Actually, Tako:

data Shape = forall a. Drawable a => Shape a

Can also be done with GADTs:

   data Shape where
       Shape :: Drawable a => a -> Shape

If wouldn't know if one approach is preferable to the other or if is just a matter of taste.

Your problem, Tad, is kind of common. I ran against it several times. I know of two ways to solve it :

- "The open way" (this is your method, with a class ShapeC and datatype ShapeD which wraps instances of ShapeC)

- "The closed way", which can be broken in two alternatives:

* Using a plain Haskell98 ADT:
    data Shape = Circle .... | Rectangle ....
    draw :: Shape -> String
    draw (Circle ...) = ...
    draw (Rectangle ...) = ...

Flexible and simple, but not safe, since you have no way to type-diferenciate Circles from Rectangles.

* Using a GADT and empty data declarations:
    data Circle
    data Rectangle
    data Shape a where
        Circle :: Double -> Double -> Double -> Shape Circle
        Rectangle :: Double -> Double -> Double -> Double -> Shape Rectangle

And then you can both use "Shape a" or "Shape Circle/Shape Rectangle", which enables you either to make lists of Shapes or to specifically use Circles or Rectangles.

The drawback of it is that since you have a closed type (the GADT Shape), you cannot add a new shape without altering it.

2011/3/29 Steffen Schuldenzucker <sschuldenzucker@uni-bonn.de>

Tad,

It doesn't look bad, but depending on what you want to do with the
[ShapeD] aftewards you might not need this level of generality.

Remember that the content of a ShapeD has type (forall a. ShapeC a =>
a), so all you can do with it is call class methods from ShapeC. So if
all you do is construct some ShapeD and pass that around, the following
solution is equivalent:

data Shape = Shape {
draw :: String
copyTo :: Double -> Double -> Shape
-- ^ We loose some information here. The original method of ShapeC
-- stated that copyTo of a Rectangle will be a rectangle again
-- etc. Feel free to add a proxy type parameter to Shape if this
-- information is necessary.
}

circle :: Double -> Double -> Double -> Shape
circle x y r = Shape dc $ \x y -> circle x y r
where dc = "Circ (" ++ show x ++ ", " ++ show y ++ ") -- "" ++ show r

rectangle :: Double -> Double -> Double -> Double -> Shape
rectangle x y w h = ... (analogous)

shapes = [rectangle 1 2 3 4, circle 4 3 2, circle 1 1 1]

-- Steffen

On 03/29/2011 07:49 AM, Tad Doxsee wrote:

I've been trying to learn Haskell for a while now, and recently
wanted to do something that's very common in the object oriented
world, subtype polymorphism with a heterogeneous collection. It took
me a while, but I found a solution that meets my needs. It's a
combination of solutions that I saw on the web, but I've never seen
it presented in a way that combines both in a short note. (I'm sure
it's out there somewhere, but it's off the beaten path that I've been
struggling along.) The related solutions are

1. section 3.6 of http://homepages.cwi.nl/~ralf/OOHaskell/paper.pdf

2. The GADT comment at the end of section 4 of
http://www.haskell.org/haskellwiki/Heterogenous_collections

I'm looking for comments on the practicality of the solution, and
references to better explanations of, extensions to, or simpler
alternatives for what I'm trying to achieve.

Using the standard example, here's the code:

data Rectangle = Rectangle { rx, ry, rw, rh :: Double } deriving (Eq,
Show)

drawRect :: Rectangle -> String drawRect r = "Rect (" ++ show (rx r)
++ ", " ++ show (ry r) ++ ") -- " ++ show (rw r) ++ " x " ++ show
(rh r)

data Circle = Circle {cx, cy, cr :: Double} deriving (Eq, Show)

drawCirc :: Circle -> String drawCirc c = "Circ (" ++ show (cx c) ++
", " ++ show (cy c)++ ") -- " ++ show (cr c)

r1 = Rectangle 0 0 3 2 r2 = Rectangle 1 1 4 5 c1 = Circle 0 0 5 c2 =
Circle 2 0 7

rs = [r1, r2] cs = [c1, c2]

rDrawing = map drawRect rs cDrawing = map drawCirc cs

-- shapes = rs ++ cs

Of course, the last line won't compile because the standard Haskell
list may contain only homogeneous types. What I wanted to do is
create a list of circles and rectangles, put them in a list, and draw
them. It was easy for me to find on the web and in books how to do
that if I controlled all of the code. What wasn't immediately obvious
to me was how to do that in a library that could be extended by
others. The references noted previously suggest this solution:

class ShapeC s where draw :: s -> String copyTo :: s -> Double ->
Double -> s

-- needs {-# LANGUAGE GADTs #-} data ShapeD where ShapeD :: ShapeC s
=> s -> ShapeD

instance ShapeC ShapeD where draw (ShapeD s) = draw s copyTo (ShapeD
s) x y = ShapeD (copyTo s x y)

mkShape :: ShapeC s => s -> ShapeD mkShape s = ShapeD s

instance ShapeC Rectangle where draw = drawRect copyTo (Rectangle _ _
rw rh) x y = Rectangle x y rw rh

instance ShapeC Circle where draw = drawCirc copyTo (Circle _ _ r) x
y = Circle x y r

r1s = ShapeD r1 r2s = ShapeD r2 c1s = ShapeD c1 c2s = ShapeD c2

shapes1 = [r1s, r2s, c1s, c2s] drawing1 = map draw shapes1

shapes2 = map mkShape rs ++ map mkShape cs drawing2 = map draw
shapes2

-- copy the shapes to the origin then draw them shapes3 = map (\s ->
copyTo s 0 0) shapes2 drawing3 = map draw shapes3

Another user could create a list of shapes that included triangles by
creating a ShapeC instance for his triangle and using mkShape to add
it to a list of ShapeDs.

Is the above the standard method in Haskell for creating an
extensible heterogeneous list of "objects" that share a common
interface? Are there better approaches? (I ran into a possible
limitation to this approach that I plan to ask about later if I can't
figure it out myself.)

- Tad

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