# Functional Sets, Part 8: Map

Elm 0.18 · Updated February 11, 2018 · 3 Minute Read · ∞ Permalink

Now that we have filter and friends, we’re almost done with our Set implementation. Once we have map, we’ll be done!

map applies a function to every item in a collection. Say we have a list containing the numbers one through five. We can use List.map to double every number:

List.map (\i -> i * 2) [1, 2, 3] -- [2, 4, 6]


We’re going to make map for our sets. So, given the same list (but converted to a set) we should get:

map (\i -> i * 2) (fromList [1, 2, 3]) -- {2, 4, 6}


Let’s do this… What if we deconstruct the set piece by piece like we did with member? That way, we’d apply the function exactly once to each item, and get a new set!

Not so fast!

What about functions that return the same value, like always 1? When applied to the set from earlier we would get a set with 1, five times. That won’t work, it’s not a valid set! Sets always have unique values, so we need a different approach.

foldl comes to our rescue here again. Since it moves values through a function to an accumulator piece by piece, we can build a new Set as we go. We’ll start with an empty list as our accumulator value, then insert the mapped values one at a time. If we get any duplicates, they’ll be removed as we go.

Here’s how it looks:

map : (comparable -> comparable2) -> Set comparable -> Set comparable2
map fn set =
foldl
(\item acc -> insert (fn item) acc)
empty
set


It works just like we said above:

map (\i -> i * 2) (fromList [1, 2, 3]) -- {2, 4, 6}


And if we use a function that returns duplicate values, they’re deduplicated automatically:

map (always 1) (fromList [1, 2, 3]) -- {1}


And… that’s it! That’s the whole Set API! If you’ve been following along this whole time, you should know a lot more about how to implement data structures in Elm. We’ll be back next week to sum up and sneak a peek at how we can extend our Sets to be Dicts.