Filtering collections with filter

There is a special built-in function called filter which can be used to keep only some of the values of a collection while discarding others. It can have any of the following types:

filter : (a → Bool) × List(a) → List(a)
filter : (a → Bool) × Bag(a) → Bag(a)
filter : (a → Bool) × Set(a) → Set(a)

In other words, filter takes two arguments: the first is a function of some arbitrary type a → Bool (i.e. a “predicate” on the type a), and the second is a collection (list, bag, or set) containing values of type a. filter then applies the function to every element in the collection, and keeps only those values for which the function returns true.

For example, we can use filter to keep only the even numbers in set:

Disco> import num
Disco> filter(even, {1 .. 7})
{2, 4, 6}

We can also write our own anonymous function to express any predicate we want:

Disco> filter(\n. (n == 1) or (n // 2 > 1), {1 .. 7})
{1, 4, 5, 6, 7}

We can also apply filter to a list or bag:

Disco> import num
Disco> filter(isPrime, [0 .. 30])
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29]
Disco> each(\x. x + 1, factor(60))
⟅3 # 2, 4, 6⟆

Note that it is always possible to use a comprehension instead of filter, if you prefer. For example, instead of writing filter(even, {1 .. 7}) we could write

Disco> {x | x in {1 .. 7}, even(x)}
{2, 4, 6}