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Author: Dale Miller
Publisher: Cambridge University Press
Published: 2012-06-11
Total Pages: 321
ISBN-13: 052187940X
DOWNLOAD EBOOK →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:
Published: 2014-05-14
Total Pages: 322
ISBN-13: 9781139518420
DOWNLOAD EBOOK →"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: Tobias Nipkow
Publisher: Springer
Published: 2003-07-31
Total Pages: 220
ISBN-13: 3540459499
DOWNLOAD EBOOK →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: Maria Manzano
Publisher: Cambridge University Press
Published: 1996-03-29
Total Pages: 414
ISBN-13: 9780521354356
DOWNLOAD EBOOK →An introduction to many-sorted logic as an extension of first-order logic.
Author: Keisuke Nakano
Publisher: Springer Nature
Published: 2020-09-08
Total Pages: 229
ISBN-13: 3030590259
DOWNLOAD EBOOK →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: Christian Prehofer
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 193
ISBN-13: 1461217784
DOWNLOAD EBOOK →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: John Longley
Publisher: Springer
Published: 2015-11-06
Total Pages: 587
ISBN-13: 3662479923
DOWNLOAD EBOOK →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: Dale Miller
Publisher: Cambridge University Press
Published: 2012-06-11
Total Pages: 321
ISBN-13: 1139510428
DOWNLOAD EBOOK →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.
Author: Matthias Blume
Publisher: Springer Science & Business Media
Published: 2010-04-09
Total Pages: 364
ISBN-13: 3642122507
DOWNLOAD EBOOK →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
Published: 2008-11-13
Total Pages: 727
ISBN-13: 3540894381
DOWNLOAD EBOOK →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.
