Programming With Higher Order Logic
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Programming With Higher Order Logic
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Author : Dale Miller
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-11
Programming With Higher Order Logic written by Dale Miller 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 2012-06-11 with Computers categories.
Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called λProlog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and λ-terms and π-calculus expressions can be encoded in λProlog.
Programming With Higher Order Logic
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Author : Dale Miller
language : en
Publisher: Cambridge University Press
Release Date : 2012-06-11
Programming With Higher Order Logic written by Dale Miller 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 2012-06-11 with Computers categories.
A programming language based on a higher-order logic provides a declarative approach to capturing computations involving types, proofs and other syntactic structures.
Isabelle Hol
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Author : Tobias Nipkow
language : en
Publisher: Springer
Release Date : 2014-03-12
Isabelle Hol written by Tobias Nipkow and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-03-12 with Mathematics categories.
This volume is a self-contained introduction to interactive proof in high- order logic (HOL), using the proof assistant Isabelle 2002. Compared with existing Isabelle documentation, it provides a direct route into higher-order logic, which most people prefer these days. It bypasses ?rst-order logic and minimizes discussion of meta-theory. It is written for potential users rather than for our colleagues in the research world. Another departure from previous documentation is that we describe Markus Wenzel’s proof script notation instead of ML tactic scripts. The l- ter make it easier to introduce new tactics on the ?y, but hardly anybody does that. Wenzel’s dedicated syntax is elegant, replacing for example eight simpli?cation tactics with a single method, namely simp, with associated - tions. The book has three parts. – The ?rst part, Elementary Techniques, shows how to model functional programs in higher-order logic. Early examples involve lists and the natural numbers. Most proofs are two steps long, consisting of induction on a chosen variable followed by the auto tactic. But even this elementary part covers such advanced topics as nested and mutual recursion. – The second part, Logic and Sets, presents a collection of lower-level tactics that you can use to apply rules selectively. It also describes I- belle/HOL’s treatment of sets, functions, and relations and explains how to de?ne sets inductively. One of the examples concerns the theory of model checking, and another is drawn from a classic textbook on formal languages.
Solving Higher Order Equations
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Author : Christian Prehofer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Solving Higher Order Equations written by Christian Prehofer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This monograph develops techniques for equational reasoning in higher-order logic. Due to its expressiveness, higher-order logic is used for specification and verification of hardware, software, and mathematics. In these applica tions, higher-order logic provides the necessary level of abstraction for con cise and natural formulations. The main assets of higher-order logic are quan tification over functions or predicates and its abstraction mechanism. These allow one to represent quantification in formulas and other variable-binding constructs. In this book, we focus on equational logic as a fundamental and natural concept in computer science and mathematics. We present calculi for equa tional reasoning modulo higher-order equations presented as rewrite rules. This is followed by a systematic development from general equational rea soning towards effective calculi for declarative programming in higher-order logic and A-calculus. This aims at integrating and generalizing declarative programming models such as functional and logic programming. In these two prominent declarative computation models we can view a program as a logical theory and a computation as a deduction.
Extensions Of First Order Logic
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Author : Maria Manzano
language : en
Publisher: Cambridge University Press
Release Date : 1996-03-29
Extensions Of First Order Logic written by Maria Manzano 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 1996-03-29 with Computers categories.
An introduction to many-sorted logic as an extension of first-order logic.
The Logic Of Programming
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Author : Eric C. R. Hehner
language : en
Publisher: Prentice Hall
Release Date : 1984
The Logic Of Programming written by Eric C. R. Hehner and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
Higher Order Computability
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Author : John Longley
language : en
Publisher: Springer
Release Date : 2015-11-06
Higher Order Computability written by John Longley and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-06 with Computers categories.
This book offers a self-contained exposition of the theory of computability in a higher-order context, where 'computable operations' may themselves be passed as arguments to other computable operations. The subject originated in the 1950s with the work of Kleene, Kreisel and others, and has since expanded in many different directions under the influence of workers from both mathematical logic and computer science. The ideas of higher-order computability have proved valuable both for elucidating the constructive content of logical systems, and for investigating the expressive power of various higher-order programming languages. In contrast to the well-known situation for first-order functions, it turns out that at higher types there are several different notions of computability competing for our attention, and each of these has given rise to its own strand of research. In this book, the authors offer an integrated treatment that draws together many of these strands within a unifying framework, revealing not only the range of possible computability concepts but the relationships between them. The book will serve as an ideal introduction to the field for beginning graduate students, as well as a reference for advanced researchers
Logic For Computer Science
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Author : Jean H. Gallier
language : en
Publisher: Courier Dover Publications
Release Date : 2015-06-18
Logic For Computer Science written by Jean H. Gallier and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-06-18 with Mathematics categories.
This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.
Programming With Higher Order Logic
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Author : Professor Dale Miller, GUI
language : en
Publisher:
Release Date : 2014-05-14
Programming With Higher Order Logic written by Professor Dale Miller, GUI and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-14 with Logic programming categories.
"Formal systems that describe computations over syntactic structures occur frequently in computer science. Logic programming provides a natural framework for encoding and animating such systems. However, these systems often embody variable binding, a notion that must be treated carefully at a computational level. This book aims to show that a programming language based on a simply typed version of higher-order logic provides an elegant, declarative means for providing such a treatment. Three broad topics are covered in pursuit of this goal. First, a proof-theoretic framework that supports a general view of logic programming is identified. Second, an actual language called [Lambda]Prolog is developed by applying this view to higher-order logic. Finally, a methodology for programming with specifications is exposed by showing how several computations over formal objects such as logical formulas, functional programs, and [lambda]-terms and [pi]-calculus expressions can be encoded in [Lambda]Prolog"--