The Haskell Road to Logic, Maths and Programming. Second Edition (Texts in Computing) by Kees Doets (2004-05-07) by (PDF)

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Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐Disclaimer: I’m still working through the book.As others have mentioned, this is really a math book that uses Haskell as a vehicle to teach the math.In my case, I already know the book’s math/logic, but I don’t know Haskell. It turns out that the book is great for learning Haskell if you already know the math. The approach offers a sustained treatment of a nontrivial domain, allowing you to build upon earlier work. For example the book starts with connectives and wffs, proceeds quickly to laws and metatheoretical concepts (validity, logical equivalence, proofs), sets, and other foundational mathematics. All the while it shows how to apply Haskell concepts to that domain. Also it is exciting to see how closely Haskell mirrors the mathematical concepts, such as Haskell’s list comprehension vs mathematical set builder notation, and people who come from that math background will better appreciate that aspect of Haskell’s awesomeness.As some reviewers have noted, I’m not so sure this is the best book for learning logic if you don’t already know Haskell or at least programming. I think logic and Haskell are sufficiently formidable individually, and learning both together sounds challenging to me. At the very least you would need to have some level of mathematical background even if not in logic. The examples concern things like the infinity of Mersenne primes. There’s an aside on Platonism vs Intuitionism. I don’t see this supporting a general ed “Intro to Logic” course, but I could see it supporting an “Intro to Logic” course for math majors.Anyway I love this book.

⭐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.

⭐I’ve always found the purer bits of maths such as set theory and the methods of mathematical proof too abstract to grasp. The use of Haskell in this book makes them much easier to understand for an old computer programmer like me, and this book presents the ideas very clearly, and starting from a pretty low level.It’s also an introduction to Haskell, which I did not know before. A very beautiful language, which is introduced in a very clear way here, but you need more than this book if you want to take it seriously as a language. There is nothing about monads, or performance issues, or any of the other things you need for real world Haskell.Necessary but not sufficient.

⭐I am interested in electronics, and a friend recommended I study logic. So I got this book because it was within my budget. Worth it.

⭐If you know your way around first order logic and model theory but don’t know where to begin with Haskell, this book is for you because it teaches you the language in terms you will be familiar with. Sometimes the chapters are more math/logic and less programming though, which is less helpful if you are looking to practice some code.

⭐If you love Haskel and you love Logic then this is a good read, if you don’t then its a bit wierd

⭐The book meets all my expectations. It came in perfect conditions. Maybe the font used in the book is a bit small…

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