sample3.txt

The 'Eq' class defines equality ('==') and inequality ('/=').
All the basic datatypes exported by the "Prelude" are instances of 'Eq',
and 'Eq' may be derived for any datatype whose constituents are also
instances of 'Eq'.

The Haskell Report defines no laws for 'Eq'. However, '==' is customarily
expected to implement an equivalence relationship where two values comparing
equal are indistinguishable by "public" functions, with a "public" function
being one not allowing to see implementation details. For example, for a
type representing non-normalised natural numbers modulo 100, a "public"
function doesn't make the difference between 1 and 201. It is expected to
have the following properties:

[__Reflexivity__]: @x '==' x@ = 'True'
[__Symmetry__]: @x == y@ = @y == x@
[__Transitivity__]: if @x == y && y == z@ = 'True', then @x == z@ = 'True'
[__Substitutivity__]: if @x == y@ = 'True' and @f@ is a "public" function
whose return type is an instance of 'Eq', then @f x == f y@ = 'True'
[__Negation__]: @x /= y@ = @not (x == y)@

Minimal complete definition: either '==' or '/='.