[Haskell-beginners] expressing constraints 101

[Dimitri DeFigueiredo]

Hi G Akash,

Is that the only solution? I thought about that. The problem with it is 
that it changes the Set type class. I want the Set type class to be able 
to contain elements of any type, not just members of Ord.

I think the type class represents a "Set" interface that is general. It 
is the implementation using trees that is only available for Ordered 
types. And there may be other implementations that don't need this 
constraint. So, if possible, I don't want to change the Set type class. 
Isn't there another way to fix it?


Thanks,


Dimitri


Em 12/08/14 23:18, akash g escreveu:
> 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 <mailto: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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