Ord -package:basic-prelude -package:basement -package:leancheck

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.

Orderings

Basic operations on type-level Orderings.

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.

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. The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

• 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

Note that 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.

TextShow instances for Ordering and Down. Since: 2

Ord properties You will need TypeApplications to use these.

Equality and ordering. Note that equality doesn't really require a class, it can be defined uniformly as TyEq.

Ord properties You will need TypeApplications to use these.

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. The Haskell Report defines no laws for Ord. However, <= is customarily expected to implement a non-strict partial order and have the following properties:

• 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

Note that 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

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

Bidirectional operations over Ordering.

Linear Orderings Linear orderings provide a strict order. The laws for (<=) for all <math>:

• reflexivity: <math>
• antisymmetry: <math>
• transitivity: <math>

and these "agree" with <:

• x <= y = not (y > x)
• x >= y = not (y < x)

Unlike in the non-linear setting, a linear compare doesn't follow from <= since it requires calls: one to <= and one to ==. However, from a linear compare it is easy to implement the others. Hence, the minimal complete definition only contains compare.

ordinal number, not spelled

• This module is deprecated and will be removed*

This module no-longer does anything since URI now has an Ord instance by default (prior to network 2.4.0.0@ this was not the case). This module used to provide an ordering for earlier versions of the network package, but with the split of URI out to the network-uri in version 2.6.0.0, the CPP needed to keep this going got annoying enough for me to just require a recent network package.

The fromEnum method restricted to the type Char.