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[java.lang]

   Definition Classes

   AnyRef

   Annotations

   @throws( ... )

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. def finalize(): Unit

    

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

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

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

    

    Definition Classes

    AnyRef → Any

16. def hashCode(): Int

    

    Definition Classes

    AnyRef → Any

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

    

    Definition Classes

    Bool → Heyting

18. final def isInstanceOf[T0]: Boolean

    

    Definition Classes

    Any

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

    

    Tests if a is one.

    Tests if a is one.

    Definition Classes

    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    

    Tests if a is zero.

    Tests if a is zero.

    Definition Classes

    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice

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

    

    Definition Classes

    GenBool → JoinSemilattice

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

    

    Definition Classes

    JoinSemilattice

23. def joinSemilattice: BoundedSemilattice[Boolean]

    

    Definition Classes

    BoundedJoinSemilattice → JoinSemilattice

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

    

    Definition Classes

    GenBool → MeetSemilattice

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

    

    Definition Classes

    MeetSemilattice

26. def meetSemilattice: BoundedSemilattice[Boolean]

    

    Definition Classes

    BoundedMeetSemilattice → MeetSemilattice

27. def multiplicative: CommutativeMonoid[Boolean]

    

    Definition Classes

    MultiplicativeCommutativeMonoid → MultiplicativeCommutativeSemigroup → MultiplicativeMonoid → MultiplicativeSemigroup

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

    

    Definition Classes

    Heyting

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

    

    Definition Classes

    AnyRef

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

    

    Definition Classes

    Heyting

31. final def notify(): Unit

    

    Definition Classes

    AnyRef

32. final def notifyAll(): Unit

    

    Definition Classes

    AnyRef

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

    

    Definition Classes

    Heyting

34. def one: Boolean

    

    Definition Classes

    BooleanAlgebra → MultiplicativeMonoid → BoundedMeetSemilattice

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

    

    Definition Classes

    BooleanAlgebra → GenBool → Heyting

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

    

    Definition Classes

    BooleanAlgebra → AdditiveSemigroup

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

    

    Attributes

    protected[this]

    Definition Classes

    MultiplicativeSemigroup

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

    

    Attributes

    protected[this]

    Definition Classes

    AdditiveSemigroup

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

    

    Definition Classes

    BooleanAlgebra → MultiplicativeMonoid → MultiplicativeSemigroup

40. 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

41. 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

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

    

    Definition Classes

    AdditiveMonoid → AdditiveSemigroup

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

    

    Definition Classes

    AnyRef

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

    

    Definition Classes

    BooleanAlgebra → MultiplicativeSemigroup

45. def toString(): String

    

    Definition Classes

    AnyRef → Any

46. 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

47. 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

48. final def wait(): Unit

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

51. 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

52. 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

53. def zero: Boolean

    

    Definition Classes

    BooleanAlgebra → AdditiveMonoid → BoundedJoinSemilattice