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Author: Kees Doets
Publisher: College Publications
ISBN:
Category : Haskell (Computer program language)
Languages : en
Pages : 448
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Book Description
Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply ``There is no royal road to mathematics.'' Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: 'Doets and van Eijck's ``The Haskell Road to Logic, Maths and Programming'' is an astonishingly extensive and accessible textbook on logic, maths, and Haskell.' Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau
Author: Kees Doets
Publisher: College Publications
ISBN:
Category : Haskell (Computer program language)
Languages : en
Pages : 448
Get Book Here
Book Description
Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply ``There is no royal road to mathematics.'' Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: 'Doets and van Eijck's ``The Haskell Road to Logic, Maths and Programming'' is an astonishingly extensive and accessible textbook on logic, maths, and Haskell.' Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau
Author: Cordelia Hall
Publisher: Springer Science & Business Media
ISBN: 1447136578
Category : Mathematics
Languages : en
Pages : 345
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Book Description
Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools such as proof checkers. These connections are emphasised throughout the book. Software tools (see Appendix A) enable the computer to serve as a calculator, but instead of just doing arithmetic and trigonometric functions, it will be used to calculate with sets, relations, functions, predicates and inferences. There are also special software tools, for example a proof checker for logical proofs using natural deduction.
Author: Peter Flach
Publisher: Wiley
ISBN: 9780471942153
Category : Computers
Languages : en
Pages : 256
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Book Description
An introduction to Prolog programming for artificial intelligence covering both basic and advanced AI material. A unique advantage to this work is the combination of AI, Prolog and Logic. Each technique is accompanied by a program implementing it. Seeks to simplify the basic concepts of logic programming. Contains exercises and authentic examples to help facilitate the understanding of difficult concepts.
Author: Richard Bird
Publisher: Cambridge University Press
ISBN: 1139490605
Category : Computers
Languages : en
Pages :
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Book Description
Richard Bird takes a radical approach to algorithm design, namely, design by calculation. These 30 short chapters each deal with a particular programming problem drawn from sources as diverse as games and puzzles, intriguing combinatorial tasks, and more familiar areas such as data compression and string matching. Each pearl starts with the statement of the problem expressed using the functional programming language Haskell, a powerful yet succinct language for capturing algorithmic ideas clearly and simply. The novel aspect of the book is that each solution is calculated from an initial formulation of the problem in Haskell by appealing to the laws of functional programming. Pearls of Functional Algorithm Design will appeal to the aspiring functional programmer, students and teachers interested in the principles of algorithm design, and anyone seeking to master the techniques of reasoning about programs in an equational style.
Author: Graham Hutton
Publisher: Cambridge University Press
ISBN: 1139461222
Category : Computers
Languages : en
Pages : 184
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Book Description
Haskell is one of the leading languages for teaching functional programming, enabling students to write simpler and cleaner code, and to learn how to structure and reason about programs. This introduction is ideal for beginners: it requires no previous programming experience and all concepts are explained from first principles via carefully chosen examples. Each chapter includes exercises that range from the straightforward to extended projects, plus suggestions for further reading on more advanced topics. The author is a leading Haskell researcher and instructor, well-known for his teaching skills. The presentation is clear and simple, and benefits from having been refined and class-tested over several years. The result is a text that can be used with courses, or for self-learning. Features include freely accessible Powerpoint slides for each chapter, solutions to exercises and examination questions (with solutions) available to instructors, and a downloadable code that's fully compliant with the latest Haskell release.
Author: Richard Bird
Publisher: Cambridge University Press
ISBN: 1107087201
Category : Computers
Languages : en
Pages : 357
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Book Description
This book introduces fundamental techniques for reasoning mathematically about functional programs. Ideal for a first- or second-year undergraduate course.
Author: Kees Doets
Publisher: MIT Press
ISBN: 9780262041423
Category : Computers
Languages : en
Pages : 240
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Book Description
This mathematically oriented introduction to the theory of logic programming presents a systematic exposition of the resolution method for propositional, first-order, and Horn- clause logics, together with an analysis of the semantic aspects of the method. It is through the inference rule of resolution that both proofs and computations can be manipulated on computers, and this book contains elegant versions and proofs of the fundamental theorems and lemmas in the proof theory of logic programming. Advanced topics such as recursive complexity and negation as failure and its semantics are covered, and streamlined setups for SLD- and SLDNF-resolution are described. No other book treats this material in such detail and with such sophistication. Doets provides a novel approach to resolution that is applied to the first-order case and the case of (positive) logic programs. In contrast to the usual approach, the concept of a resolvent is defined nonconstructively, without recourse to the concept of unification, allowing the soundness and completeness proofs to be carried out in a more economic way. Other new material includes computability results dealing with analytical hierarchy, results on infinite derivations and an exposition on general logic programs using 3-valued logic.
Author: Rob Aley
Publisher: Apress
ISBN: 1484229584
Category : Computers
Languages : en
Pages : 301
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Book Description
Bring the power of functional programming to your PHP applications. From performance optimizations to concurrency, improved testability to code brevity, functional programming has a host of benefits when compared to traditional imperative programming. Part one of Pro Functional PHP Programming takes you through the basics of functional programming, outlining the key concepts and how they translate into standard PHP functions and code. Part two takes this theory and shows you the strategies for implementing it to solve real problems in your new or existing PHP applications. Functional programming is popular in languages such as Lisp, Scheme and Clojure, but PHP also contains all you need to write functional code. This book will show you how to take advantage of functional programming in your own projects, utilizing the PHP programming language that you already know. What You'll Learn Discover functional programming in PHP Work with functional programming functions Design strategies for high-performance applications Manage business logic with functions Use functional programming in object-oriented and procedural applications Employ helper libraries in your application Process big data with functional PHP Who This Book Is For Programmers and web developers with experience of PHP who are looking to get more out of their PHP coding and be able to do more with PHP.
