BoolFromBoolRing

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 and(a: A, b: A): A

   Definition Classes

   GenBoolFromBoolRng → GenBool

7. def asBoolRing: BoolRing[A]

   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

   BoolFromBoolRing → Bool → GenBoolFromBoolRng → GenBool

8. def asCommutativeRig: CommutativeRig[A]

   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

9. final def asInstanceOf[T0]: T0

   Definition Classes

   Any

10. def clone(): AnyRef

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

11. def complement(a: A): A

    Definition Classes

    BoolFromBoolRing → Heyting

12. def dual: Bool[A]

    This is the lattice with meet and join swapped

    This is the lattice with meet and join swapped

    Definition Classes

    Bool → BoundedDistributiveLattice → BoundedLattice → Lattice

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

    Definition Classes

    AnyRef

14. def equals(arg0: Any): Boolean

    Definition Classes

    AnyRef → Any

15. def finalize(): Unit

    Attributes

    protected[java.lang]

    Definition Classes

    AnyRef

    Annotations

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

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

    Definition Classes

    AnyRef → Any

17. def hashCode(): Int

    Definition Classes

    AnyRef → Any

18. def imp(a: A, b: A): A

    Definition Classes

    Bool → Heyting

19. final def isInstanceOf[T0]: Boolean

    Definition Classes

    Any

20. def isOne(a: A)(implicit ev: Eq[A]): Boolean

    Definition Classes

    BoundedMeetSemilattice

21. def isZero(a: A)(implicit ev: Eq[A]): Boolean

    Definition Classes

    BoundedJoinSemilattice

22. def join(a: A, b: A): A

    Definition Classes

    Heyting → JoinSemilattice

23. def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

    Definition Classes

    JoinSemilattice

24. def joinSemilattice: BoundedSemilattice[A]

    Definition Classes

    BoundedJoinSemilattice → JoinSemilattice

25. def meet(a: A, b: A): A

    Definition Classes

    Heyting → MeetSemilattice

26. def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

    Definition Classes

    MeetSemilattice

27. def meetSemilattice: BoundedSemilattice[A]

    Definition Classes

    BoundedMeetSemilattice → MeetSemilattice

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

    Definition Classes

    Heyting

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

    Definition Classes

    AnyRef

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

    Definition Classes

    Heyting

31. final def notify(): Unit

    Definition Classes

    AnyRef

32. final def notifyAll(): Unit

    Definition Classes

    AnyRef

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

    Definition Classes

    Heyting

34. def one: A

    Definition Classes

    BoolFromBoolRing → BoundedMeetSemilattice

35. def or(a: A, b: A): A

    Definition Classes

    GenBoolFromBoolRng → GenBool

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

    Definition Classes

    AnyRef

37. def toString(): String

    Definition Classes

    AnyRef → Any

38. final def wait(): Unit

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

41. def without(a: A, b: A): A

    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

    BoolFromBoolRing → Bool → GenBoolFromBoolRng → GenBool

42. def xor(a: A, b: A): A

    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

43. def zero: A

    Definition Classes

    GenBoolFromBoolRng → BoundedJoinSemilattice