Basic Simple Type Theory
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Basic Simple Type Theory
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Author : J. Roger Hindley
language : en
Publisher: Cambridge University Press
Release Date : 1997
Basic Simple Type Theory written by J. Roger Hindley and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Computers categories.
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.
Simple Type Theory
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Author : William M. Farmer
language : en
Publisher: Springer Nature
Release Date : 2025-04-23
Simple Type Theory written by William M. Farmer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-04-23 with Computers categories.
This unique textbook, in contrast to a standard logic text, provides the reader with a logic that 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. For this second edition, more than 400 additions, corrections, and improvements have been made, including a new chapter on inductive sets and types. Topics and features: !-- [if !supportLists]--· !--[endif]--Offers the first book-length introduction to simple type theory as a predicate logic !-- [if !supportLists]--· !--[endif]--Provides the reader with a logic that is close to mathematical practice !-- [if !supportLists]--· !--[endif]--Includes a module system for building libraries of mathematical knowledge !-- [if !supportLists]--· !--[endif]--Employs two semantics, one for mathematics and one for logic !-- [if !supportLists]--· !--[endif]--Emphasizes the model-theoretic view of predicate logic !-- [if !supportLists]--· !--[endif]--Presents several important topics, such as definite description and theory morphisms, not usually found in standard logic textbooks Aimed at students of mathematics and computing at the graduate or upper-undergraduate level, this book is 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.
Lambda Calculus With Types
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Author : Henk Barendregt
language : en
Publisher: Cambridge University Press
Release Date : 2013-06-20
Lambda Calculus With Types written by Henk Barendregt and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-20 with Mathematics categories.
This handbook with exercises reveals in formalisms, hitherto mainly used for hardware and software design and verification, unexpected mathematical beauty. The lambda calculus forms a prototype universal programming language, which in its untyped version is related to Lisp, and was treated in the first author's classic The Lambda Calculus (1984). The formalism has since been extended with types and used in functional programming (Haskell, Clean) and proof assistants (Coq, Isabelle, HOL), used in designing and verifying IT products and mathematical proofs. In this book, the authors focus on three classes of typing for lambda terms: simple types, recursive types and intersection types. It is in these three formalisms of terms and types that the unexpected mathematical beauty is revealed. The treatment is authoritative and comprehensive, complemented by an exhaustive bibliography, and numerous exercises are provided to deepen the readers' understanding and increase their confidence using types.
Applied Logic For Computer Scientists
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Author : Mauricio Ayala-Rincón
language : en
Publisher: Springer
Release Date : 2017-02-04
Applied Logic For Computer Scientists written by Mauricio Ayala-Rincón and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-04 with Computers categories.
This book provides an introduction to logic and mathematical induction which are the basis of any deductive computational framework. A strong mathematical foundation of the logical engines available in modern proof assistants, such as the PVS verification system, is essential for computer scientists, mathematicians and engineers to increment their capabilities to provide formal proofs of theorems and to certify the robustness of software and hardware systems. The authors present a concise overview of the necessary computational and mathematical aspects of ‘logic’, placing emphasis on both natural deduction and sequent calculus. Differences between constructive and classical logic are highlighted through several examples and exercises. Without neglecting classical aspects of computational logic, the authors also highlight the connections between logical deduction rules and proof commands in proof assistants, presenting simple examples of formalizations of the correctness of algebraic functions and algorithms in PVS. Applied Logic for Computer Scientists will not only benefit students of computer science and mathematics but also software, hardware, automation, electrical and mechatronic engineers who are interested in the application of formal methods and the related computational tools to provide mathematical certificates of the quality and accuracy of their products and technologies.
Trends In Functional Programming
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Author : William J. Bowman
language : en
Publisher: Springer Nature
Release Date : 2020-05-11
Trends In Functional Programming written by William J. Bowman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-05-11 with Computers categories.
This book constitutes the thoroughly refereed revised selected papers of the 20th International Symposium on Trends in Functional Programming, TFP 2019, held in Vancouver, Canada, in June 2019. The 6 revised full papers were selected from 11 submissions and present papers in all aspects of functional programming, taking a broad view of current and future trends in the area. It aspires to be a lively environment for presenting the latest research results, and other contributions, described in draft papers submitted prior to the symposium.
Typed Lambda Calculi And Applications
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Author : Simona Ronchi Della Rocca
language : en
Publisher: Springer
Release Date : 2007-07-11
Typed Lambda Calculi And Applications written by Simona Ronchi Della Rocca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-07-11 with Mathematics categories.
This book constitutes the refereed proceedings of the 8th International Conference on Typed Lambda Calculi and Applications, TLCA 2007, held in Paris, France in June 2007 in conjunction with RTA 2007, the 18th International Conference on Rewriting Techniques and Applications as part of RDP 2007, the 4th International Conference on Rewriting, Deduction, and Programming. The 25 revised full papers presented together with 2 invited talks were carefully reviewed and selected from 52 submissions. The papers present original research results that are broadly relevant to the theory and applications of typed calculi and address a wide variety of topics such as proof-theory, semantics, implementation, types, and programming.
Handbook Of Automated Reasoning
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Author : Alan J.A. Robinson
language : en
Publisher: Elsevier
Release Date : 2001-06-21
Handbook Of Automated Reasoning written by Alan J.A. Robinson and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-21 with Computers categories.
Handbook of Automated Reasoning.
Axiomatic Thinking I
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Author : Fernando Ferreira
language : en
Publisher: Springer Nature
Release Date : 2022-10-13
Axiomatic Thinking I written by Fernando Ferreira and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-13 with Mathematics categories.
In this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere. The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come. The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations. Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Logic Methodology And Philosophy Of Science Iii
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Author : Lev D. Beklemishev
language : en
Publisher: Elsevier
Release Date : 2000-04-01
Logic Methodology And Philosophy Of Science Iii written by Lev D. Beklemishev and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-04-01 with Computers categories.
Logic, Methodology and Philosophy of Science III
Dictionary Of World Philosophy
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Author : A. Pablo Iannone
language : en
Publisher: Routledge
Release Date : 2013-04-15
Dictionary Of World Philosophy written by A. Pablo Iannone and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-15 with Philosophy categories.
The Dictionary of World Philosophy covers the diverse and challenging terminology, concepts, schools and traditions of the vast field of world philosophy. Providing an extremely comprehensive resource and an essential point of reference in a complex and expanding field of study the Dictionary covers all major subfields of the discipline. Key features: * Cross-references are used to highlight interconnections and the cross-cultural diffusion and adaptation of terms which has taken place over time * The user is led from specific terms to master entries which provide valuable historical and cultural context * Each master entry is followed by at least two suggestions for further reading on the subject, creating a substantial bibliography of world philosophy * References extend beyond philosophy to related areas such as cognitive science, computer science, language and physics Subdisciplines covered include:* aesthetics * ethics * sociopolitical philosophy * the philosophy of law * epistemology * logic * the philosophy of science * the philosophy of mind * the philosophy of culture and history * metaphysics * the philosophy of religion Entries are drawn from West Africa, Arabic, Chinese, Indian, Japanese, Jewish, Korean, Latin American, Maori and Native American philosophy including the important and so far largely neglected instance of Pre-Hispanic thought: Nahua philosophy.