trait Lattice[A] extends JoinSemilattice[A] with MeetSemilattice[A]
A lattice is a set A together with two operations (meet and
join). Both operations individually constitute semilattices (join-
and meet-semilattices respectively): each operation is commutative,
associative, and idempotent.
Join can be thought of as finding a least upper bound (supremum), and meet can be thought of as finding a greatest lower bound (infimum).
The join and meet operations are also linked by absorption laws:
meet(a, join(a, b)) = join(a, meet(a, b)) = a
- Self Type
- Lattice[A]
- Source
- Lattice.scala
Linear Supertypes
Known Subclasses
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Inherited
- Lattice
- MeetSemilattice
- JoinSemilattice
- Serializable
- Serializable
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Visibility
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Abstract Value Members
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abstract
def
getClass(): Class[_]
- Definition Classes
- Any
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abstract
def
join(lhs: A, rhs: A): A
- Definition Classes
- JoinSemilattice
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abstract
def
meet(lhs: A, rhs: A): A
- Definition Classes
- MeetSemilattice
Concrete Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
- Any
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final
def
##(): Int
- Definition Classes
- Any
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final
def
==(arg0: Any): Boolean
- Definition Classes
- Any
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
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def
dual: Lattice[A]
This is the lattice with meet and join swapped
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def
equals(arg0: Any): Boolean
- Definition Classes
- Any
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def
hashCode(): Int
- Definition Classes
- Any
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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def
joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- JoinSemilattice
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def
joinSemilattice: Semilattice[A]
- Definition Classes
- JoinSemilattice
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def
meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- MeetSemilattice
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def
meetSemilattice: Semilattice[A]
- Definition Classes
- MeetSemilattice
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def
toString(): String
- Definition Classes
- Any