Class

algebra.std

BooleanAlgebra

Related Doc: package std

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class BooleanAlgebra extends Bool[Boolean] with Order[Boolean] with CommutativeRig[Boolean]

This commutative rig is different than the one obtained from GF(2).

It uses || for plus, and && for times.

Linear Supertypes
CommutativeRig[Boolean], MultiplicativeCommutativeMonoid[Boolean], MultiplicativeCommutativeSemigroup[Boolean], Rig[Boolean], MultiplicativeMonoid[Boolean], Semiring[Boolean], MultiplicativeSemigroup[Boolean], AdditiveCommutativeMonoid[Boolean], AdditiveCommutativeSemigroup[Boolean], AdditiveMonoid[Boolean], AdditiveSemigroup[Boolean], Order[Boolean], PartialOrder[Boolean], Eq[Boolean], Bool[Boolean], GenBool[Boolean], Heyting[Boolean], BoundedDistributiveLattice[Boolean], DistributiveLattice[Boolean], BoundedLattice[Boolean], BoundedJoinSemilattice[Boolean], BoundedMeetSemilattice[Boolean], Lattice[Boolean], MeetSemilattice[Boolean], JoinSemilattice[Boolean], Serializable, Serializable, AnyRef, Any
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Inherited
  1. BooleanAlgebra
  2. CommutativeRig
  3. MultiplicativeCommutativeMonoid
  4. MultiplicativeCommutativeSemigroup
  5. Rig
  6. MultiplicativeMonoid
  7. Semiring
  8. MultiplicativeSemigroup
  9. AdditiveCommutativeMonoid
  10. AdditiveCommutativeSemigroup
  11. AdditiveMonoid
  12. AdditiveSemigroup
  13. Order
  14. PartialOrder
  15. Eq
  16. Bool
  17. GenBool
  18. Heyting
  19. BoundedDistributiveLattice
  20. DistributiveLattice
  21. BoundedLattice
  22. BoundedJoinSemilattice
  23. BoundedMeetSemilattice
  24. Lattice
  25. MeetSemilattice
  26. JoinSemilattice
  27. Serializable
  28. Serializable
  29. AnyRef
  30. Any
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Visibility
  1. Public
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Instance Constructors

  1. new BooleanAlgebra()

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Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  2. final def ##(): Int

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    Definition Classes
    AnyRef → Any

  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  4. def additive: CommutativeMonoid[Boolean]

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    Definition Classes
    AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveMonoid → AdditiveSemigroup

  5. def and(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → GenBool → Heyting

  6. def and(that: Eq[Boolean]): Eq[Boolean]

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    Definition Classes
    Eq

  7. def asBoolRing: BoolRing[Boolean]

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    Definition Classes
    Bool → GenBool

  8. def asCommutativeRig: CommutativeRig[Boolean]

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    Definition Classes
    BoundedDistributiveLattice

  9. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any

  10. def clone(): AnyRef

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  11. def compare(x: Boolean, y: Boolean): Int

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    Definition Classes
    BooleanAlgebra → Order

  12. def complement(x: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Heyting

  13. def dual: Bool[Boolean]

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    Definition Classes
    Bool → BoundedDistributiveLattice → BoundedLattice → Lattice

  14. final def eq(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef

  15. def equals(arg0: Any): Boolean

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    Definition Classes
    AnyRef → Any

  16. def eqv(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order → PartialOrder → Eq

  17. def finalize(): Unit

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    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  18. final def getClass(): Class[_]

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    Definition Classes
    AnyRef → Any

  19. def gt(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order → PartialOrder

  20. def gteqv(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order → PartialOrder

  21. def hashCode(): Int

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    Definition Classes
    AnyRef → Any

  22. def imp(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    Bool → Heyting

  23. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any

  24. def isOne(x: Boolean)(implicit ev: Eq[Boolean]): Boolean

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    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

  25. def isZero(x: Boolean)(implicit ev: Eq[Boolean]): Boolean

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    Definition Classes
    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

  26. def join(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    GenBool → JoinSemilattice

  27. def joinPartialOrder(implicit ev: Eq[Boolean]): PartialOrder[Boolean]

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    Definition Classes
    JoinSemilattice

  28. def joinSemilattice: BoundedSemilattice[Boolean]

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    Definition Classes
    BoundedJoinSemilattice → JoinSemilattice

  29. def lt(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order → PartialOrder

  30. def lteqv(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order → PartialOrder

  31. def max(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order

  32. def meet(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    GenBool → MeetSemilattice

  33. def meetPartialOrder(implicit ev: Eq[Boolean]): PartialOrder[Boolean]

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    Definition Classes
    MeetSemilattice

