BoundedLattice

A bounded lattice is a lattice that additionally has one element that is the bottom (zero, also written as ⊥), and one element that is the top (one, also written as ⊤).

This means that for any a in A:

join(zero, a) = a = meet(one, a)

Or written using traditional notation:

(0 ∨ a) = a = (1 ∧ a)

Self Type: BoundedLattice[A]

Linear Supertypes

BoundedJoinSemilattice[A], BoundedMeetSemilattice[A], Lattice[A], MeetSemilattice[A], JoinSemilattice[A], Serializable, Serializable, Any

Known Subclasses

Bool, BoolFromBoolRing, BoundedDistributiveLattice, DualBool, Heyting, MinMaxBoundedDistributiveLattice

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
abstract def one: A

Definition Classes
BoundedMeetSemilattice
abstract def zero: A

Definition Classes
BoundedJoinSemilattice

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: BoundedLattice[A]

This is the lattice with meet and join swapped
This is the lattice with meet and join swapped

Definition Classes
BoundedLattice → Lattice
def equals(arg0: Any): Boolean

Definition Classes
Any
def hashCode(): Int

Definition Classes
Any
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def isOne(a: A)(implicit ev: Eq[A]): Boolean

Definition Classes
BoundedMeetSemilattice
def isZero(a: A)(implicit ev: Eq[A]): Boolean

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

Definition Classes
JoinSemilattice
def joinSemilattice: BoundedSemilattice[A]

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

Definition Classes
MeetSemilattice
def meetSemilattice: BoundedSemilattice[A]

Definition Classes
BoundedMeetSemilattice → MeetSemilattice
def toString(): String

Definition Classes
Any

Related Docs: object BoundedLattice | package lattice

trait BoundedLattice[A] extends Lattice[A] with BoundedMeetSemilattice[A] with BoundedJoinSemilattice[A]

Abstract Value Members

abstract def getClass(): Class[_]

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

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

abstract def one: A

abstract def zero: A

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def dual: BoundedLattice[A]

def equals(arg0: Any): Boolean

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def isOne(a: A)(implicit ev: Eq[A]): Boolean

def isZero(a: A)(implicit ev: Eq[A]): Boolean

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

def joinSemilattice: BoundedSemilattice[A]

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

def meetSemilattice: BoundedSemilattice[A]

def toString(): String

Inherited from BoundedJoinSemilattice[A]

Inherited from BoundedMeetSemilattice[A]

Inherited from Lattice[A]

Inherited from MeetSemilattice[A]

Inherited from JoinSemilattice[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

Ungrouped