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 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

9. 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

10. final def asInstanceOf[T0]: T0

    Definition Classes

    Any

11. def clone(): AnyRef

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

12. def complement(x: Boolean): Boolean

    Definition Classes

    BooleanAlgebra → Heyting

13. 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

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

    Definition Classes

    AnyRef

15. def equals(arg0: Any): Boolean

    Definition Classes

    AnyRef → Any

16. def finalize(): Unit

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

    @throws( classOf[java.lang.Throwable] )

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

    Definition Classes

    AnyRef → Any

18. def hashCode(): Int

    Definition Classes

    AnyRef → Any

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

    Definition Classes

    Bool → Heyting

20. final def isInstanceOf[T0]: Boolean

    Definition Classes

    Any

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

    Tests if a is one.

    Tests if a is one.

    Definition Classes

    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes

    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

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

    Definition Classes

    GenBool → JoinSemilattice

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

    Definition Classes

    JoinSemilattice

25. def joinSemilattice: BoundedSemilattice[Boolean]

    Definition Classes

    BoundedJoinSemilattice → JoinSemilattice

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

    Definition Classes

    GenBool → MeetSemilattice

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

    Definition Classes

    MeetSemilattice

28. def meetSemilattice: BoundedSemilattice[Boolean]

    Definition Classes

    BoundedMeetSemilattice → MeetSemilattice

29. def multiplicative: CommutativeMonoid[Boolean]

    Definition Classes

    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

    Definition Classes

    Heyting

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

    Definition Classes

    AnyRef

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

    Definition Classes

    Heyting

33. final def notify(): Unit

    Definition Classes

    AnyRef

34. final def notifyAll(): Unit

    Definition Classes

    AnyRef

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

    Definition Classes

    Heyting

36. def one: Boolean

    Definition Classes

    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    Definition Classes

    BooleanAlgebra → GenBool → Heyting

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

    Definition Classes

    BooleanAlgebra → AdditiveSemigroup

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

    Attributes

    protected[this]

    Definition Classes

    MultiplicativeSemigroup

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

    Attributes

    protected[this]

    Definition Classes

    AdditiveSemigroup

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

    Definition Classes

    BooleanAlgebra → MultiplicativeMonoid → MultiplicativeSemigroup

42. 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

43. 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

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

    Definition Classes

    AdditiveMonoid → AdditiveSemigroup

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

    Definition Classes

    AnyRef

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

    Definition Classes

    BooleanAlgebra → MultiplicativeSemigroup

47. def toString(): String

    Definition Classes

    AnyRef → Any

48. 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

49. 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

50. final def wait(): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

53. 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

54. 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

55. def zero: Boolean

    Definition Classes

    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice