Trait/Object

algebra.lattice

GenBool

Related Docs: object GenBool | package lattice

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trait GenBool[A] extends DistributiveLattice[A] with BoundedJoinSemilattice[A]

Generalized Boolean algebra, that is, a Boolean algebra without the top element. Generalized Boolean algebras do not (in general) have (absolute) complements, but they have relative complements (see GenBool.without).

Self Type
GenBool[A]
Linear Supertypes
Known Subclasses
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Inherited
  1. GenBool
  2. BoundedJoinSemilattice
  3. DistributiveLattice
  4. Lattice
  5. MeetSemilattice
  6. JoinSemilattice
  7. Serializable
  8. Serializable
  9. Any
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Visibility
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Abstract Value Members

  1. abstract def and(a: A, b: A): A

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  2. abstract def getClass(): Class[_]

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    Definition Classes
    Any
  3. abstract def or(a: A, b: A): A

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  4. abstract def without(a: A, b: A): A

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    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).

  5. abstract def zero: A

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    Definition Classes
    BoundedJoinSemilattice

Concrete Value Members

  1. final def !=(arg0: Any): Boolean

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    Definition Classes
    Any
  2. final def ##(): Int

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    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean

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    Definition Classes
    Any
  4. def asBoolRing: BoolRng[A]

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    Every generalized Boolean algebra is also a BoolRng, with multiplication defined as and and addition defined as xor.

  5. final def asInstanceOf[T0]: T0

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    Definition Classes
    Any
  6. def dual: Lattice[A]

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    This is the lattice with meet and join swapped

    This is the lattice with meet and join swapped

    Definition Classes
    Lattice
  7. def equals(arg0: Any): Boolean

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    Definition Classes
    Any
  8. def hashCode(): Int

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    Definition Classes
    Any
  9. final def isInstanceOf[T0]: Boolean

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    Definition Classes
    Any
  10. def isZero(a: A)(implicit ev: Eq[A]): Boolean

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    Definition Classes
    BoundedJoinSemilattice
  11. def join(a: A, b: A): A

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    Definition Classes
    GenBoolJoinSemilattice
  12. def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

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    Definition Classes
    JoinSemilattice
  13. def joinSemilattice: BoundedSemilattice[A]

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

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    Definition Classes
    GenBoolMeetSemilattice
  15. def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

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    Definition Classes
    MeetSemilattice
  16. def meetSemilattice: Semilattice[A]

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    Definition Classes
    MeetSemilattice
  17. def toString(): String

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    Definition Classes
    Any
  18. def xor(a: A, b: A): A

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    Logical exclusive or, set-theoretic symmetric difference.

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

Inherited from BoundedJoinSemilattice[A]

Inherited from DistributiveLattice[A]

Inherited from Lattice[A]

Inherited from MeetSemilattice[A]

Inherited from JoinSemilattice[A]

Inherited from Serializable

Inherited from Serializable

Inherited from Any

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