Re: [Haskell-beginners] Constructor classes and type classes.

Hi Patrick, I am not sure I understand what you are trying to do, but here are some thoughts. - your use of the names `typeVar` and `typeCons` make total sense to me. But your name `dataCons` in the definition of SetClass2 does not. You are only talking about types here. All you are doing is talking about *type* constructors. You are not constructing a specific value of that type. Maybe one way to see the difference between the type constructors and the data constructors is to change your first line to: data SetType typeVar = SetTypeDataConstructor [typeVar] deriving Show - I also don't understand why you named your type variable `dataVariable` instead of sticking to `typeVar` in SetClass3. It is a *type* variable in the type signature of the functions in the type class. - I don't understand what you mean by a "constructor class". My simple understanding of what a type constructors and data constructors are is here https://wiki.haskell.org/Constructor#Type_constructor. - I don't see the terms super class and sub class ever used in haskell land. Although I do understand they make sense, I think they are really OO terms. I've tried to map OO concepts into haskell and there are many different ways to do it. The best description of all those ways that I found was in Oleg Kiselyov's work https://arxiv.org/pdf/cs/0509027.pdf - I think parametric polymorphism as used in haskell forces us to compare types in terms of equality constraints (this type is "the same" as that), whereas subtype polymorphism as used in OO languages forces us to think in terms of inequalities (this type is "more specific" than that). I think those force fundamentally different ways to think about and model your problems. I would encourage you to use equality as much as possible, but if you want to model subtyping in haskell, I think Oleg's work above has a few approaches that I think are better than type classes. In particular, in OO there was always an ambiguity between modelling subtyping with inheritance or with a "has a" relationship when the subclass explicitly contains an object of the superclass. You can use the latter idea in haskell, Oleg's work has a good way to do it. Hope this helps. Cheers, Dimitri

From: PATRICK BROWNE To: The Haskell-Beginners Mailing List - Discussion of primarily beginner-level topics related to Haskell Subject: [Haskell-beginners] Constructor classes and type classes. Message-ID: Content-Type: text/plain; charset="utf-8"

{- I am trying to understand constructor classes and their relationship with ordinary type classes. I wrote the code below to help me understand the distinction. The code is only for explanatory purposes, set operations use a tuple syntax.

I use the naming convention of 'typeVar', 'typeCons', and 'dataCons' for type variables, type constructors, and data constructors respectively. Question1: Is my naming convention correct? I am particularly concerned about SetClass3 where the super class seems to use a type constructor but the subclass seems to use the same term as a data constructor.

Q2: In this case constructor classes and type classes seem to provide similar functionality. In general what situation are each best suited? -}

import Data.List data SetType typeVar = SetType [typeVar] deriving Show

class SetClass1 typeCons where member1 :: Eq typeVar => (typeVar, typeCons typeVar) -> Bool intersect1 :: (Eq typeVar,Show typeVar) => (typeCons typeVar, typeCons typeVar) -> typeCons typeVar

class SetClass2 dataCons typeVar where member2 :: (typeVar, (dataCons typeVar)) -> Bool intersect2 :: (dataCons typeVar, dataCons typeVar) -> dataCons typeVar

class SetClass1 typeCons => SetClass3 typeCons dataVariable where union3 :: (Eq dataVariable,Show dataVariable) => (typeCons dataVariable, typeCons dataVariable) -> typeCons dataVariable

instance SetClass1 SetType where member1 (x ,(SetType y)) = elem x y intersect1 ((SetType x),(SetType y)) = SetType (intersect x y)

instance SetClass2 SetType Int where member2 (x ,SetType y) = elem x y intersect2 (SetType x,SetType y) = SetType (intersect x y)

instance SetClass3 SetType Int where union3 (SetType x,SetType y) = SetType (union x y)

test1a = member1 (1, (SetType [1,2])) test1b = intersect1 ((SetType [1,3,4]),(SetType [1,2])) test2a = member2 (1, (SetType [1::Int])) test2b = intersect2 ((SetType [1::Int]), (SetType [(1::Int)])) test3a = union3 ((SetType [1::Int,2::Int,3::Int]),(SetType [4::Int,5::Int]))

-- 2E45 D376 A744 C671 5100 A261 210B 8461 0FB0 CA1F -- 2E45 D376 A744 C671 5100 A261 210B 8461 0FB0 CA1F