BooleanIsBool

trait BooleanIsBool extends Bool[Boolean]
trait Bool[Boolean]
trait GenBool[Boolean]
trait Heyting[Boolean]
trait BoundedDistributiveLattice[Boolean]
trait DistributiveLattice[Boolean]
trait BoundedLattice[Boolean]
trait BoundedJoinSemilattice[Boolean]
trait BoundedMeetSemilattice[Boolean]
trait Lattice[Boolean]
trait MeetSemilattice[Boolean]
trait JoinSemilattice[Boolean]
trait Serializable
class Object
trait Matchable
class Any

Value members

Concrete methods

def and(a: Boolean, b: Boolean): Boolean
def complement(a: Boolean): Boolean
def one: Boolean
def or(a: Boolean, b: Boolean): Boolean
override
def xor(a: Boolean, b: Boolean): Boolean
Definition Classes
Bool -> GenBool -> Heyting
def zero: Boolean

Inherited methods

override
def asBoolRing: BoolRing[Boolean]

Every Boolean algebra is a BoolRing, with multiplication defined as and and addition defined as xor. Bool does not extend BoolRing because, e.g. we might want a Bool[Int] and CommutativeRing[Int] to refer to different structures, by default.

Every Boolean algebra is a BoolRing, with multiplication defined as and and addition defined as xor. Bool does not extend BoolRing because, e.g. we might want a Bool[Int] and CommutativeRing[Int] to refer to different structures, by default.

Note that the ring returned by this method is not an extension of the Rig returned from BoundedDistributiveLattice.asCommutativeRig.

Definition Classes
Bool -> GenBool
Inherited from
Bool
def asCommutativeRig: CommutativeRig[Boolean]

Return a CommutativeRig using join and meet. Note this must obey the commutative rig laws since meet(a, one) = a, and meet and join are associative, commutative and distributive.

Return a CommutativeRig using join and meet. Note this must obey the commutative rig laws since meet(a, one) = a, and meet and join are associative, commutative and distributive.

Inherited from
BoundedDistributiveLattice
override
def dual: Bool[Boolean]
Definition Classes
Bool -> BoundedDistributiveLattice -> BoundedLattice -> Lattice
Inherited from
Bool
def imp(a: Boolean, b: Boolean): Boolean
Inherited from
Bool
def isOne(a: Boolean)(implicit ev: Eq[Boolean]): Boolean
Inherited from
BoundedMeetSemilattice
def isZero(a: Boolean)(implicit ev: Eq[Boolean]): Boolean
Inherited from
BoundedJoinSemilattice
override
def join(a: Boolean, b: Boolean): Boolean
Definition Classes
GenBool -> JoinSemilattice
Inherited from
GenBool
def joinPartialOrder(implicit ev: Eq[Boolean]): PartialOrder[Boolean]
Inherited from
JoinSemilattice
override
def joinSemilattice: BoundedSemilattice[Boolean]
Definition Classes
BoundedJoinSemilattice -> JoinSemilattice
Inherited from
BoundedJoinSemilattice
override
def meet(a: Boolean, b: Boolean): Boolean
Definition Classes
GenBool -> MeetSemilattice
Inherited from
GenBool
def meetPartialOrder(implicit ev: Eq[Boolean]): PartialOrder[Boolean]
Inherited from
MeetSemilattice
override
def meetSemilattice: BoundedSemilattice[Boolean]
Definition Classes
BoundedMeetSemilattice -> MeetSemilattice
Inherited from
BoundedMeetSemilattice
def nand(a: Boolean, b: Boolean): Boolean
Inherited from
Heyting
def nor(a: Boolean, b: Boolean): Boolean
Inherited from
Heyting
def nxor(a: Boolean, b: Boolean): Boolean
Inherited from
Heyting
def without(a: Boolean, b: Boolean): Boolean
Inherited from
Bool