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
Linear Supertypes
Known Subclasses
Ordering
- Alphabetic
- By Inheritance
Inherited
- BoundedLattice
- BoundedJoinSemilattice
- BoundedMeetSemilattice
- Lattice
- MeetSemilattice
- JoinSemilattice
- Serializable
- Any
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Visibility
- Public
- Protected
Abstract Value Members
- abstract def getClass(): Class[_ <: AnyRef]
- 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