Programming With Higher Order Logic

Author : Dale Miller
Publisher : Cambridge University Press
ISBN 13 : 052187940X
Total Pages : 321 pages
Book Rating : 4.08/5 ( download)

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Download or read book Programming with Higher-Order Logic written by Dale Miller and published by Cambridge University Press. This book was released on 2012-06-11 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: A programming language based on a higher-order logic provides a declarative approach to capturing computations involving types, proofs and other syntactic structures.

Author : Professor Dale Miller, GUI
Publisher :
ISBN 13 : 9781139518420
Total Pages : 322 pages
Book Rating : 4.29/5 ( download)

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Download or read book Programming with Higher-Order Logic written by Professor Dale Miller, GUI and published by . This book was released on 2014-05-14 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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"--

Author : Maria Manzano
Publisher : Cambridge University Press
ISBN 13 : 9780521354356
Total Pages : 414 pages
Book Rating : 4.58/5 ( download)

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Download or read book Extensions of First-Order Logic written by Maria Manzano and published by Cambridge University Press. This book was released on 1996-03-29 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to many-sorted logic as an extension of first-order logic.

Author : Tobias Nipkow
Publisher : Springer
ISBN 13 : 3540459499
Total Pages : 226 pages
Book Rating : 4.91/5 ( download)

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Download or read book Isabelle/HOL written by Tobias Nipkow and published by Springer. This book was released on 2003-07-31 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Christian Prehofer
Publisher : Springer Science & Business Media
ISBN 13 : 1461217784
Total Pages : 193 pages
Book Rating : 4.87/5 ( download)

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Download or read book Solving Higher-Order Equations written by Christian Prehofer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Keisuke Nakano
Publisher : Springer Nature
ISBN 13 : 3030590259
Total Pages : 229 pages
Book Rating : 4.53/5 ( download)

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Download or read book Functional and Logic Programming written by Keisuke Nakano and published by Springer Nature. This book was released on 2020-09-08 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the proceedings of the 15th International Symposium on Functional and Logic Programming, FLOPS 2020, held in Akita, Japan*, in September 2020. The 12 papers presented in this volume were carefully reviewed and selected from 25 submissions. They cover all aspects of the design, semantics, theory, applications, implementations, and teaching of declarative programming focusing on topics such as functional programming, logic programming, declarative programming, constraint programming, formal method, model checking, program transformation, program refinement, and type theory. *The conference was held virtually due to the COVID-19 pandemic.

Author : John Longley
Publisher : Springer
ISBN 13 : 3662479923
Total Pages : 571 pages
Book Rating : 4.26/5 ( download)

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Download or read book Higher-Order Computability written by John Longley and published by Springer. This book was released on 2015-11-06 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Matthias Blume
Publisher : Springer Science & Business Media
ISBN 13 : 3642122507
Total Pages : 364 pages
Book Rating : 4.07/5 ( download)

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Download or read book Functional and Logic Programming written by Matthias Blume and published by Springer Science & Business Media. This book was released on 2010-04-09 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 10th International Symposium on Functional and Logic Programming, FLOPS 2010, held in Sendai, Japan, in April 2010. The 21 revised full papers presented together with 3 invited talks were carefully reviewed and selected from 49 submissions. The papers are organized in topical sections on types; program analysis and transformation; foundations; logic programming; evaluation and normalization; term rewriting; and parallelism and control.

Author : Iliano Cervesato
Publisher : Springer Science & Business Media
ISBN 13 : 3540894381
Total Pages : 727 pages
Book Rating : 4.84/5 ( download)

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Download or read book Logic for Programming, Artificial Intelligence, and Reasoning written by Iliano Cervesato and published by Springer Science & Business Media. This book was released on 2008-11-13 with total page 727 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2008, which took place in Doha, Qatar, during November 22-27, 2008. The 45 revised full papers presented together with 3 invited talks were carefully revised and selected from 153 submissions. The papers address all current issues in automated reasoning, computational logic, programming languages and their applications and are organized in topical sections on automata, linear arithmetic, verification knowledge representation, proof theory, quantified constraints, as well as modal and temporal logics.

Author : Andrew W. Appel
Publisher : Cambridge University Press
ISBN 13 : 110704801X
Total Pages : 469 pages
Book Rating : 4.10/5 ( download)

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Download or read book Program Logics for Certified Compilers written by Andrew W. Appel and published by Cambridge University Press. This book was released on 2014-04-21 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This tutorial for graduate students covers practical and theoretical aspects of separation logic with constructions and proofs in Coq.