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]
Linear Supertypes
Known Subclasses
Ordering
- Alphabetic
- By Inheritance
Inherited
- BoundedLattice
- BoundedJoinSemilattice
- BoundedMeetSemilattice
- Lattice
- MeetSemilattice
- JoinSemilattice
- Serializable
- Serializable
- Any
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Visibility
- Public
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Abstract Value Members
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abstract
def
getClass(): Class[_]
- Definition Classes
- Any
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abstract
def
join(lhs: A, rhs: A): A
- Definition Classes
- JoinSemilattice
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abstract
def
meet(lhs: A, rhs: A): A
- Definition Classes
- MeetSemilattice
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abstract
def
one: A
- Definition Classes
- BoundedMeetSemilattice
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abstract
def
zero: A
- Definition Classes
- BoundedJoinSemilattice
Concrete Value Members
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final
def
!=(arg0: Any): Boolean
- Definition Classes
- Any
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final
def
##(): Int
- Definition Classes
- Any
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final
def
==(arg0: Any): Boolean
- Definition Classes
- Any
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final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
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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
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
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def
isOne(a: A)(implicit ev: Eq[A]): Boolean
- Definition Classes
- BoundedMeetSemilattice
-
def
isZero(a: A)(implicit ev: Eq[A]): Boolean
- Definition Classes
- BoundedJoinSemilattice
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def
joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- JoinSemilattice
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def
joinSemilattice: BoundedSemilattice[A]
- Definition Classes
- BoundedJoinSemilattice → JoinSemilattice
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def
meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- MeetSemilattice
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def
meetSemilattice: BoundedSemilattice[A]
- Definition Classes
- BoundedMeetSemilattice → MeetSemilattice
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def
toString(): String
- Definition Classes
- Any