c

algebra.instances

BooleanAlgebra

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

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Inherited
  1. BooleanAlgebra
  2. CommutativeRig
  3. MultiplicativeCommutativeMonoid
  4. CommutativeSemiring
  5. MultiplicativeCommutativeSemigroup
  6. Rig
  7. MultiplicativeMonoid
  8. Semiring
  9. MultiplicativeSemigroup
  10. AdditiveCommutativeMonoid
  11. AdditiveCommutativeSemigroup
  12. AdditiveMonoid
  13. AdditiveSemigroup
  14. Bool
  15. GenBool
  16. Heyting
  17. BoundedDistributiveLattice
  18. DistributiveLattice
  19. BoundedLattice
  20. BoundedJoinSemilattice
  21. BoundedMeetSemilattice
  22. Lattice
  23. MeetSemilattice
  24. JoinSemilattice
  25. Serializable
  26. Serializable
  27. AnyRef
  28. Any
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Visibility
  1. Public
  2. All

Instance Constructors

  1. new BooleanAlgebra()

Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. def additive: CommutativeMonoid[Boolean]
    Definition Classes
    AdditiveCommutativeMonoid → AdditiveCommutativeSemigroup → AdditiveMonoid → AdditiveSemigroup
  5. def and(x: Boolean, y: Boolean): Boolean
    Definition Classes
    BooleanAlgebra → GenBool → Heyting
  6. def asBoolRing: BoolRing[Boolean]

    Every Boolean algebra is a BoolRing, with multiplication defined as and and addition defined as xor.

    Every Boolean algebra is a BoolRing, with multiplication defined as and and addition defined as xor. 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 from BoundedDistributiveLattice.asCommutativeRig.

    Definition Classes
    Bool → GenBool
  7. def asCommutativeRig: CommutativeRig[Boolean]

    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
  8. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  9. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native() @HotSpotIntrinsicCandidate()
  10. def complement(x: Boolean): Boolean
    Definition Classes
    BooleanAlgebra → Heyting
  11. def dual: Bool[Boolean]

    This is the lattice with meet and join swapped

    This is the lattice with meet and join swapped

    Definition Classes
    Bool → BoundedDistributiveLattice → BoundedLattice → Lattice
  12. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  13. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  14. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  15. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  16. def imp(a: Boolean, b: Boolean): Boolean
    Definition Classes
    Bool → Heyting
  17. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  18. def isOne(x: Boolean)(implicit ev: Eq[Boolean]): Boolean

    Tests if a is one.

    Tests if a is one.

    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice
  19. def isZero(x: Boolean)(implicit ev: Eq[Boolean]): Boolean

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes
    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice
  20. def join(a: Boolean, b: Boolean): Boolean
    Definition Classes
    GenBool → JoinSemilattice
  21. def joinPartialOrder(implicit ev: Eq[Boolean]): PartialOrder[Boolean]
    Definition Classes
    JoinSemilattice
  22. def joinSemilattice: BoundedSemilattice[Boolean]
    Definition Classes
    BoundedJoinSemilattice → JoinSemilattice
  23. def meet(a: Boolean, b: Boolean): Boolean
    Definition Classes
    GenBool → MeetSemilattice
  24. def meetPartialOrder(implicit ev: Eq[Boolean]): PartialOrder[Boolean]
    Definition Classes
    MeetSemilattice
  25. def meetSemilattice: BoundedSemilattice[Boolean]
    Definition Classes
    BoundedMeetSemilattice → MeetSemilattice
  26. def multiplicative: CommutativeMonoid[Boolean]
    Definition Classes
    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup
  27. def nand(a: Boolean, b: Boolean): Boolean
    Definition Classes
    Heyting
  28. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  29. def nor(a: Boolean, b: Boolean): Boolean
    Definition Classes
    Heyting
  30. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  31. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native() @HotSpotIntrinsicCandidate()
  32. def nxor(a: Boolean, b: Boolean): Boolean
    Definition Classes
    Heyting
  33. def one: Boolean
    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice
  34. def or(x: Boolean, y: Boolean): Boolean
    Definition Classes
    BooleanAlgebra → GenBool → Heyting
  35. def plus(a: Boolean, b: Boolean): Boolean
    Definition Classes
    BooleanAlgebra → AdditiveSemigroup
  36. def positivePow(a: Boolean, n: Int): Boolean
    Attributes
    protected[this]
    Definition Classes
    MultiplicativeSemigroup
  37. def positiveSumN(a: Boolean, n: Int): Boolean
    Attributes
    protected[this]
    Definition Classes
    AdditiveSemigroup
  38. def pow(a: Boolean, b: Int): Boolean
    Definition Classes
    BooleanAlgebra → MultiplicativeMonoid → MultiplicativeSemigroup
  39. def product(as: TraversableOnce[Boolean]): Boolean

    Given a sequence of as, compute the product.

    Given a sequence of as, compute the product.

    Definition Classes
    MultiplicativeMonoid
  40. def sum(as: TraversableOnce[Boolean]): Boolean

    Given a sequence of as, compute the sum.

    Given a sequence of as, compute the sum.

    Definition Classes
    AdditiveMonoid
  41. def sumN(a: Boolean, n: Int): Boolean
    Definition Classes
    AdditiveMonoid → AdditiveSemigroup
  42. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  43. def times(a: Boolean, b: Boolean): Boolean
    Definition Classes
    BooleanAlgebra → MultiplicativeSemigroup
  44. def toString(): String
    Definition Classes
    AnyRef → Any
  45. def tryProduct(as: TraversableOnce[Boolean]): Option[Boolean]

    Given a sequence of as, combine them and return the total.

    Given a sequence of as, combine them and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    MultiplicativeMonoid → MultiplicativeSemigroup
  46. def trySum(as: TraversableOnce[Boolean]): Option[Boolean]

    Given a sequence of as, combine them and return the total.

    Given a sequence of as, combine them and return the total.

    If the sequence is empty, returns None. Otherwise, returns Some(total).

    Definition Classes
    AdditiveMonoid → AdditiveSemigroup
  47. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  48. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  49. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  50. def without(a: Boolean, b: Boolean): Boolean

    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).

    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).

    Definition Classes
    Bool → GenBool
  51. def xor(a: Boolean, b: Boolean): Boolean

    Logical exclusive or, set-theoretic symmetric difference.

    Logical exclusive or, set-theoretic symmetric difference. Defined as a\b ∨ b\a.

    Definition Classes
    Bool → GenBool → Heyting
  52. def zero: Boolean
    Definition Classes
    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

Deprecated Value Members

  1. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] ) @Deprecated @deprecated
    Deprecated

    (Since version ) see corresponding Javadoc for more information.

Inherited from CommutativeRig[Boolean]

Inherited from MultiplicativeCommutativeMonoid[Boolean]

Inherited from CommutativeSemiring[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 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