algebra.lattice

Lattice

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]
Linear Supertypes
MeetSemilattice[A], JoinSemilattice[A], Serializable, Serializable, Any
Known Subclasses
BitSetAlgebra, Bool, BoolFromBoolRing, BooleanAlgebra, BoundedDistributiveLattice, BoundedLattice, DistributiveLattice, DualBool, GenBool, GenBoolFromBoolRng, Heyting, MinMaxBoundedDistributiveLattice, MinMaxLattice, SetLattice
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Inherited
  1. Lattice
  2. MeetSemilattice
  3. JoinSemilattice
  4. Serializable
  5. Serializable
  6. Any
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Abstract Value Members

  1. abstract def getClass(): Class[_]

    Definition Classes
    Any

  2. abstract def join(lhs: A, rhs: A): A

    Definition Classes
    JoinSemilattice

  3. abstract def meet(lhs: A, rhs: A): A

    Definition Classes
    MeetSemilattice

Concrete Value Members

  1. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  2. final def ##(): Int

    Definition Classes
    Any

  3. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  4. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  5. def dual: Lattice[A]

    This is the lattice with meet and join swapped

  6. def equals(arg0: Any): Boolean

    Definition Classes
    Any

  7. def hashCode(): Int

    Definition Classes
    Any

  8. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  9. def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

    Definition Classes
    JoinSemilattice

  10. def joinSemilattice: Semilattice[A]

    Definition Classes
    JoinSemilattice

  11. def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

    Definition Classes
    MeetSemilattice

  12. def meetSemilattice: Semilattice[A]

    Definition Classes
    MeetSemilattice

  13. def toString(): String

    Definition Classes
    Any

Inherited from MeetSemilattice[A]

Inherited from JoinSemilattice[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

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