GHC.Classes

The syntax ?x :: a is desugared into IP "x" a IP is declared very early, so that libraries can take advantage of the implicit-call-stack feature

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, instances are encouraged to follow these properties:

Reflexivity

x == x

=

True

Symmetry

x == y

=

y == x

Transitivity

if

x == y && y == z

=

True

, then

x == z

=

True

Extensionality

if

x == y

=

True

and

f

is a function whose return type is an instance of

Eq

, then

f x == f y

=

True

Negation

x /= y

=

not (x == y)

The Ord class is used for totally ordered datatypes.

Instances of Ord can be derived for any user-defined datatype whose constituent types are in Ord. The declared order of the constructors in the data declaration determines the ordering in derived Ord instances. The Ordering datatype allows a single comparison to determine the precise ordering of two objects.

Ord, as defined by the Haskell report, implements a total order and has the following properties:

Comparability

x <= y || y <= x

=

True

Transitivity

if

x <= y && y <= z

=

True

, then

x <= z

=

True

Reflexivity

x <= x

=

True

Antisymmetry

if

x <= y && y <= x

=

True

, then

x == y

=

True

The following operator interactions are expected to hold:

1. x >= y = y <= x

2. x < y = x <= y && x /= y

3. x > y = y < x

4. x < y = compare x y == LT

5. x > y = compare x y == GT

6. x == y = compare x y == EQ

7. min x y == if x <= y then x else y = True

8. max x y == if x >= y then x else y = True

Note that (7.) and (8.) do not require min and max to return either of their arguments. The result is merely required to equal one of the arguments in terms of (==).

Minimal complete definition: either compare or <=. Using compare can be more efficient for complex types.

Boolean "and", lazy in the second argument

Boolean "or", lazy in the second argument

Boolean "not"