Reasoning In Simple Type Theory PDF Download
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Author | : J. Roger Hindley |
Publisher | : Cambridge University Press |
Total Pages | : 200 |
Release | : 1997 |
Genre | : Computers |
ISBN | : 0521465184 |
Download Basic Simple Type Theory Book in PDF, ePub and Kindle
Type theory is one of the most important tools in the design of higher-level programming languages, such as ML. This book introduces and teaches its techniques by focusing on one particularly neat system and studying it in detail. By concentrating on the principles that make the theory work in practice, the author covers all the key ideas without getting involved in the complications of more advanced systems. This book takes a type-assignment approach to type theory, and the system considered is the simplest polymorphic one. The author covers all the basic ideas, including the system's relation to propositional logic, and gives a careful treatment of the type-checking algorithm that lies at the heart of every such system. Also featured are two other interesting algorithms that until now have been buried in inaccessible technical literature. The mathematical presentation is rigorous but clear, making it the first book at this level that can be used as an introduction to type theory for computer scientists.
Author | : Christoph Benzmüller |
Publisher | : |
Total Pages | : 467 |
Release | : 2008 |
Genre | : Mathematics |
ISBN | : 9781904987703 |
Download Reasoning in Simple Type Theory Book in PDF, ePub and Kindle
Reasoning in Simple Type Theory is a collection of papers that includes reprints of eight seminal papers in this area as well as thirteen new contributed articles. For the reprints we have chosen a paper by Alonzo Church (introducing his simple theory of types), a paper by Leon Henkin (proving completeness of Church's type theory relative to Henkin's semantics) and some of the most important papers by Peter Andrews. The new articles were contributed by Peter Andrews and his students and collaborators as well as a number of researchers his work has influenced. The volume intends to show the historical development of this important area of formal reasoning up to its current state of art and appears in honor of Peter Andrews on his 70th birthday.
Author | : William M. Farmer |
Publisher | : Springer Nature |
Total Pages | : 309 |
Release | : 2023-02-02 |
Genre | : Computers |
ISBN | : 303121112X |
Download Simple Type Theory Book in PDF, ePub and Kindle
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.
Author | : |
Publisher | : Univalent Foundations |
Total Pages | : 484 |
Release | : |
Genre | : |
ISBN | : |
Download Homotopy Type Theory: Univalent Foundations of Mathematics Book in PDF, ePub and Kindle
Author | : William Michael Farmer |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : Computer science |
ISBN | : 9783031211133 |
Download Simple Type Theory Book in PDF, ePub and Kindle
Author | : Chad E. Brown |
Publisher | : |
Total Pages | : 0 |
Release | : 2007 |
Genre | : Automatic theorem proving |
ISBN | : 9781904987574 |
Download Automated Reasoning in Higher-order Logic Book in PDF, ePub and Kindle
Many mathematical and computational concepts can be represented in a natural way using higher-order logic. Consequently, higher-order logic has become an important topic of research. /Automated Reasoning in Higher-Order Logic/ presents both a theoretical analysis of fragments of higher-order logic as well as a complete automated search procedure for an extensional form of higher-order logic. The first part of the book provides a detailed presentation of the theory (syntax and semantics) of fragments of higher-order logic. The fragments differ in the amount of extensionality and set comprehension principles included. Three families of sequent calculi are defined and proven sound and complete with respect to appropriate model classes. Using the model constructions in the book, different versions of Cantor's theorem are determined to not be provable in certain fragments. In fact, some versions of Cantor's theorem are independent of other versions (in sufficiently weak fragments). In the second part of the book, an automated proof procedure for extensional type theory is described. Proving completeness of such a higher-order search procedure is a nontrivial task. The book provides such a completeness proof by first proving completeness of the ground case and then proving appropriate lifting results. /Automated Reasoning in Higher-Order Logic/ is an essential document for researchers in higher-order logic and higher-order theorem proving. The book is also essential reading for programmers implementing or extending higher-order search procedures. Users of higher-order theorem provers can use the book to improve their understanding of the underlying logical systems.
Author | : Giovanni Sambin |
Publisher | : Clarendon Press |
Total Pages | : 294 |
Release | : 1998-10-15 |
Genre | : Mathematics |
ISBN | : 0191589039 |
Download Twenty Five Years of Constructive Type Theory Book in PDF, ePub and Kindle
Per Martin-Löf's work on the development of constructive type theory has been of huge significance in the fields of logic and the foundations of mathematics. It is also of broader philosophical significance, and has important applications in areas such as computing science and linguistics. This volume draws together contributions from researchers whose work builds on the theory developed by Martin-Löf over the last twenty-five years. As well as celebrating the anniversary of the birth of the subject it covers many of the diverse fields which are now influenced by type theory. It is an invaluable record of areas of current activity, but also contains contributions from N. G. de Bruijn and William Tait, both important figures in the early development of the subject. Also published for the first time is one of Per Martin-Löf's earliest papers.
Author | : Audun Jøsang |
Publisher | : Springer |
Total Pages | : 355 |
Release | : 2016-10-27 |
Genre | : Computers |
ISBN | : 3319423371 |
Download Subjective Logic Book in PDF, ePub and Kindle
This is the first comprehensive treatment of subjective logic and all its operations. The author developed the approach, and in this book he first explains subjective opinions, opinion representation, and decision-making under vagueness and uncertainty, and he then offers a full definition of subjective logic, harmonising the key notations and formalisms, concluding with chapters on trust networks and subjective Bayesian networks, which when combined form general subjective networks. The author shows how real-world situations can be realistically modelled with regard to how situations are perceived, with conclusions that more correctly reflect the ignorance and uncertainties that result from partially uncertain input arguments. The book will help researchers and practitioners to advance, improve and apply subjective logic to build powerful artificial reasoning models and tools for solving real-world problems. A good grounding in discrete mathematics is a prerequisite.
Author | : Zhaohui Luo |
Publisher | : |
Total Pages | : 0 |
Release | : 2023 |
Genre | : Computer science |
ISBN | : 9781383026337 |
Download Computation and Reasoning Book in PDF, ePub and Kindle
The book develops a type theory, studies its properties, and explains its uses in applications to computer science. In particular, it shows how the study of type theory may offer a powerful and uniform language for programming, program specification and development, and logical reasoning.
Author | : B. Jacobs |
Publisher | : Gulf Professional Publishing |
Total Pages | : 784 |
Release | : 2001-05-10 |
Genre | : Computers |
ISBN | : 9780444508539 |
Download Categorical Logic and Type Theory Book in PDF, ePub and Kindle
This book is an attempt to give a systematic presentation of both logic and type theory from a categorical perspective, using the unifying concept of fibred category. Its intended audience consists of logicians, type theorists, category theorists and (theoretical) computer scientists.