home libri books Fumetti ebook dvd top ten sconti 0 Carrello

Torna Indietro

farmer william m. - simple type theory

Simple Type Theory A Practical Logic for Expressing and Reasoning About Mathematical Ideas

Disponibilità: Normalmente disponibile in 15 giorni

91,98 €
87,38 €

Questo prodotto usufruisce delle SPEDIZIONI GRATIS
selezionando l'opzione Corriere Veloce in fase di ordine.

Pagabile anche con 18App Bonus Cultura e Carta del Docente

Facebook Twitter Aggiungi commento

Spese Gratis


Lingua: Inglese


Pubblicazione: 01/2023
Edizione: 1st ed. 2023


This unique textbook, in contrast to a standard logic text, provides the reader with a logic that actually can be used in practice to express and reason about mathematical ideas.

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.


Preface.- 1 Introduction.- 2  Answers to Readers’ Questions.- 3 Preliminary Concepts.- 4 Syntax.- 5 Semantics.- 6 Additional Notation.- 7 Beta-reduction and Substitution.- 8 Proof Systems.- 9 Theories.- 10 Sequences.- 11 Developments.- 12 Real Number Mathematics.- 13 Morphisms 14 Alonzo Variants.- 15 Software Support.- Appendix A: Metatheorems of µ.- Appendix B: Soundness of µ.- Appendix C: Henkin’s Theorem for µ.- Bibliography.- List of Figures.- List of Tables.- List of Theorems, Examples, Remarks, and Modules.- Index


William M. Farmer has over 35 years of experience working in industry and academia in computing and mathematics. He received a B.A. in mathematics from the University of Notre Dame in 1978 and an M.A. in mathematics in 1980, an M.S. in computer sciences in 1983, and a Ph.D. in mathematics in 1984 from the University of Wisconsin-Madison. He is currently a Professor in the Department of Computing and Software at McMaster University. Before joining McMaster in 1999, he conducted research in computer science for twelve years at The MITRE Corporation in Bedford, Massachusetts, USA and taught computer programming and networking courses for two years at St. Cloud State University. 

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. Joshua Guttman 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.

Altre Informazioni



Condizione: Nuovo
Collana: Computer Science Foundations and Applied Logic
Dimensioni: 235 x 155 mm Ø 635 gr
Formato: Copertina rigida
Illustration Notes:XIV, 295 p. 10 illus., 3 illus. in color.
Pagine Arabe: 295
Pagine Romane: xiv

Dicono di noi