algebra.std

BooleanAlgebra

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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Instance Constructors

  1. new BooleanAlgebra()

Value Members

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

    Definition Classes
    AnyRef

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

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

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

    Definition Classes
    Any

  6. def additive: CommutativeMonoid[Boolean]

    Definition Classes
    AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveMonoid → AdditiveSemigroup

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

    Definition Classes
    BooleanAlgebra → GenBool → Heyting

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

    Definition Classes
    Eq

  9. def asBoolRing: BoolRing[Boolean]

    Definition Classes
    Bool → GenBool

  10. def asCommutativeRig: CommutativeRig[Boolean]

    Definition Classes
    BoundedDistributiveLattice

  11. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  12. def clone(): AnyRef

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

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

    Definition Classes
    BooleanAlgebra → Order

  14. def complement(x: Boolean): Boolean

    Definition Classes
    BooleanAlgebra → Heyting

  15. def dual: Bool[Boolean]

    Definition Classes
    Bool → BoundedDistributiveLattice → BoundedLattice → Lattice

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

    Definition Classes
    AnyRef

  17. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder → Eq

  19. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

  23. def hashCode(): Int

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    Bool → Heyting

  25. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    Definition Classes
    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

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

    Definition Classes
    GenBool → JoinSemilattice

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

    Definition Classes
    JoinSemilattice

  30. def joinSemilattice: BoundedSemilattice[Boolean]

    Definition Classes
    BoundedJoinSemilattice → JoinSemilattice

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → Order

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

    Definition Classes
    GenBool → MeetSemilattice

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

    Definition Classes
    MeetSemilattice

  36. def meetSemilattice: BoundedSemilattice[Boolean]

    Definition Classes
    BoundedMeetSemilattice → MeetSemilattice

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

    Definition Classes
    BooleanAlgebra → Order

  38. def multiplicative: CommutativeMonoid[Boolean]

    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

    Definition Classes
    Heyting

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

    Definition Classes
    AnyRef

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

    Definition Classes
    BooleanAlgebra → Order → Eq

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

    Definition Classes
    Heyting

  43. final def notify(): Unit

    Definition Classes
    AnyRef

  44. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

    Definition Classes
    Heyting

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

    Definition Classes
    Order → PartialOrder → Eq

  47. def one: Boolean

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    Definition Classes
    BooleanAlgebra → GenBool → Heyting

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

    Definition Classes
    Eq

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

    Definition Classes
    Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → AdditiveSemigroup

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

    Definition Classes
    PartialOrder

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

    Definition Classes
    PartialOrder

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

    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

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

    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

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

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → MultiplicativeSemigroup

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

    Definition Classes
    MultiplicativeMonoid

  58. def reverse: Order[Boolean]

    Definition Classes
    Order → PartialOrder

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

    Definition Classes
    AdditiveMonoid

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

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

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

    Definition Classes
    AnyRef

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

    Definition Classes
    BooleanAlgebra → MultiplicativeSemigroup

  63. def toOrdering: Ordering[Boolean]

    Definition Classes
    Order

  64. def toString(): String

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    PartialOrder

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

    Definition Classes
    MultiplicativeSemigroup

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

    Definition Classes
    AdditiveSemigroup

  68. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    Order

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

    Definition Classes
    Bool → GenBool

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

    Definition Classes
    Bool → GenBool → Heyting

  74. def zero: Boolean

    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