GenBoolFromBoolRng

Every Boolean rng gives rise to a Boolean algebra without top:

0 is preserved;
ring multiplication (times) corresponds to and;
ring addition (plus) corresponds to xor;
a or b is then defined as a xor b xor (a and b);
relative complement a\b is defined as a xor (a and b).

BoolRng.asBool.asBoolRing gives back the original BoolRng.

See also: algebra.lattice.GenBool.asBoolRing

Linear Supertypes

GenBool[A], BoundedJoinSemilattice[A], DistributiveLattice[A], Lattice[A], MeetSemilattice[A], JoinSemilattice[A], Serializable, Serializable, AnyRef, Any

Known Subclasses

BoolFromBoolRing

Instance Constructors

new GenBoolFromBoolRng(orig: BoolRng[A])

Value Members

final def !=(arg0: Any): Boolean

Definition Classes
AnyRef → Any
final def ##(): Int

Definition Classes
AnyRef → Any
final def ==(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def and(a: A, b: A): A

Definition Classes
GenBoolFromBoolRng → GenBool
def asBoolRing: BoolRng[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
GenBoolFromBoolRng → GenBool
final def asInstanceOf[T0]: T0

Definition Classes
Any
def clone(): AnyRef

Attributes
protected[java.lang]
Definition Classes
AnyRef
Annotations
@throws( ... )
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
final def eq(arg0: AnyRef): Boolean

Definition Classes
AnyRef
def equals(arg0: Any): Boolean

Definition Classes
AnyRef → Any
def finalize(): Unit

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

Definition Classes
AnyRef → Any
def hashCode(): Int

Definition Classes
AnyRef → 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
final def ne(arg0: AnyRef): Boolean

Definition Classes
AnyRef
final def notify(): Unit

Definition Classes
AnyRef
final def notifyAll(): Unit

Definition Classes
AnyRef
def or(a: A, b: A): A

Definition Classes
GenBoolFromBoolRng → GenBool
final def synchronized[T0](arg0: ⇒ T0): T0

Definition Classes
AnyRef
def toString(): String

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

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

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

Definition Classes
AnyRef
Annotations
@throws( ... )
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).
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
GenBoolFromBoolRng → GenBool
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.

Definition Classes
GenBool
def zero: A

Definition Classes
GenBoolFromBoolRng → BoundedJoinSemilattice

Related Doc: package lattice

class GenBoolFromBoolRng[A] extends GenBool[A]

Instance Constructors

new GenBoolFromBoolRng(orig: BoolRng[A])

Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

def and(a: A, b: A): A

def asBoolRing: BoolRng[A]

final def asInstanceOf[T0]: T0

def clone(): AnyRef

def dual: Lattice[A]

final def eq(arg0: AnyRef): Boolean

def equals(arg0: Any): Boolean

def finalize(): Unit

final def getClass(): Class[_]

def hashCode(): Int

final def isInstanceOf[T0]: Boolean

def isZero(a: A)(implicit ev: Eq[A]): Boolean

def join(a: A, b: A): A

def joinPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

def joinSemilattice: BoundedSemilattice[A]

def meet(a: A, b: A): A

def meetPartialOrder(implicit ev: Eq[A]): PartialOrder[A]

def meetSemilattice: Semilattice[A]

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

def or(a: A, b: A): A

final def synchronized[T0](arg0: ⇒ T0): T0

def toString(): String

final def wait(): Unit

final def wait(arg0: Long, arg1: Int): Unit

final def wait(arg0: Long): Unit

def without(a: A, b: A): A

def xor(a: A, b: A): A

def zero: A

Inherited from GenBool[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 AnyRef

Inherited from Any

Ungrouped