Cool. It's more and more clear guys. Thanks a lot. I'll check that "expression problem". "Existential types" sounds a bit scary :) On Tue, Sep 15, 2009 at 3:26 PM, Sean Leather wrote:

...

Perimeter doesn't make sense for Sphere or Cylinder. So we could define a type class for objects that have perimeter and make an instance of it only for Circle (data Circle = Circle Position Radius). Make sense. But these three functions above have desired behaviour. If user has a list of objects like [Sphere, Circle, Circle, Cylinder] he would like to calculate perimeters of each object using map perimerer list (in this case we also have to modify Geometry data type). So we could make instances of "perimeter" type class for all objects and return zero in case if perimeter doesn't make sense. Same as previous version but with typeclasses and with additional constructors (constructors for each type of object + constructors in Geometry data). Looks a bit overcomplicated. Any reasons to use type classes in this case? Maybe there is something I'm missing?

If you're talking about a single datatype with multiple constructors, then the function 'perimeter :: Geometry -> Maybe Double' makes sense. If you're talking about multiple datatypes, then you probably want to go type class route.

data Sphere = Sphere ... data Circle = Circle ...

class Perimeter a where perimeter :: a -> Double instance Perimeter Circle where perimeter (Circle ...) = ... -- No instance for Sphere

class Volume a where volume :: a -> Double instance Volume Sphere where volume (Sphere ...) = ... -- No instance for Circle

You have to decide whether (1) a datatype Geometry makes sense or (2) a datatype per geometric entity is better. One advantage to #1 is that writing functions over the datatype is easy. One advantage to #2 is that you have fewer (partial) 'Maybe' functions. This is also related to the "expression problem," a Googleable term.

As for having a list of objects, you can do it with either approach. The second approach may require existential types.

Regards, Sean

Thanks for explanation Sean! On Tue, Sep 15, 2009 at 4:30 PM, Sean Leather wrote:

...

"Existential types" sounds a bit scary :)

...

It's unfortunate that they've developed a scariness feeling associated with them. They can be used in strange ways, but simple uses are quite approachable. One way to think of them is like implementing an object-oriented interface. You know it's an object, but you can't do anything with it except use the methods of the interface.

---

{-# LANGUAGE ExistentialQuantification #-}

data Square = Square ... data Circle = Circle ...

class Perimeter a where perimeter :: a -> Double instance Perimeter Square where perimeter (Square ...) = ... instance Perimeter Circle where perimeter (Circle ...) = ...

-- The 'a' is hidden here. The interface is defined by the class constraint. data Perimeterizable = forall a . (Perimeter a) => P a

-- This is the accessor method for things Perimeterizable. getPerimeter (P x) = perimeter x

vals :: [Perimeterizable] vals = [P Square, P Circle]

perims = map getPerimeter vals

---

Regards, Sean

It's hard to say what really is 2d or 3d. Think about closed 3d curve (points placed in 3d space somehow). Is it 2d or 3d? Depends on the interpretation. Usually DCC packages don't care about this. And I wouldn't too :p Who needs extra level of complexity without any reason? On Tue, Sep 15, 2009 at 3:48 PM, Tom Nielsen wrote:

I think you are in trouble because you have mixed 2D and 3D shapes in one data type.

--not checked for typos, syntax, idiocy etc. {-# LANGUAGE GADTs #-}

data Z data S n

type Two = S (S Z) type Three = S Two

data Geometry dims where Sphere :: Position -> Radius -> Geometry Three Cylinder :: Position -> Radius -> Height -> Geometry Three Circle :: Position -> Radius -> Geometry Two

Postcard :: Position -> Orientation -> Geometry Two -> Geometry Three

perimeter :: Geometry Two -> Double perimeter (Circle _ r) = 2*pi*r

Tom

On Tue, Sep 15, 2009 at 11:29 AM, Olex P wrote:

...

Hey guys,

It's a dumb question but I'd like to know a right answer... Let's say we have some geometry data that can be Sphere, Cylinder, Circle and so on. We can implement it as new data type plus a bunch of functions that work on this data:

data Geometry = Sphere Position Radius | Cylinder Position Radius Height | Circle Position Radius deriving (Show)

perimeter (Sphere _ r) = 0.0 perimeter (Cylinder _ r h) = 0.0 perimeter (Circle _ r) = 2.0 * pi * r

Perimeter doesn't make sense for Sphere or Cylinder. So we could define a type class for objects that have perimeter and make an instance of it only for Circle (data Circle = Circle Position Radius). Make sense. But these three functions above have desired behaviour. If user has a list of objects like [Sphere, Circle, Circle, Cylinder] he would like to calculate perimeters of each object using map perimerer list (in this case we also have to modify Geometry data type). So we could make instances of "perimeter" type class for all objects and return zero in case if perimeter doesn't make sense. Same as previous version but with typeclasses and with additional constructors (constructors for each type of object + constructors in Geometry data). Looks a bit overcomplicated. Any reasons to use type classes in this case? Maybe there is something I'm missing?

Cheers, -O

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