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The Concepts Equal and Ordering

The Concepts Equal and Ordering

Apply theoretical knowledge to define advanced concepts: 'Ordering' and 'Equal'.

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Haskell’s type classes Eq and Ord

In the previous lessons, I answered two essential questions about concepts: “How can a concept be used?” and “How can you define your concepts?”. In this lesson and the lesson ahead, I want to apply the theoretical knowledge provided in those sections to define more advanced concepts such as Ordering, SemiRegular, and Regular.

I presented already in the short detour to the long, long history of concepts a part of Haskell’s type classes hierarchy:

The class hierarchy shows that the type class Ord is a refinement of the type class Eq. Haskell expresses this elegantly.

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class Eq a where
    (==) :: a -> a -> Bool
    (/=) :: a -> a -> Bool
class Eq a => Ord a where
    compare :: a -> a -> Ordering
    (<) :: a -> a -> Bool
    (<=) :: a -> a -> Bool
    (>) :: a -> a -> Bool
    (>=) :: a -> a -> Bool
    max :: a -> a -> a

Each type a supporting the type class Eq (line ...