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
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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