haskell set data type

Question

hey everyone I am trying to figure out how to make a set data type in haskell, but I cannot figure this out, this is what i have so far, i am a bit confused

data Set a = Node a | List {
    list :: [a]
}deriving(Eq,Show,Ord)

insert :: Set Integer -> Set Integer -> Bool
insert (Node itemToInsert) (List list)
    |contains (List list) (Node itemToInsert) == False = List(list:(Node itemToInsert))


contains :: Set Integer -> Set Integer -> Bool
contains (List []) (Node numberToFind) = False
contains (List (x:xs)) (Node numberToFind)
    |x == (Node numberToFind) = True
    |otherwise = contains (List (xs)) (Node numberToFind)

Thanks for the help!

Answer 1

From your code it seems you have already understood, that a set can be seen as a list without duplicates. So let us express this in a simple type definition:

data Set a = Set [a]

In order to ensure that there are no duplicates, one can introduce 'smart constructors' which are functions that aren't technically a constructor, but which are used as such.

empty :: Set a
empty = Set []

We'll need another one to create non-empty sets. Let's have a look at your insert function. Why does it return a Bool ? Shouldn't it return a set? Why does insert expect two sets? So to insert an integer into a set of integers one could you use the following type signature:

insert :: Integer -> Set Integer -> Set Integer

The implementation consists of two cases: 1. the given integer is not in the given set, and 2. the given integer is in the given set.

insert x (Set xs)
    | not (x `elem` xs) = Set (x:xs)
    | otherwise         = Set xs

Since, this question seems to be part of a homework assignment. I'd say you should try to figure out how to implement elem yourself.