The Haskell Road to Logic, Maths and Programming

Author: Kees Doets
Publisher: College Publications
ISBN:
Category : Haskell (Computer program language)
Languages : en
Pages : 448

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

The Haskell Road to Logic, Maths and Programming. Second Edition

Author: Kees Doets
Publisher:
ISBN: 9781954300699
Category :
Languages : en
Pages : 450

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

Structures and Norms in Science

Author: Maria Luisa Dalla Chiara
Publisher: Springer Science & Business Media
ISBN: 9401705380
Category : Science
Languages : en
Pages : 442

Book Description
This book gives a state-of-the-art survey of current research in logic and philosophy of science, as viewed by invited speakers selected by the most prestigious international organization in the field. In particular, it gives a coherent picture of foundational research into the various sciences, both natural and social. In addition, it has special interest items such as symposia on interfaces between logic and methodology, semantics and semiotics, as well as updates on the current state of the field in Eastern Europe and the Far East.

Haskell Programming from First Principles

Author: Christopher Allen
Publisher:
ISBN: 9781945388033
Category :
Languages : en
Pages :

Book Description
Haskell Programming makes Haskell as clear, painless, and practical as it can be, whether you're a beginner or an experienced hacker. Learning Haskell from the ground up is easier and works better. With our exercise-driven approach, you'll build on previous chapters such that by the time you reach the notorious Monad, it'll seem trivial.

Haskell Programming

Author: Emma William
Publisher:
ISBN:
Category :
Languages : en
Pages : 274

Book Description
A balance of flexible and inflexible qualities make Haskell a fascinating programming language to learn and use. First, the Haskell programming language is not named after Eddie Haskell, the sneaky double-dealing neighbor kid in the ancient TV sitcom, Leave It To Beaver. Haskell is named after Haskell Brooks Curry, an American mathematician and logician. If you don't know, logicians create models to describe and define human reasoning, for example, problems in mathematics, computer science, and philosophy. Haskell's main work was in combinatory logic, a notation designed to eliminate the need for variables in mathematical logic. Combinatory logic captures many key features of computation and, as a result, is useful in computer science. Haskell has three programming languages named after him: Haskell, Brooks, and Curry. Haskell the language is built around functions, useful blocks of code that do specific tasks. They are called and used only when needed. Another interesting feature of functional languages like Haskell: functions are treated as values like integers (numbers) and strings. You can add a function to another function the way you can add an integer to an integer, 1 + 1 or 35 + 53. Perhaps the best way to describe this quality is a spreadsheet: in a cell in the spreadsheet, you can add numbers as well as a combination of functions to work on numbers. For example, you might specify each number in cells 1-10 be added up as a sum. In Excel, at least, you also can use SUMIF to look for a pattern in cells 1-10 and, if the pattern is found, perform an action on any cells with the pattern. What Makes Haskell Special? Technically, Haskell is a general-purpose functional programming language with non-strict semantics and strong static typing. The primary control construct is the function. (Say that fast ten times!) Here's what it means: - Every language has a strategy to evaluate when to process the input arguments used in a call to a function. The simplest strategy is to evaluate the input arguments passed then run the function with the arguments. Non-strict semantics means the input arguments are not evaluated unless the arguments passed into the function are used to evaluate what is in the body of the function. - Programming languages have rules to assign properties -- called a type -- to the components of the language: variables, functions, expressions, and modules. A type is a general description of possible values the variable, function, expression, or module can store. Typing helps minimize bugs, for example, when a calculation uses a string ("house" or "cat") instead of a number (2 or 3). Strong static typing evaluates the code before runtime, when the code is static and possibly as code is written. - The order in which statements, instructions and functions are evaluated and executed determines the results of any piece of code. Control constructs define the order of evaluation. Constructs use an initial keyword to flag the type of control structure used. Initial keywords might be "if" or "do" or "loop" while final keywords might be "end if" or "enddo" or "end loop". Instead of a final keyword, Haskell uses indentation level (tabs) or curly brackets, or a mix, to indicate the end of a control structure. Perhaps what makes Haskell special is how coders have to think when they use the language. Functional programming languages work in very different ways than imperative languages where the coder manages many low-level details of what happens in their code and when. While it is true all languages have things in common, it's also true languages are mostly functional or mostly imperative, the way people are mostly right handed or left handed. Except functional programming languages require a different way of thinking about software as you code

A Programmer's Introduction to Mathematics

Author: Jeremy Kun
Publisher:
ISBN:
Category :
Languages : en
Pages : 400

Book Description
A Programmer's Introduction to Mathematics uses your familiarity with ideas from programming and software to teach mathematics. You'll learn about the central objects and theorems of mathematics, including graphs, calculus, linear algebra, eigenvalues, optimization, and more. You'll also be immersed in the often unspoken cultural attitudes of mathematics, learning both how to read and write proofs while understanding why mathematics is the way it is. Between each technical chapter is an essay describing a different aspect of mathematical culture, and discussions of the insights and meta-insights that constitute mathematical intuition. As you learn, we'll use new mathematical ideas to create wondrous programs, from cryptographic schemes to neural networks to hyperbolic tessellations. Each chapter also contains a set of exercises that have you actively explore mathematical topics on your own. In short, this book will teach you to engage with mathematics. A Programmer's Introduction to Mathematics is written by Jeremy Kun, who has been writing about math and programming for 10 years on his blog "Math Intersect Programming." As of 2020, he works in datacenter optimization at Google.The second edition includes revisions to most chapters, some reorganized content and rewritten proofs, and the addition of three appendices.

