Lattice

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, DeMorgan, DistributiveLattice, DualBool, GenBool, GenBoolFromBoolRng, Heyting, Logic, MinMaxBoundedDistributiveLattice, MinMaxLattice, SetLattice

Abstract Value Members

abstract def getClass(): Class[_]

Definition Classes
Any
abstract def join(lhs: A, rhs: A): A

Definition Classes
JoinSemilattice
abstract def meet(lhs: A, rhs: A): A

Definition Classes
MeetSemilattice

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
Any
final def ##(): Int

Definition Classes
Any
final def ==(arg0: Any): Boolean

Definition Classes
Any
final def asInstanceOf[T0]: T0

Definition Classes
Any
def dual: Lattice[A]

This is the lattice with meet and join swapped
def equals(arg0: Any): Boolean

Definition Classes
Any
def hashCode(): Int

Definition Classes
Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

Definition Classes
JoinSemilattice
def joinSemilattice: Semilattice[A]

Definition Classes
JoinSemilattice
def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

Definition Classes
MeetSemilattice
def meetSemilattice: Semilattice[A]

Definition Classes
MeetSemilattice
def toString(): String

Definition Classes
Any

Related Docs: object Lattice | package lattice

trait Lattice[A] extends JoinSemilattice[A] with MeetSemilattice[A]

Abstract Value Members

abstract def getClass(): Class[_]

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

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

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def dual: Lattice[A]

def equals(arg0: Any): Boolean

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

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

def joinSemilattice: Semilattice[A]

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

def meetSemilattice: Semilattice[A]

def toString(): String

Inherited from MeetSemilattice[A]

Inherited from JoinSemilattice[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped