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The Haskell Road to Logic, Maths and Programming. Second edition (Texts in Computing) [Englisch] [Taschenbuch]

Kees Doets , van Jan Eijck
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Kurzbeschreibung

7. Mai 2004 Texts in Computing
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

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Produktinformation

  • Taschenbuch: 450 Seiten
  • Verlag: College Publications; Auflage: 04000 (7. Mai 2004)
  • Sprache: Englisch
  • ISBN-10: 0954300696
  • ISBN-13: 978-0954300692
  • Größe und/oder Gewicht: 23,4 x 15,6 x 2,5 cm
  • Durchschnittliche Kundenbewertung: 5.0 von 5 Sternen  Alle Rezensionen anzeigen (1 Kundenrezension)
  • Amazon Bestseller-Rang: Nr. 5.302 in Fremdsprachige Bücher (Siehe Top 100 in Fremdsprachige Bücher)

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8 von 8 Kunden fanden die folgende Rezension hilfreich
Format:Taschenbuch
"The Haskell Road to Logic, Math and Programming" sollte treffender
"Einführung in die diskrete Mathematik mit Haskell" heißen. Eine
Einführung in Haskell und eine Einführung in Diskrete Mathematik sind
eine ideale Kombination, weil gerade Haskell sich wegen seines sehr
mathematischen Formalismusses dazu anbietet. So können die häufig sehr
abstrakten Konzepte konkret in einer Programmiersprache ausprobiert
werden. Behandelt werden Logik, Mengen, Relationen, Funktionen,
Induktion/Rekursion, Zahlentheorie, Polynome. Einem Anfänger würde ich
das Buch nicht empfehlen, weil sowohl Diskrete Mathematik und Haskell
gewöhnungsbedürftig sein können, und damit schon einzeln schwierig
genug sind. Insbesondere Vorkenntnisse in Haskell können nicht
schaden, da das Buch hier sehr schnell voranschreitet. Funktionen
höherer Ordnung werden bspw. schon auf Seite 21 eingeführt. Wer
Vorkenntnisse mitbringt, kann sie mit diesem Buch wunderbar vertiefen.
Sehr gut gefallen haben mir die Übungsaufgaben, die genau den
richtigen Schwierigkeitsgrad haben. Kommt man mal nicht weiter, kann
man beim Autor die Musterlösungen per Mail anfordern. Darüber hinaus
sind viele der Beispielprogramme in einem sehr schönen Stil
programmiert, von dem ich mir noch ein paar Tricks abgucken konnte.

Gerade für diesen Preis eine uneingeschränkte Empfehlung!
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Amazon.com: 4.6 von 5 Sternen  14 Rezensionen
69 von 81 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen The Haskell Road to Discrete Math 9. April 2006
Von John J. Rood - Veröffentlicht auf Amazon.com
Format:Taschenbuch
Want to learn discrete math as in the non-calculus version of Math 101? Willing to work hard to learn it? Then this is the book for you! It is written in a user friendly style. The book has a chatty tone when explaining serious topics. The chat is the talk of experts, however, so it should never be underestimated. The book will teach you the functional programming language Haskell. This language is the most modern version of the Lisp family to have received any significant attention. It features advanced type features and lazy evaluation. The book covers all the "classic" topics of a discrete math course, to a considerable depth. Best of all, they are all implemented in Haskell. All except for the predicate calculus, that is. It would be a major piece of work indeed to have any implementation of this topic in a work at this level! The book teaches logic by example. One is taught the meaning, the rules and the insider's "recipes" of mathematical proofs. The book then covers the standard topics of sets, relations, functions, and induction / recursion with impressive computer implementations. The book goes on to a quick overview of the construction of the number systems of mathematics. It proceeds to a substantial treatment of combinatorics in a short space which includes implementation of polynomial solutions to recursion relations. Then it is on to corecursion, power series, and a hint of domain theory. The book ends with a modern chapter on the elements of set theory. All in all an excellent book! IMHO it is the best book out there on the topics in a discrete math course. It is amazing that all of this (except the serious parts of logic) could be implemented in Haskell so successfully. The one caveat about the book is that if you want to benefit fully from it, you are going to have to do some hard work.
24 von 26 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen The math book all programmers should read 2. Dezember 2009
Von Code Monkey - Veröffentlicht auf Amazon.com
Format:Taschenbuch
The 'Haskell Road to Logic' is a wonderful introduction to the mathematics that lie behind functional programming and computer science. Readers should however be aware that this book is not, and does not pretend to be, a book about programming in Haskell. It is really a text book about topics in mathematics that are of particular interest to computer scientists. What distinguishes the book from many others is its use of Haskell to implement mathematical structures that are usually taught as abstract concepts. This approach makes the mathematics far more approachable for computer programmers than many other text books. Presumably it should also make for an excellent introduction to computer programming for the mathematically inclined.

While the book is easy to read and has a friendly writing style, it not particularly well suited to casual reading. To really understand the subject being discussed the reader will probably need to solve most of the exercises in the text. The good news is this requires minimal prior mathematical training (the authors expect familiarity with "secondary school mathematics"). Solving the exercises will also train the reader in writing, and proving the correctness of, short functional programs.

