reasoning about mathematical ideas.
William M. Farmer is a Professor in the Department of Computing and Software at McMaster University in Hamilton, Ontario, Canada.
Reviews
Authors and Affiliations
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Department of Computing and Software, McMaster University, Hamilton, Canada
William M. Farmer
About the author
Dr. Farmer's research interests are logic, mechanized mathematics, mathematical knowledge management, and formal methods. One of his most significant achievements is the design and implementation of the IMPS proof assistant, which was done at MITRE in partnership with Dr. JoshuaGuttman and Dr. Javier Thayer. His work on IMPS has lead to research on developing practice-oriented logics and set theories and on organizing mathematical knowledge as a network of interconnected axiomatic theories. He and Dr. Jacques Carette are currently leading the MathScheme project at McMaster with the aim of developing a framework for integrating axiomatic and algorithmic mathematics. On this project Dr. Farmer has focused on how to reason about the interplay of syntax and semantics, as exhibited in syntax-based mathematical algorithms like symbolic differentiation, within a logic equipped with global quotation and evaluation operators. Dr. Farmer has had a career-long interest in using simple type theory as a practical logic for expressing and reasoning about mathematical ideas. He is the author of "The Seven Virtues of Simple Type Theory", Journal of Applied Logic, 6:267-286, 2008, one of the leading references on simple type theory.
Bibliographic Information
Book Title: Simple Type Theory
Book Subtitle: A Practical Logic for Expressing and Reasoning About Mathematical Ideas
Authors: William M. Farmer
Series Title: Computer Science Foundations and Applied Logic
DOI: https://doi.org/10.1007/978-3-031-21112-6
Publisher: Birkhäuser Cham
eBook Packages: Computer Science, Computer Science (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-21111-9Published: 02 January 2023
Softcover ISBN: 978-3-031-21114-0Published: 03 January 2024
eBook ISBN: 978-3-031-21112-6Published: 01 January 2023
Series ISSN: 2731-5754
Series E-ISSN: 2731-5762
Edition Number: 1
Number of Pages: XIV, 295
Number of Illustrations: 7 b/w illustrations, 3 illustrations in colour
Topics: Logics and Meanings of Programs, Mathematical Logic and Foundations, Theory of Computation, Philosophy of Science