List Comprehension

In the final lesson on lists, we take a look at another powerful syntactic element to build complex lists: the list comprehension syntax.

List comprehensions by example

List comprehensions are a concept inspired by set definitions in mathematical notation. In mathematics, the definition

$$\{ x^2 \ |\ x \in \mathbb{N}, x \text{ is even} \}$$

defines the set of even squares. It is advised to start reading such a set definition from the right of the separating pipe symbol |.

1. The elements $x$ are drawn from the set of natural numbers $\mathbb{N}$.
2. Only the even $x$ are kept.
3. Finally (to the left of the pipe |), the set consists of the squares of these even $x$.

Similarly, we can define a list of the even squares in Haskell by using the closely related list comprehension syntax.