How to use list comprehension in Haskell

Prerequisites

Understanding Lists in Haskell
Optional: Basic understanding of set theory

List Comprehension

I couldn't find a more concise and better definition than the one by Miran Lipovača:

List comprehensions are a way to filter, transform, and combine lists.

Fundamental Understanding

Our prof liked to describe the process of list comprehensions as "swoosh", meaning that we can imagine list comprehension as something that manipulates all list elements at the same time. In contrast, recursion was described as "ticky ticky ticky", something which manipulates a list item successively – I know, some weird first year teaching techniques. But they really helped me to understand those processes, so no blame at this point.

Let's dive right into an example:

ghci> [x*10 | x <- [1..5]]
[10,20,30,40,50]

Look's rather confusing, right? It's not too bad if we look at this example part for part.

Generators

Everything after the pipe | is the Generator.

A Generator:

Generates the set of values we can work with.
Binds each element from that set of values to x .
We draw our elements from that set (<- is pronounced "drawn from").

Everything before the pipe determines the output of the list comprehension. It's basically what we want to do with the list elements.

In our example, we generate a set of values from the list 1..5 . We bind each element of the list to x. In the expression (before |) we defined that every element (x) should be multiplied by 10. Therefore, our resulting list is [10,20,30,40,50].

If you didn't completely understand what I was talking about, don't worry! Just re-read the important paragraphs and each time it should make a bit more sense.

Predicates

If we do not want to draw all elements from a list, we can add a condition, a predicate. A predicate is a function which takes an element and returns a boolean value.

Continuing with our first example, let's say we only want to bind numbers to x which are strictly greater than 2:

ghci> [x*10 | x <- [1..5], x > 2]
[30,40,50]

As you can see, we only have to add a comma and the predicate, that's it! You can add as many predicates as you want, separated by commas.

So concluding the structure of a list comprehension, this might help memorise everything:

[ Output | Generator, predicate 1, predicate 2, ... ]

Using predicates to get exactly the elements of a list you want is called filtering.

We can also have multiple generators to draw values from several lists:

ghci> [x*y | x <- [1,3,6], y <- [10,11,12]]
[10,11,12,30,33,36,60,66,72]

In this case, the length of the resulting list is 9 because we get the products of all possible combinations of numbers.

Conclusion

List comprehension is a great technique to manipulate lists. We can imagine the process as something which acts on each list element at the same time.

We first generate a set of values from some list. The set can be filtered using predicates. In the expression before the pipe, we define what to do with the generated elements, and the output of the list comprehension.

Off-Road Knowledge

_ is an undefined variable, a wildcard variable. We can use it when we don't care about the value which is assigned to _
It's always a good exercise to define library functions on your own

length' :: [a] -> int
length' ls = sum[1 | _ <- ls]

Infix functions are functions notated with a ` around them, apart from infix operators such as + or *
Infix functions are syntactic sugar, both prefix and infix functions can be written the other way

λ> zip [1..] "ABCD" == [1..] `zip` "ABCD"
True
λ> (+) 4 5 == 4 + 5
True