  34. def meetSemilattice: BoundedSemilattice[Boolean]

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    Definition Classes
    BoundedMeetSemilattice → MeetSemilattice

  35. def min(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order

  36. def multiplicative: CommutativeMonoid[Boolean]

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    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

  37. def nand(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    Heyting

  38. final def ne(arg0: AnyRef): Boolean

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    Definition Classes
    AnyRef

  39. def neqv(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → Order → Eq

  40. def nor(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    Heyting

  41. final def notify(): Unit

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    Definition Classes
    AnyRef

  42. final def notifyAll(): Unit

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    Definition Classes
    AnyRef

  43. def nxor(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    Heyting

  44. def on[B](f: (B) ⇒ Boolean): Order[B]

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    Definition Classes
    Order → PartialOrder → Eq

  45. def one: Boolean

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    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

  46. def or(x: Boolean, y: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → GenBool → Heyting

  47. def or(that: Eq[Boolean]): Eq[Boolean]

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    Definition Classes
    Eq

  48. def partialCompare(x: Boolean, y: Boolean): Double

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    Definition Classes
    Order → PartialOrder

  49. def plus(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → AdditiveSemigroup

  50. def pmax(x: Boolean, y: Boolean): Option[Boolean]

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    Definition Classes
    PartialOrder

  51. def pmin(x: Boolean, y: Boolean): Option[Boolean]

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    Definition Classes
    PartialOrder

  52. def positivePow(a: Boolean, n: Int): Boolean

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    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

  53. def positiveSumN(a: Boolean, n: Int): Boolean

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    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

  54. def pow(a: Boolean, b: Int): Boolean

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    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → MultiplicativeSemigroup

  55. def product(as: TraversableOnce[Boolean]): Boolean

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    Definition Classes
    MultiplicativeMonoid

  56. def reverse: Order[Boolean]

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    Definition Classes
    Order → PartialOrder

  57. def sum(as: TraversableOnce[Boolean]): Boolean

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    Definition Classes
    AdditiveMonoid

  58. def sumN(a: Boolean, n: Int): Boolean

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    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

  59. final def synchronized[T0](arg0: ⇒ T0): T0

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    Definition Classes
    AnyRef

  60. def times(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    BooleanAlgebra → MultiplicativeSemigroup

  61. def toOrdering: Ordering[Boolean]

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    Definition Classes
    Order

  62. def toString(): String

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    Definition Classes
    AnyRef → Any

  63. def tryCompare(x: Boolean, y: Boolean): Option[Int]

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    Definition Classes
    PartialOrder

  64. def tryProduct(as: TraversableOnce[Boolean]): Option[Boolean]

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    Definition Classes
    MultiplicativeSemigroup

  65. def trySum(as: TraversableOnce[Boolean]): Option[Boolean]

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    Definition Classes
    AdditiveSemigroup

  66. final def wait(): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  67. final def wait(arg0: Long, arg1: Int): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  68. final def wait(arg0: Long): Unit

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    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  69. def whenEqual(o: Order[Boolean]): Order[Boolean]

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    Definition Classes
    Order

  70. def without(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    Bool → GenBool

  71. def xor(a: Boolean, b: Boolean): Boolean

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    Definition Classes
    Bool → GenBool → Heyting

  72. def zero: Boolean

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    Definition Classes
    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

Inherited from CommutativeRig[Boolean]

Inherited from MultiplicativeCommutativeMonoid[Boolean]

Inherited from MultiplicativeCommutativeSemigroup[Boolean]

Inherited from Rig[Boolean]

Inherited from MultiplicativeMonoid[Boolean]

Inherited from Semiring[Boolean]

Inherited from MultiplicativeSemigroup[Boolean]

Inherited from AdditiveCommutativeMonoid[Boolean]

Inherited from AdditiveCommutativeSemigroup[Boolean]

Inherited from AdditiveMonoid[Boolean]

Inherited from AdditiveSemigroup[Boolean]

Inherited from Order[Boolean]

Inherited from PartialOrder[Boolean]

Inherited from Eq[Boolean]

Inherited from Bool[Boolean]

Inherited from GenBool[Boolean]

Inherited from Heyting[Boolean]

Inherited from BoundedDistributiveLattice[Boolean]

Inherited from DistributiveLattice[Boolean]

Inherited from BoundedLattice[Boolean]

Inherited from BoundedJoinSemilattice[Boolean]

Inherited from BoundedMeetSemilattice[Boolean]

Inherited from Lattice[Boolean]

Inherited from MeetSemilattice[Boolean]

Inherited from JoinSemilattice[Boolean]

Inherited from Serializable

Inherited from Serializable

Inherited from AnyRef

Inherited from Any

Ungrouped