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Some kind of equality in programming

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Let us focus here on equality of data as it is used in programming. Different kinds of equality exist: structural equality, semantic equality, reference equality, and possibly others. For example, trivially, the following equalities or inequalities hold as demonstrated at the interpreter prompt of Language:Haskell:

> 42 == 42
True
> 42 == 41
False
> True == True
True
> "Foo" == "Bar"
False

In various programming languages, equality may be defined by the programmer. For instance, Language:Haskell designates a type class Eq to equality (readily defined in the Haskell Prelude:

-- A type class for equality
class Eq a
  where
    (==) :: a -> a -> Bool

For instance, equality of Booleans would be defined by the following type-class instance:

-- Equality of Booleans
instance Eq Bool
  where
    True == True = True
    False == False = True
    _ == _ = False

More interestingly, equality of lists would be defined such that the two lists need to be of the same length and their elements need to be equal in a pairwise manner; thus we also need equality for the element type, which is expressed by the extra constraint in the instance:

-- Equality of lists
instance Eq a => Eq [a]
  where
    x == y =  length x == length y
           && and (map (uncurry (==)) (zip x y))

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