Question

I’ve just seen I can do:

Set(1, 2, 3).map(Set(1))

which yields the result:

Set(true, false)

But I thought that the map function can only take another function not a new Set. If anything I’d expect this to return a set of sets. What’s going on and what does the result mean?

Answer 1

But I thought that the map function can only take another function not a new Set.

A Set is a function. It is a function from its elements to booleans: when you pass it an element, it tells you whether that element is part of the Set.

Set(1, 2, 3).map(Set(1))

Iterates over the Set(1, 2, 3), passing each each element to the Set(1). I.e. it first asks “is 1 a member of set {1}“, which is true, then it asks the same question for 2 and 3, which is false.

So, the result is Set(true, false, false), which of course is just Set(true, false).

Similarly, a sequence is a function from integers to elements, a map is a function from keys to values.