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
- Alphabetic
- By Inheritance
- GenBool
- BoundedJoinSemilattice
- DistributiveLattice
- Lattice
- MeetSemilattice
- JoinSemilattice
- Serializable
- Any
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- Public
- Protected
Abstract Value Members
- abstract def and(a: A, b: A): A
- abstract def getClass(): Class[_ <: AnyRef]
- Definition Classes
- Any
- abstract def or(a: A, b: A): A
- 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). - abstract def zero: A
- Definition Classes
- BoundedJoinSemilattice
Concrete Value Members
- final def !=(arg0: Any): Boolean
- Definition Classes
- Any
- final def ##: Int
- Definition Classes
- Any
- final def ==(arg0: Any): Boolean
- Definition Classes
- Any
- final def asInstanceOf[T0]: T0
- Definition Classes
- Any
- 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
- def equals(arg0: Any): Boolean
- Definition Classes
- Any
- def hashCode(): Int
- Definition Classes
- Any
- final def isInstanceOf[T0]: Boolean
- Definition Classes
- Any
- def isZero(a: A)(implicit ev: Eq[A]): Boolean
- Definition Classes
- BoundedJoinSemilattice
- def join(a: A, b: A): A
- Definition Classes
- GenBool → JoinSemilattice
- def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- JoinSemilattice
- def joinSemilattice: BoundedSemilattice[A]
- Definition Classes
- BoundedJoinSemilattice → JoinSemilattice
- def meet(a: A, b: A): A
- Definition Classes
- GenBool → MeetSemilattice
- def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]
- Definition Classes
- MeetSemilattice
- def meetSemilattice: Semilattice[A]
- Definition Classes
- MeetSemilattice
- def toString(): String
- Definition Classes
- Any
- 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
.
Deprecated Value Members
- def asBoolRing: BoolRng[A]
Every generalized Boolean algebra is also a
BoolRng
, with multiplication defined asand
and addition defined asxor
.Every generalized Boolean algebra is also a
BoolRng
, with multiplication defined asand
and addition defined asxor
.- Annotations
- @deprecated
- Deprecated
(Since version 2.7.0) See typelevel/algebra#108 for discussion