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

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]
Source
BoundedLattice.scala
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. BoundedLattice
  2. BoundedJoinSemilattice
  3. BoundedMeetSemilattice
  4. Lattice
  5. MeetSemilattice
  6. JoinSemilattice
  7. Serializable
  8. Serializable
  9. Any
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Visibility
  1. Public
  2. All

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
  4. abstract def one: A
    Definition Classes
    BoundedMeetSemilattice
  5. abstract def zero: A
    Definition Classes
    BoundedJoinSemilattice

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: BoundedLattice[A]

    This is the lattice with meet and join swapped

    This is the lattice with meet and join swapped

    Definition Classes
    BoundedLatticeLattice
  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 isOne(a: A)(implicit ev: Eq[A]): Boolean
    Definition Classes
    BoundedMeetSemilattice
  10. def isZero(a: A)(implicit ev: Eq[A]): Boolean
    Definition Classes
    BoundedJoinSemilattice
  11. def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
    Definition Classes
    JoinSemilattice
  12. def joinSemilattice: BoundedSemilattice[A]
  13. def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
    Definition Classes
    MeetSemilattice
  14. def meetSemilattice: BoundedSemilattice[A]
  15. def toString(): String
    Definition Classes
    Any

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