algebra.instances

SetLattice

class SetLattice[A] extends GenBool[Set[A]]

Linear Supertypes
GenBool[Set[A]], BoundedJoinSemilattice[Set[A]], DistributiveLattice[Set[A]], Lattice[Set[A]], MeetSemilattice[Set[A]], JoinSemilattice[Set[A]], Serializable, Serializable, AnyRef, Any
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Inherited
  1. SetLattice
  2. GenBool
  3. BoundedJoinSemilattice
  4. DistributiveLattice
  5. Lattice
  6. MeetSemilattice
  7. JoinSemilattice
  8. Serializable
  9. Serializable
  10. AnyRef
  11. Any
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Visibility
  1. Public
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Instance Constructors

  1. new SetLattice()

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(lhs: Set[A], rhs: Set[A]): Set[A]

    Definition Classes
    SetLatticeGenBool
  7. def asBoolRing: BoolRng[Set[A]]

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

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

    Definition Classes
    GenBool
  8. final def asInstanceOf[T0]: T0

    Definition Classes
    Any
  9. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  10. def dual: Lattice[Set[A]]

    This is the lattice with meet and join swapped

    This is the lattice with meet and join swapped

    Definition Classes
    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]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  14. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any
  15. def hashCode(): Int

    Definition Classes
    AnyRef → Any
  16. final def isInstanceOf[T0]: Boolean

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

    Definition Classes
    BoundedJoinSemilattice
  18. def join(a: Set[A], b: Set[A]): Set[A]

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

    Definition Classes
    JoinSemilattice
  20. def joinSemilattice: BoundedSemilattice[Set[A]]

  21. def meet(a: Set[A], b: Set[A]): Set[A]

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

    Definition Classes
    MeetSemilattice
  23. def meetSemilattice: Semilattice[Set[A]]

    Definition Classes
    MeetSemilattice
  24. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef
  25. final def notify(): Unit

    Definition Classes
    AnyRef
  26. final def notifyAll(): Unit

    Definition Classes
    AnyRef
  27. def or(lhs: Set[A], rhs: Set[A]): Set[A]

    Definition Classes
    SetLatticeGenBool
  28. final def synchronized[T0](arg0: ⇒ T0): T0

    Definition Classes
    AnyRef
  29. def toString(): String

    Definition Classes
    AnyRef → Any
  30. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  31. final def wait(arg0: Long, arg1: Int): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  32. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  33. def without(lhs: Set[A], rhs: Set[A]): Set[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
    SetLatticeGenBool
  34. def xor(a: Set[A], b: Set[A]): Set[A]

    Logical exclusive or, set-theoretic symmetric difference.

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

    Definition Classes
    GenBool
  35. def zero: Set[A]

    Definition Classes
    SetLatticeBoundedJoinSemilattice

Inherited from GenBool[Set[A]]

Inherited from BoundedJoinSemilattice[Set[A]]

Inherited from DistributiveLattice[Set[A]]

Inherited from Lattice[Set[A]]

Inherited from MeetSemilattice[Set[A]]

Inherited from JoinSemilattice[Set[A]]

Inherited from Serializable

Inherited from Serializable

Inherited from AnyRef

Inherited from Any

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