In a nutshell:

1. • Functional programming is a method of program construction that emphasises functions and their application rather than commands and their execution.

2. • Functional programming uses simple mathematical notation that allows problems to be described clearly and concisely.

3. • Functional programming has a simple mathematical basis that supports equational reasoning about the properties of programs.

Our aim in this book is to illustrate these three key points, using a specific functional language called Haskell.

Functions and types

We will use the Haskell notation

to assert that f is a function taking arguments of type X and returning results of type Y. For example,

Float is the type of floating-point numbers, things like 3.14159, and Int is the type of limited-precision integers, integers n that lie in a restricted range such as −229 ≤ n < 229. The restriction is lifted with the type Integer, which is the type of unlimited-precision integers. As we will see in Chapter 3, numbers in Haskell come in many flavours.

In mathematics one usually writes f(x) to denote the application of the function f to the argument x.