[Haskell-beginners] expressing constraints 101

[akash g]

Hi Dimitri,

You can express the constraints as below

class Set s where
  empty  :: s a               -- returns an empty set of type Set of a
  insert :: (Ord a) => a -> s a -> s a   -- returns set with new element
inserted
  member :: (Ord a) => a -> s a -> Bool  -- True if element is a member of
the Set

This is because when you define tree as an instance of the typeclass 'Set',
you don't match the constraints on the functions that the functions that it
wants you to implement  That is, when you do:


treeInsert :: Ord a => a -> Tree a -> Tree a
treeInsert = undefined

instance Set Tree where
  empty  = treeEmpty
  insert = treeInsert
  member = treeMember

The type signature doesn't match when you do insert=treeInsert or
member=treeMember, since you have

class Set s where
   insert :: a -> s a -> s a

Hope this helps

- G Akash



On Wed, Aug 13, 2014 at 8:44 AM, Dimitri DeFigueiredo <
defigueiredo at ucdavis.edu> wrote:

> Hi All,
>
> I am working through an exercise in Chris Okasaki's book (#2.2). In the
> book, he is trying to implement a minimal interface for a Set. I wrote that
> simple interface in Haskell as:
>
> class Set s where
>     empty  :: s a                -- returns an empty set of type Set of a
>     insert :: a -> s a -> s a   -- returns set with new element inserted
>     member :: a -> s a -> Bool  -- True if element is a member of the Set
>
> To implement that interface with the appropriately O(log n) insert and
> member functions he suggests the use of a Binary Search Tree, which I
> translated to Haskell as:
>
> data Tree a = Empty | MkTree (Tree a) a (Tree a)
>
> But for the tree to work, we also need the "a"s to be totally ordered.
> I.e. (Ord a) is a constraint. So, it makes sense to write:
>
> treeEmpty :: Tree a
> treeEmpty = Empty
>
> treeInsert :: Ord a => a -> Tree a -> Tree a
> treeInsert = undefined
>
> treeMember :: Ord a => a -> Tree a -> Bool
> treeMember = undefined
>
> Now, I would like to bind this implementation using Trees of an ordered
> type "a" to the set type class. So, I would like to write something like:
>
> instance Set Tree where
>     empty  = treeEmpty
>     insert = treeInsert
>     member = treeMember
>
> But that doesn't work. Using GHC 7.6.3, I get a:
>
>     No instance for (Ord a) arising from a use of `treeInsert'
>     Possible fix:
>       add (Ord a) to the context of
>         the type signature for insert :: a -> Tree a -> Tree a
>     In the expression: treeInsert a
>     In an equation for `insert': insert a = treeInsert a
>     In the instance declaration for `Set Tree'
>
> Which makes sense, but I'm not sure how to express this constraint.
> So, what is the proper way to do this?
> Where have I gone wrong?
>
>
> Thanks!
>
> Dimitri
>
>
>
>
>
>
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