Book Image

Soar with Haskell

By : Tom Schrijvers
Book Image

Soar with Haskell

By: Tom Schrijvers

Overview of this book

With software systems reaching new levels of complexity and programmers aiming for the highest productivity levels, software developers and language designers are turning toward functional programming because of its powerful and mature abstraction mechanisms. This book will help you tap into this approach with Haskell, the programming language that has been leading the way in pure functional programming for over three decades. The book begins by helping you get to grips with basic functions and algebraic datatypes, and gradually adds abstraction mechanisms and other powerful language features. Next, you’ll explore recursion, formulate higher-order functions as reusable templates, and get the job done with laziness. As you advance, you’ll learn how Haskell reconciliates its purity with the practical need for side effects and comes out stronger with a rich hierarchy of abstractions, such as functors, applicative functors, and monads. Finally, you’ll understand how all these elements are combined in the design and implementation of custom domain-specific languages for tackling practical problems such as parsing, as well as the revolutionary functional technique of property-based testing. By the end of this book, you’ll have mastered the key concepts of functional programming and be able to develop idiomatic Haskell solutions.
Table of Contents (23 chapters)
Free Chapter
1
Part 1:Basic Functional Programming
6
Part 2: Haskell-Specific Features
11
Part 3: Functional Design Patterns
16
Part 4: Practical Programming

Eta reduction

The third feature that Haskell has borrowed from the lambda calculus is eta reduction. Eta reduction is named after the Greek letter eta, written as η. It allows us to shorten function definitions of a particular form. Its inverse is known as eta expansion, and collectively, they are known as eta conversion.

Basic eta reduction

We will illustrate the idea using a basic anonymous function:

\x -> sin x

This function takes a parameter, x, and computes its sine by calling the sin function on it. The observation that eta reduction makes is that this anonymous function behaves in exactly the same way as the sin function itself; both functions produce the same output given the same input. In other words, this anonymous function is indistinguishable from sin and, therefore, equal to it. For example, consider the following:

map (\x -> sin x) [1.0, 2.0, 3.0]

We can rewrite that as the following:

map sin [1.0, 2.0, 3.0]

This idea also works at the...