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]
Source
GenBool.scala
Linear Supertypes
BoundedJoinSemilattice[A], DistributiveLattice[A], Lattice[A], MeetSemilattice[A], JoinSemilattice[A], Serializable, Serializable, Any
Known Subclasses
BitSetAlgebra, BooleanAlgebra, SetLattice, Bool, BoolFromBoolRing, DualBool, GenBoolFromBoolRng
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. GenBool
  2. BoundedJoinSemilattice
  3. DistributiveLattice
  4. Lattice
  5. MeetSemilattice
  6. JoinSemilattice
  7. Serializable
  8. Serializable
  9. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def and(a: A, b: A): A
  2. abstract def getClass(): Class[_]
    Definition Classes
    Any
  3. abstract def or(a: A, b: A): A
  4. abstract 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).

  5. abstract def zero: A
    Definition Classes
    BoundedJoinSemilattice

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    Any
  2. final def ##(): Int
    Definition Classes
    Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    Any
  4. def asBoolRing: BoolRng[A]

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

  5. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  6. def dual: Lattice[A]

    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
    Definition Classes
    Any
  8. def hashCode(): Int
    Definition Classes
    Any
  9. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  10. def isZero(a: A)(implicit ev: Eq[A]): Boolean
    Definition Classes
    BoundedJoinSemilattice
  11. def join(a: A, b: A): A
    Definition Classes
    GenBool → JoinSemilattice
  12. def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
    Definition Classes
    JoinSemilattice
  13. def joinSemilattice: BoundedSemilattice[A]
    Definition Classes
    BoundedJoinSemilattice → JoinSemilattice
  14. def meet(a: A, b: A): A
    Definition Classes
    GenBool → MeetSemilattice
  15. def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
    Definition Classes
    MeetSemilattice
  16. def meetSemilattice: Semilattice[A]
    Definition Classes
    MeetSemilattice
  17. def toString(): String
    Definition Classes
    Any
  18. 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.

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

Ungrouped