what's the difference?

[Emre Tezel]

Cagdas Ozgenc wrote:

> Greetings.
> 
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> What is the difference between the following two scenarios:
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> 1)
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> class Eq a where
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>     (==) :: a -> a -> Bool
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> class Eq a => Ord a where
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>     ( < ) :: a -> a -> Bool


Here you are doing subtyping. A variable of type Ord can be substitued 
for variable of type Eq. (==) belongs to Ord interface.


> 
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> 2)
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> class Eq a where
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>     (==) :: a -> a -> Bool
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> class Ord a where
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>     (eq),( < ) :: a -> a -> Bool
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> instance Ord a => Eq a where
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>      (==) = eq


Here Ord is not a subtype of Eq. Even (eq) and (==) have the same 
definition, (==) is not part of Ord's interface. You are doing 
delegation. For those instances of Eq who happens to implement Ord 
interface, delegate (==) to (eq).

The second case is similar to private inheritance in C++. You are 
overiding the virtual (==) of base class (Eq) in the derived class 
(Ord), but (==) is not part of  derived class' interface.


> 
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> eq is just a rename for == to avoid the nameclash
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> The second scenario resembles Russell's Paradox. Typeclass of a 
> typeclass. Anyhow we are loosing orthogonality here.
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> Thanks
>