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], Heyting[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. Heyting
  18. BoundedLattice
  19. BoundedJoinSemilattice
  20. BoundedMeetSemilattice
  21. Lattice
  22. MeetSemilattice
  23. JoinSemilattice
  24. Serializable
  25. Serializable
  26. AnyRef
  27. 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 → Heyting

  8. def asCommutativeRing: CommutativeRing[Boolean]

    Definition Classes
    Heyting

  9. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  10. def clone(): AnyRef

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

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

    Definition Classes
    BooleanAlgebra → Order

  12. def complement(x: Boolean): Boolean

    Definition Classes
    BooleanAlgebra → Heyting

  13. def dual: Bool[Boolean]

    Definition Classes
    Bool

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

    Definition Classes
    AnyRef

  15. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder → Eq

  17. def finalize(): Unit

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

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

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

  21. def hashCode(): Int

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    Bool → Heyting

  23. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

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

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    Definition Classes
    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

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

    Definition Classes
    Heyting → JoinSemilattice

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

    Definition Classes
    JoinSemilattice

  28. def joinSemilattice: BoundedSemilattice[Boolean]

    Definition Classes
    BoundedJoinSemilattice → JoinSemilattice

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → Order

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

    Definition Classes
    Heyting → MeetSemilattice

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

    Definition Classes
    MeetSemilattice

  34. def meetSemilattice: BoundedSemilattice[Boolean]

    Definition Classes
    BoundedMeetSemilattice → MeetSemilattice

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

    Definition Classes
    BooleanAlgebra → Order

  36. def multiplicative: CommutativeMonoid[Boolean]

    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

    Definition Classes
    Heyting

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

    Definition Classes
    AnyRef

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

    Definition Classes
    BooleanAlgebra → Order → Eq

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

    Definition Classes
    Heyting

  41. final def notify(): Unit

    Definition Classes
    AnyRef

  42. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

    Definition Classes
    Heyting

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

    Definition Classes
    Order → PartialOrder → Eq

  45. def one: Boolean

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    Definition Classes
    BooleanAlgebra → Heyting

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

    Definition Classes
    Order → PartialOrder

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

    Definition Classes
    BooleanAlgebra → AdditiveSemigroup

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

    Definition Classes
    PartialOrder

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

    Definition Classes
    PartialOrder

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

    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup

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

    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup

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

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → MultiplicativeSemigroup

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

    Definition Classes
    MultiplicativeMonoid

  55. def reverse: Order[Boolean]

    Definition Classes
    Order → PartialOrder

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

    Definition Classes
    AdditiveMonoid

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

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup

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

    Definition Classes
    AnyRef

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

    Definition Classes
    BooleanAlgebra → MultiplicativeSemigroup

  60. def toString(): String

    Definition Classes
    AnyRef → Any

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

    Definition Classes
    PartialOrder

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

    Definition Classes
    MultiplicativeSemigroup

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

    Definition Classes
    AdditiveSemigroup

  64. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    Heyting

  68. 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 Heyting[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