Author: Kees Doets
Publisher:
ISBN: 9781954300699
Category :
Languages : en
Pages : 450
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Book Description
Long ago, when Alexander the Great asked the mathematician Menaechmus for a crash course in geometry, he got the famous reply There is no royal road to mathematics. Where there was no shortcut for Alexander, there is no shortcut for us. Still, the fact that we have access to computers and mature programming languages means that there are avenues for us that were denied to the kings and emperors of yore. The purpose of this book is to teach logic and mathematical reasoning in practice, and to connect logical reasoning with computer programming in Haskell. Haskell emerged in the 1990s as a standard for lazy functional programming, a programming style where arguments are evaluated only when the value is actually needed. Haskell is a marvelous demonstration tool for logic and maths because its functional character allows implementations to remain very close to the concepts that get implemented, while the laziness permits smooth handling of infinite data structures. This book does not assume the reader to have previous experience with either programming or construction of formal proofs, but acquaintance with mathematical notation, at the level of secondary school mathematics is presumed. Everything one needs to know about mathematical reasoning or programming is explained as we go along. After proper digestion of the material in this book, the reader will be able to write interesting programs, reason about their correctness, and document them in a clear fashion. The reader will also have learned how to set up mathematical proofs in a structured way, and how to read and digest mathematical proofs written by others. This is the updated, expanded, and corrected second edition of a much-acclaimed textbook. Praise for the first edition: Doets and van Eijck s The Haskell Road to Logic, Maths and Programming is an astonishingly extensive and accessible textbook on logic, maths, and Haskell. Ralf Laemmel, Professor of Computer Science, University of Koblenz-Landau
Author: Ethan D. Bloch
Publisher: Springer Science & Business Media
ISBN: 1441971270
Category : Mathematics
Languages : en
Pages : 378
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Book Description
“Proofs and Fundamentals: A First Course in Abstract Mathematics” 2nd edition is designed as a "transition" course to introduce undergraduates to the writing of rigorous mathematical proofs, and to such fundamental mathematical ideas as sets, functions, relations, and cardinality. The text serves as a bridge between computational courses such as calculus, and more theoretical, proofs-oriented courses such as linear algebra, abstract algebra and real analysis. This 3-part work carefully balances Proofs, Fundamentals, and Extras. Part 1 presents logic and basic proof techniques; Part 2 thoroughly covers fundamental material such as sets, functions and relations; and Part 3 introduces a variety of extra topics such as groups, combinatorics and sequences. A gentle, friendly style is used, in which motivation and informal discussion play a key role, and yet high standards in rigor and in writing are never compromised. New to the second edition: 1) A new section about the foundations of set theory has been added at the end of the chapter about sets. This section includes a very informal discussion of the Zermelo– Fraenkel Axioms for set theory. We do not make use of these axioms subsequently in the text, but it is valuable for any mathematician to be aware that an axiomatic basis for set theory exists. Also included in this new section is a slightly expanded discussion of the Axiom of Choice, and new discussion of Zorn's Lemma, which is used later in the text. 2) The chapter about the cardinality of sets has been rearranged and expanded. There is a new section at the start of the chapter that summarizes various properties of the set of natural numbers; these properties play important roles subsequently in the chapter. The sections on induction and recursion have been slightly expanded, and have been relocated to an earlier place in the chapter (following the new section), both because they are more concrete than the material found in the other sections of the chapter, and because ideas from the sections on induction and recursion are used in the other sections. Next comes the section on the cardinality of sets (which was originally the first section of the chapter); this section gained proofs of the Schroeder–Bernstein theorem and the Trichotomy Law for Sets, and lost most of the material about finite and countable sets, which has now been moved to a new section devoted to those two types of sets. The chapter concludes with the section on the cardinality of the number systems. 3) The chapter on the construction of the natural numbers, integers and rational numbers from the Peano Postulates was removed entirely. That material was originally included to provide the needed background about the number systems, particularly for the discussion of the cardinality of sets, but it was always somewhat out of place given the level and scope of this text. The background material about the natural numbers needed for the cardinality of sets has now been summarized in a new section at the start of that chapter, making the chapter both self-contained and more accessible than it previously was. 4) The section on families of sets has been thoroughly revised, with the focus being on families of sets in general, not necessarily thought of as indexed. 5) A new section about the convergence of sequences has been added to the chapter on selected topics. This new section, which treats a topic from real analysis, adds some diversity to the chapter, which had hitherto contained selected topics of only an algebraic or combinatorial nature. 6) A new section called ``You Are the Professor'' has been added to the end of the last chapter. This new section, which includes a number of attempted proofs taken from actual homework exercises submitted by students, offers the reader the opportunity to solidify her facility for writing proofs by critiquing these submissions as if she were the instructor for the course. 7) All known errors have been corrected. 8) Many minor adjustments of wording have been made throughout the text, with the hope of improving the exposition.