The book has a minor few faults. One is a relatively large number of minor errors (many of which are noted in the errata available on the book's website). Another is that some major topics are introduced in exercises without much discussion, particularly in the later chapters. But these are but quibbles in a review of a fantastic math book for programmers.
28 von 31 Kunden fanden die folgende Rezension hilfreich
3.0 von 5 Sternen Lives up to the title but not for beginners! 31. Januar 2011
Von Jason Schorn - Veröffentlicht auf Amazon.com
Format:Taschenbuch
After dabbling in several other programming languages I came across references to Haskell and quickly became interested in learning the language given (1) my disdain for over-sized and almost convoluted languages such as Java and C# and, (2) my background in Mathematics. Yes this is an interesting book that does an excellent job showing how well the abstraction of Mathematics can be quantified using Haskell yet, I do not believe that this book does any justice to those individuals the author claims the book is written for-"[t]his book does not assume the reader to have previous experience with either programming or construction of formal proof ...". Any inexperienced programmer or person with minimal Mathematical experience will, in no way, benefit from this book unless they have a quality teacher who can explain as well as expand on the material. In my humble opinion the person's who can utilize and benefit from this book are either semi-experienced functional programmers, young (possibly old) whiz-kids or the auto-didactic types who have the patience to refer to other sources for more explanation. As an example of the later claim, Exercise 1.10 asks the reader to "define a function called removeFst that removes the first occurrence of an integer m from a list of integers ..." without reference to working with/on lists. Further, this user defined function is expected to be used in the very next example (1.11) which, without assurance of the readers ability to define such a function, i.e. providing a solution, is pedagogically unsound. Either include a reference to the solution(s) on the authors website, include them in the book, or do a better job of NOT asking for chicken without providing the egg.

This is not meant to be a negative review! Instead, it is a warning to those with minimal programming/Mathematics background expecting to learn Haskell. Personally, I loved this book and wish I came across it years ago. In fact, I wish I had come across functional programming years ago and therefore had not wasted years trying abstract other less abstract-able languages.
12 von 13 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Enlightening 17. September 2010
Von Qual Highety - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
As a professional programmer who dropped out of college too early to get a good grounding in mathematics, this book has been a wonder to me. I've been trying to learn more advanced mathematics in the last year or so, and struggled because I didn't know how to do proofs.

Haskell is prominent in the title, but is secondary in the book. The vast majority of my time has been spent reading and performing proofs with with pencil and paper. The mathematics portions are all fairly rigorous. Once proofs are fully introduced, nearly all the exercises are proving theorems given in the book, or providing counter examples. There isn't much in the way of computational type exercises I've seen in some other discrete math texts, stuff like "what's the transitive closure of this relation". Instead, a theorem will be given and the author will ask you to prove it.

The Haskell exercises typically follow pure math introductions and exercises, and are used to help develop a stronger, more intuitive understating of the subjects. I can now write enough Haskell to take on the exercises, but to this point, the Haskell has all be very compact - 10 lines of code to answer a question at the max, usually more like 3. There's no way I could go and do something 'practical' with Haskell at this point, but I can grok some of it and am starting to appreciate functional programming.

This is easily the most challenging self study book I've taken on, but also the most rewarding. Not only have I gained proof writing knowledge, and a solid understanding of the fundamentals of modern mathematics, but it's helped me develop a measure of discipline in thought. I've noticed improvements in the clarity of my day to day software development - in design, development, and verification. The methodical approach to breaking down a proof into cases and sub-cases has been most helpful in that regard.

I recommend this to anyone, especially developers who haven't had the benefit of a thorough mathematical education.
14 von 16 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen modern approach to Mathematics foundations 7. Juni 2009
Von Herbert C. Meyer - Veröffentlicht auf Amazon.com
Format:Taschenbuch|Verifizierter Kauf
When I was a Math undergrad back in the 70's, we had a 5 hr course called Foundations of Mathematics. This was an intro to symbolic logic, propositional calculus, and methods of proof. Deadly boring, dry material that we either knew, grasped by intuition, or ignored.

This textbook covers this material in a constructive fashion by using the Haskell programming language. Haskell is a modern form of lisp, one of the original programming languages, from the '50's, the language used for most Artificial Intelligence work. The breadth of Haskell allows it to be used for logic and proof, as well as the usual numerical and string processing. Pattern matching and list processing is built into the basic structure of the Haskell language.

This text's exercises are mostly Haskell programming assignments. Turning the abstract ideas of the math into the concrete statements of Haskell (if statements in a program can be considered concrete) will make the ideas familiar and real. Free, useful versions of Haskell (Hugs) are available for readers or students to use, even on Windows systems. Any familiarity with any programming system and a text editor should be enough to get started.

What is the difference between proving a theorem and debugging a program ? The way I do it, not much. That has much to do with me, I am a programmer first, and a Math second. This statement is the Curry-Howard correspondence, connecting computability and proof or truth. This text is a step on that road to truth.

There are several other titles in this series. All of them sound fascinating. I will read them later.
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