trait GenBool[A] extends DistributiveLattice[A] with BoundedJoinSemilattice[A]
Generalized Boolean algebra, that is, a Boolean algebra without the top element. Generalized Boolean algebras do not (in general) have (absolute) complements, but they have relative complements (see GenBool.without).
- Self Type
- GenBool[A]
Linear Supertypes
Known Subclasses
Ordering
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- By Inheritance
Inherited
- GenBool
- BoundedJoinSemilattice
- DistributiveLattice
- Lattice
- MeetSemilattice
- JoinSemilattice
- Serializable
- Serializable
- Any
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Visibility
- Public
- All
Abstract Value Members
- abstract def and(a: A, b: A): A
-
abstract
def
getClass(): Class[_]
- Definition Classes
- Any
- abstract def or(a: A, b: A): A
-
abstract
def
without(a: A, b: A): A
The operation of relative complement, symbolically often denoted
a\b
(the symbol for set-theoretic difference, which is the meaning of relative complement in the lattice of sets). -
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
-
def
asBoolRing: BoolRng[A]
Every generalized Boolean algebra is also a
BoolRng
, with multiplication defined asand
and addition defined asxor
. -
final
def
asInstanceOf[T0]: T0
- Definition Classes
- Any
-
def
dual: Lattice[A]
This is the lattice with meet and join swapped
This is the lattice with meet and join swapped
- Definition Classes
- Lattice
-
def
equals(arg0: Any): Boolean
- Definition Classes
- Any
-
def
hashCode(): Int
- Definition Classes
- Any
-
final
def
isInstanceOf[T0]: Boolean
- Definition Classes
- Any
-
def
isZero(a: A)(implicit ev: Eq[A]): Boolean
- Definition Classes
- BoundedJoinSemilattice
-
def
join(a: A, b: A): A
- Definition Classes
- GenBool → JoinSemilattice
-
def
joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- JoinSemilattice
-
def
joinSemilattice: BoundedSemilattice[A]
- Definition Classes
- BoundedJoinSemilattice → JoinSemilattice
-
def
meet(a: A, b: A): A
- Definition Classes
- GenBool → MeetSemilattice
-
def
meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- MeetSemilattice
-
def
meetSemilattice: Semilattice[A]
- Definition Classes
- MeetSemilattice
-
def
toString(): String
- Definition Classes
- Any
-
def
xor(a: A, b: A): A
Logical exclusive or, set-theoretic symmetric difference.
Logical exclusive or, set-theoretic symmetric difference. Defined as
a\b ∨ b\a
.