BoolFromBoolRing

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

   

   Definition Classes

   GenBoolFromBoolRng → GenBool

5. 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

6. 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

7. final def asInstanceOf[T0]: T0

   

   Definition Classes

   Any

8. def clone(): AnyRef

   

   Attributes

   protected[java.lang]

   Definition Classes

   AnyRef

   Annotations

   @throws( ... )

9. def complement(a: A): A

   

   Definition Classes

   BoolFromBoolRing → Heyting

10. 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

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

    

    Definition Classes

    AnyRef

12. def equals(arg0: Any): Boolean

    

    Definition Classes

    AnyRef → Any

13. def finalize(): Unit

    

    Attributes

    protected[java.lang]

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    Annotations

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

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

    

    Definition Classes

    AnyRef → Any

15. def hashCode(): Int

    

    Definition Classes

    AnyRef → Any

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

    

    Definition Classes

    Bool → Heyting

17. final def isInstanceOf[T0]: Boolean

    

    Definition Classes

    Any

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

    

    Definition Classes

    BoundedMeetSemilattice

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

    

    Definition Classes

    BoundedJoinSemilattice

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

    

    Definition Classes

    Heyting → JoinSemilattice

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

    

    Definition Classes

    JoinSemilattice

22. def joinSemilattice: BoundedSemilattice[A]

    

    Definition Classes

    BoundedJoinSemilattice → JoinSemilattice

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

    

    Definition Classes

    Heyting → MeetSemilattice

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

    

    Definition Classes

    MeetSemilattice

25. def meetSemilattice: BoundedSemilattice[A]

    

    Definition Classes

    BoundedMeetSemilattice → MeetSemilattice

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

    

    Definition Classes

    Heyting

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

    

    Definition Classes

    AnyRef

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

    

    Definition Classes

    Heyting

29. final def notify(): Unit

    

    Definition Classes

    AnyRef

30. final def notifyAll(): Unit

    

    Definition Classes

    AnyRef

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

    

    Definition Classes

    Heyting

32. def one: A

    

    Definition Classes

    BoolFromBoolRing → BoundedMeetSemilattice

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

    

    Definition Classes

    GenBoolFromBoolRng → GenBool

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

    

    Definition Classes

    AnyRef

35. def toString(): String

    

    Definition Classes

    AnyRef → Any

36. final def wait(): Unit

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

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

    

    Definition Classes

    AnyRef

    Annotations

    @throws( ... )

39. 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

40. 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

41. def zero: A

    

    Definition Classes

    GenBoolFromBoolRng → BoundedJoinSemilattice