Superclass & Subclass

[klequis]

Brief

A type has a superclass if its definition contains a type constraint.

Num does not have any superclasses

class Num a where

Fractional has Num as a superclass

class Num a => Fractional a where

• A subclass can use the methods defined in its superclass(es).
• A superclass cannot use the methods defined in its subclass(es).

Int is not a class

data Int

And therefore, cannot be a subclass nor a superclass.

Superclass

• Fractional is a type class that requires types to already have an instance of the Num type class. Therefore Num is a superclass of Fractional.
• Therefore, + & other functions from the Num typeclass can be used with Fractional

The methods of Num are

• (+) :: a -> a -> a
• (-) :: a -> a -> a
• (*) :: a -> a -> a
• negate :: a -> a
• abs :: a -> a
• signum :: a -> a
• fromInteger :: Integer -> a

The methods of Fractional are

• (/) :: a -> a -> a
• recip :: a -> a
• fromRational :: Rational -> a

However, a value of type Fractional can use all the methods of Num because the definition for Fractional says that all values that are Fractional must be Num.

class Num a => Fractional a where

Subclass

Again:

• Fractional is a type class that requires types to already have an instance of the Num type class.

Therefore Num is a subclass of Fractional.