Haskell

Author: Mem Lnc
Publisher:
ISBN:
Category :
Languages : en
Pages : 276

Book Description
A balance of flexible and inflexible qualities make Haskell a fascinating programming language to learn and use.First, the Haskell programming language is not named after Eddie Haskell, the sneaky double-dealing neighbor kid in the ancient TV sitcom, Leave It To Beaver.Haskell is named after Haskell Brooks Curry, an American mathematician and logician. If you don't know, logicians create models to describe and define human reasoning, for example, problems in mathematics, computer science, and philosophy. Haskell's main work was in combinatory logic, a notation designed to eliminate the need for variables in mathematical logic. Combinatory logic captures many key features of computation and, as a result, is useful in computer science. Haskell has three programming languages named after him: Haskell, Brooks, and Curry.Haskell the language is built around functions, useful blocks of code that do specific tasks. They are called and used only when needed.Another interesting feature of functional languages like Haskell: functions are treated as values like integers (numbers) and strings. You can add a function to another function the way you can add an integer to an integer, 1 + 1 or 35 + 53. Perhaps the best way to describe this quality is a spreadsheet: in a cell in the spreadsheet, you can add numbers as well as a combination of functions to work on numbers. For example, you might specify each number in cells 1-10 be added up as a sum. In Excel, at least, you also can use SUMIF to look for a pattern in cells 1-10 and, if the pattern is found, perform an action on any cells with the pattern.What Makes Haskell Special?Technically, Haskell is a general-purpose functional programming language with non-strict semantics and strong static typing. The primary control construct is the function. (Say that fast ten times!) Here's what it means: - Every language has a strategy to evaluate when to process the input arguments used in a call to a function. The simplest strategy is to evaluate the input arguments passed then run the function with the arguments. Non-strict semantics means the input arguments are not evaluated unless the arguments passed into the function are used to evaluate what is in the body of the function.- Programming languages have rules to assign properties - called a type - to the components of the language: variables, functions, expressions, and modules. A type is a general description of possible values the variable, function, expression, or module can store. Typing helps minimize bugs, for example, when a calculation uses a string ("house" or "cat") instead of a number (2 or 3). Strong static typing evaluates the code before runtime, when the code is static and possibly as code is written.- The order in which statements, instructions and functions are evaluated and executed determines the results of any piece of code. Control constructs define the order of evaluation. Constructs use an initial keyword to flag the type of control structure used. Initial keywords might be "if" or "do" or "loop" while final keywords might be "end if" or "enddo" or "end loop". Instead of a final keyword, Haskell uses indentation level (tabs) or curly brackets, or a mix, to indicate the end of a control structure.Perhaps what makes Haskell special is how coders have to think when they use the language. Functional programming languages work in very different ways than imperative languages where the coder manages many low-level details of what happens in their code and when. While it is true all languages have things in common, it's also true languages are mostly functional or mostly imperative, the way people are mostly right handed or left handed. Except functional programming languages require a different way of thinking about software as you code.

Category Theory for Programmers (New Edition, Hardcover)

Author: Bartosz Milewski
Publisher:
ISBN: 9780464243878
Category :
Languages : en
Pages :

Book Description
Category Theory is one of the most abstract branches of mathematics. It is usually taught to graduate students after they have mastered several other branches of mathematics, like algebra, topology, and group theory. It might, therefore, come as a shock that the basic concepts of category theory can be explained in relatively simple terms to anybody with some experience in programming.That's because, just like programming, category theory is about structure. Mathematicians discover structure in mathematical theories, programmers discover structure in computer programs. Well-structured programs are easier to understand and maintain and are less likely to contain bugs. Category theory provides the language to talk about structure and learning it will make you a better programmer.

Discrete Mathematics Using a Computer

Author: Cordelia Hall
Publisher: Springer Science & Business Media
ISBN: 1447136578
Category : Mathematics
Languages : en
Pages : 345

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.

Exercises for Programmers

Author: Brian P. Hogan
Publisher: Pragmatic Bookshelf
ISBN: 1680503480
Category : Computers
Languages : en
Pages : 120

Book Description
When you write software, you need to be at the top of your game. Great programmers practice to keep their skills sharp. Get sharp and stay sharp with more than fifty practice exercises rooted in real-world scenarios. If you're a new programmer, these challenges will help you learn what you need to break into the field, and if you're a seasoned pro, you can use these exercises to learn that hot new language for your next gig. One of the best ways to learn a programming language is to use it to solve problems. That's what this book is all about. Instead of questions rooted in theory, this book presents problems you'll encounter in everyday software development. These problems are designed for people learning their first programming language, and they also provide a learning path for experienced developers to learn a new language quickly. Start with simple input and output programs. Do some currency conversion and figure out how many months it takes to pay off a credit card. Calculate blood alcohol content and determine if it's safe to drive. Replace words in files and filter records, and use web services to display the weather, store data, and show how many people are in space right now. At the end you'll tackle a few larger programs that will help you bring everything together. Each problem includes constraints and challenges to push you further, but it's up to you to come up with the solutions. And next year, when you want to learn a new programming language or style of programming (perhaps OOP vs. functional), you can work through this book again, using new approaches to solve familiar problems. What You Need: You need access to a computer, a programming language reference, and the programming language you want to use.