[Haskell-cafe] specifying using type class

[Ertugrul Söylemez]

Patrick Browne <patrick.browne at dit.ie> wrote:

> {-
> Below is a *specification* of a queue.
> If possible I would like to write the equations in type class.
> Does the type class need two type variables?
> How do I represent the constructors?
> Can the equations be written in the type class rather than the
> instance? -}

(Side note:  When opening a new topic, please don't /reply/ to a post,
but post it separately by creating a new mail.)

The type class needs to know the element type, so your observation is
correct.  Usually, as in your case, the element type follows from the
data structure type, and you will want to inform the type system about
this connection.  There are basically three ways to do it.  The first is
using MultiParamTypeClasses and FunctionalDependencies:

    class Stacklike a s | s -> a where
        empty :: s a
        null  :: s a -> Bool
        push  :: a -> s a -> s a
        pop   :: s a -> Maybe a
        size  :: s a -> Int
        tail  :: s a -> Maybe (s a)

Another way is using an associated type (TypeFamilies).  This is
cleaner, but much more noisy in the type signatures:

    class Stacklike s where
        type StackElement s

        empty :: s (StackElement s)
        null  :: s (StackElement s) -> Bool
        push  :: StackElement s -> s (StackElement s) -> s (StackElement s)
        pop   :: s (StackElement s) -> Maybe (StackElement s)
        size  :: s (StackElement s) -> Int
        tail  :: s (StackElement s) -> Maybe (s (StackElement s))

Finally once you realize that there is really no need to fix the element
type in the type class itself, you can simply write a type class for the
type constructor, similar to how classes like Functor are defined:

    class Stacklike s where
        empty :: s a
        null  :: s a -> Bool
        push  :: a -> s a -> s a
        pop   :: s a -> Maybe a
        size  :: s a -> Int
        tail  :: s a -> Maybe (s a)

The big question is whether you want to write a class at all.  Usually
classes are used to capture patterns, not operations.


Greets,
Ertugrul

-- 
Not to be or to be and (not to be or to be and (not to be or to be and
(not to be or to be and ... that is the list monad.
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