Wed Mar 30 07:03:13 CEST 2011

```Hi Steffen,

class has 100 methods and
that 1000 fully evaluated shapes are placed in a list.  In this
technique require more memory than the GADT technique, because each
instance of the Shape data
type would have  to carry 100 pointers to functions, whereas in the
of the ShapeD data type would only have to "remember" what type
(Circle, Rect, etc.) it is?  (I'm asking
under the covers.)

On Tue, Mar 29, 2011 at 2:53 AM, Steffen Schuldenzucker
<sschuldenzucker at uni-bonn.de> wrote:
>
>
> 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
>>
>> 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.)
>>