[Haskell-cafe] Data structure containing elements which are instances of the same type class

[Alexander Solla]

On Tue, Aug 7, 2012 at 11:03 AM, Daniel Trstenjak <
daniel.trstenjak at gmail.com> wrote:

>
> Hi all,
>
> it should be possible a call a function on all elements of the data
> structure, to add and remove elements.
>
> What I currently have:
>
> the type class:
>
> class Foo a where
>    hasId :: a -> Int -> Maybe a
>
>
> a few instances:
>
> data A = A deriving Show
> instance Foo A where
>    hasId a 1 = Just a
>    hasId _ _ = Nothing
>
> data B = B deriving Show
> instance Foo B where
>    hasId a 2 = Just a
>    hasId _ _ = Nothing
>
> data C = C deriving Show
> instance Foo C where
>    hasId a 3 = Just a
>    hasId _ _ = Nothing
>
>
> the data structure holding any instance of Foo, which itself is a
> instance of Foo:
>
> data Foos l r = Foos l r
>               | FooL l
>               | FooR r
>               | NoFoos deriving Show
>
> instance (Foo l, Foo r) => Foo (Foos l r) where
>    hasId (Foos l r) id =
>       case (hasId l id, hasId r id) of
>            (Just l, Just r) -> Just $ Foos l r
>            (Just l, _     ) -> Just $ FooL l
>            (_     , Just r) -> Just $ FooR r
>            _                -> Nothing
>
>
> combinator for Foos:
>
> (+++) :: l -> r -> Foos l r
> l +++ r = Foos l r
> infixr 5 +++
>
>
> Now I can write:
>
> *Main> A +++ B +++ C +++ A
> Foos A (Foos B (Foos C A))
> *Main> (A +++ B +++ C +++ A) `hasId` 1
> Just (Foos A (FooR (FooR A)))
>
>
> Doesn't seem that nice. For every operation I would have to extend the
> type class. After some operations the data structure contains many
> dummy nodes (FooR, FooL).
>
> Is there some nicer way?
>

Read "Data types a la carte".  You can use the "free" package for most of
the plumbing (I think -- it definitely does free monads, which are a
tangentially related idea, but it has a module for dealing with these funny
functors, if I recall correctly.)
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