FunSet Elm- fold operation

Question

I am trying to solve this question.

type alias FunSet = Int -> Bool          
contains : FunSet -> Int -> Bool   
contains set elem = set elem

singletonSet : Int -> FunSet  
singletonSet elem = \inputElem -> elem == inputElem

union : FunSet -> FunSet -> FunSet   
union a b = (\x -> (contains a x) || (contains b x))   

          

My fold function should do the following: Takes a list of sets and returns a new set, which is build by applying a fold using operation function.

fold: List FunSet -> ( FunSet -> FunSet -> FunSet ) -> FunSet
fold operation sets = 

Example:

(fold union [(singletonSet 1), (singletonSet 2), (singletonSet 3)]) 1 == True

It is not clear to me how should I do this. Hope someone can help ^^

Answer 1

You can use List.foldl or List.foldr for this:

fold sets f = 
  case sets of
    [] -> \_ -> False
    x :: xs -> List.foldl f x xs

I feel it would be easier to define emptySet _ = False and directly use List.foldl:

List.foldl union emptySet [(singletonSet 1), (singletonSet 2), (singletonSet 3)]

Note that the first parameter of List.foldl is a function that takes first an element and then the accumulator, rather than the other way around, so you can't simply use fold sets diff, you'd have to use fold sets (flip diff) to flip the arguments.