Order
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object Order
| package algebra
Returns true if x and y are equivalent, false otherwise.
Returns true if x and y are equivalent, false otherwise.
Returns false if x and y are equivalent, true otherwise.
Returns false if x and y are equivalent, true otherwise.
Defines an order on B by mapping B to A using f and using As
order to order B.
Defines an order on B by mapping B to A using f and using As
order to order B.
Result of comparing x with y.
Result of comparing x with y. Returns NaN if operands
are not comparable. If operands are comparable, returns a
Double whose sign is:
- negative iff x < y
- zero iff x === y
- positive iff x > y
Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.
Returns Some(x) if x >= y, Some(y) if x < y, otherwise None.
Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.
Returns Some(x) if x <= y, Some(y) if x > y, otherwise None.
Defines an ordering on A where all arrows switch direction.
Defines an ordering on A where all arrows switch direction.
Result of comparing x with y.
Result of comparing x with y. Returns None if operands
are not comparable. If operands are comparable, returns Some[Int]
where the Int sign is:
- negative iff x < y
- zero iff x == y
- positive iff x > y
The
Ordertype class is used to define a total ordering on some typeA. An order is defined by a relation <=, which obeys the following laws:- either x <= y or y <= x (totality) - if x <= y and y <= x, then x == y (antisymmetry) - if x <= y and y <= z, then x <= z (transitivity)
The truth table for compare is defined as follows:
x <= y x >= y Int true true = 0 (corresponds to x == y) true false < 0 (corresponds to x < y) false true > 0 (corresponds to x > y)
By the totality law, x <= y and y <= x cannot be both false.