trait Bool[A] extends Heyting[A]

A boolean algebra is a structure that defines a few basic operations, namely as conjunction (&), disjunction (|), and negation (~). Both conjunction and disjunction must be associative, commutative and should distribute over each other. Also, both have an identity and they obey the absorption law; that is x & (y | x) == x and x | (x & y) == x.

Linear Supertypes
Heyting[A], BoundedLattice[A], BoundedJoinSemilattice[A], BoundedMeetSemilattice[A], Lattice[A], MeetSemilattice[A], JoinSemilattice[A], Any
Known Subclasses
DualBool, BitString, BooleanIsBool, BooleanStructure, ByteIsBitString, IntIsBitString, LongIsBitString, ShortIsBitString
Ordering
  1. Alphabetic
  2. By Inheritance
Inherited
  1. Bool
  2. Heyting
  3. BoundedLattice
  4. BoundedJoinSemilattice
  5. BoundedMeetSemilattice
  6. Lattice
  7. MeetSemilattice
  8. JoinSemilattice
  9. Any
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Visibility
  1. Public
  2. All

Abstract Value Members

  1. abstract def and(a: A, b: A): A
    Definition Classes
    Heyting
  2. abstract def complement(a: A): A
    Definition Classes
    Heyting
  3. abstract def getClass(): Class[_]
    Definition Classes
    Any
  4. abstract def one: A
    Definition Classes
    BoundedMeetSemilattice
  5. abstract def or(a: A, b: A): A
    Definition Classes
    Heyting
  6. 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. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def dual: Bool[A]
  6. def equals(arg0: Any): Boolean
    Definition Classes
    Any
  7. def hashCode(): Int
    Definition Classes
    Any
  8. def imp(a: A, b: A): A
    Definition Classes
    Bool → Heyting
  9. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  10. def isOne(a: A)(implicit ev: Eq[A]): Boolean
    Definition Classes
    BoundedMeetSemilattice
  11. def isZero(a: A)(implicit ev: Eq[A]): Boolean
    Definition Classes
    BoundedJoinSemilattice
  12. def join(a: A, b: A): A
    Definition Classes
    Heyting → JoinSemilattice
  13. def meet(a: A, b: A): A
    Definition Classes
    Heyting → MeetSemilattice
  14. def nand(a: A, b: A): A
  15. def nor(a: A, b: A): A
  16. def nxor(a: A, b: A): A
  17. def toString(): String
    Definition Classes
    Any
  18. def xor(a: A, b: A): A

Inherited from Heyting[A]

Inherited from BoundedLattice[A]

Inherited from BoundedJoinSemilattice[A]

Inherited from BoundedMeetSemilattice[A]

Inherited from Lattice[A]

Inherited from MeetSemilattice[A]

Inherited from JoinSemilattice[A]

Inherited from Any

Ungrouped