PartialOrder
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object PartialOrder
| package numbers
Result of comparing x with y.
Result of comparing x with y. Returns ValidIO[ComparisonBundle]
with valid false if operands are not comparable. If operands are
comparable, bits.lt will be true if x < y and bits.eq will
be true if x = y
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 a partial order on B by mapping B to A using f and using As
order to order B.
Defines a partial order on B by mapping B to A using f and using As
order to order B.
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 a partial order on A where all arrows switch direction.
The
PartialOrdertype class is used to define a partial ordering on some typeA.A partial order is defined by a relation <=, which obeys the following laws:
- x <= x (reflexivity) - if x <= y and y <= x, then x === y (anti-symmetry) - if x <= y and y <= z, then x <= z (transitivity)
To compute both <= and >= at the same time, we use a Double number to encode the result of the comparisons x <= y and x >= y. The truth table is defined as follows:
x <= y x >= y Double true true = 0.0 (corresponds to x === y) false false = NaN (x and y cannot be compared) true false = -1.0 (corresponds to x < y) false true = 1.0 (corresponds to x > y)