class DualBool[A] extends Bool[A]
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- DualBool
- Bool
- GenBool
- Heyting
- BoundedDistributiveLattice
- DistributiveLattice
- BoundedLattice
- BoundedJoinSemilattice
- BoundedMeetSemilattice
- Lattice
- MeetSemilattice
- JoinSemilattice
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final
def
!=(arg0: Any): Boolean
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final
def
##(): Int
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final
def
==(arg0: Any): Boolean
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- def and(a: A, b: A): A
-
def
asBoolRing: BoolRing[A]
Every Boolean algebra is a BoolRing, with multiplication defined as
and
and addition defined asxor
.Every Boolean algebra is a BoolRing, with multiplication defined as
and
and addition defined asxor
. Bool does not extend BoolRing because, e.g. we might want a Bool[Int] and CommutativeRing[Int] to refer to different structures, by default.Note that the ring returned by this method is not an extension of the
Rig
returned fromBoundedDistributiveLattice.asCommutativeRig
. -
def
asCommutativeRig: CommutativeRig[A]
Return a CommutativeRig using join and meet.
Return a CommutativeRig using join and meet. Note this must obey the commutative rig laws since meet(a, one) = a, and meet and join are associative, commutative and distributive.
- Definition Classes
- BoundedDistributiveLattice
-
final
def
asInstanceOf[T0]: T0
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def
clone(): AnyRef
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- protected[java.lang]
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- def complement(a: A): A
-
def
dual: Bool[A]
This is the lattice with meet and join swapped
This is the lattice with meet and join swapped
- Definition Classes
- DualBool → Bool → BoundedDistributiveLattice → BoundedLattice → Lattice
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final
def
eq(arg0: AnyRef): Boolean
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def
equals(arg0: Any): Boolean
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def
finalize(): Unit
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final
def
getClass(): Class[_]
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def
hashCode(): Int
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final
def
isInstanceOf[T0]: Boolean
- Definition Classes
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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
join(a: A, b: A): A
- Definition Classes
- GenBool → JoinSemilattice
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def
joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- JoinSemilattice
-
def
joinSemilattice: BoundedSemilattice[A]
- Definition Classes
- BoundedJoinSemilattice → JoinSemilattice
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def
meet(a: A, b: A): A
- Definition Classes
- GenBool → MeetSemilattice
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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
- def nand(a: A, b: A): A
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final
def
ne(arg0: AnyRef): Boolean
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- def nor(a: A, b: A): A
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final
def
notify(): Unit
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final
def
notifyAll(): Unit
- Definition Classes
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- @native()
- def nxor(a: A, b: A): A
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def
one: A
- Definition Classes
- DualBool → BoundedMeetSemilattice
- def or(a: A, b: A): A
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final
def
synchronized[T0](arg0: ⇒ T0): T0
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def
toString(): String
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final
def
wait(): Unit
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final
def
wait(arg0: Long, arg1: Int): Unit
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final
def
wait(arg0: Long): Unit
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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). -
def
xor(a: A, b: A): A
Logical exclusive or, set-theoretic symmetric difference.
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def
zero: A
- Definition Classes
- DualBool → BoundedJoinSemilattice