trait UpperSemilattice[X] extends AnyRef
Represents a upper-semilattice, i.e., a partially-ordered set in which every finite non-empty subset has a least upper bound.
An instance of this typeclass should satisfy the following axioms:
- Supremum associativity: ∀a, b, c∈X, sup(a, sup(b, c)) == sup(sup(a, b), c).
- Supremum commutativity: ∀a, b∈X, sup(a, b) == sup(b, a).
- Supremum idempotency: ∀a∈X, sup(a, a) == a.
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- UpperSemilattice[X]
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abstract
def
sup(x: X, y: X): X
Returns the supremum (join, a.k.a.
Returns the supremum (join, a.k.a. least upper bound) of the two arguments.
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- def asSemigroupWithSup: CSemigroup[X]
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