Bool

Contains implementation for Bool and typeconstructor aliases that make usage more pleasant

The operations can be shown to satisfy:

1. Associativity of Or: ||[A, B || C] =:= ||[A || B, C]

2. Associativity of And: &&[A, B && C] =:= &&[A && B, C]

3. Commutativity of Or: ||[A, B] =:= ||[B, A]

4. Commutativity of And: &&[A, B] =:= &&[B, A]

5. Distributivity of Or over And: ||[A, B && C] =:= &&[A || B, A || C]

6. Distributivity of And over Or: &&[A, B || C] =:= ||[A && B, A && C]

7. Identity for Or: ||[A, False] =:= A

8. Identity for And: &&[A, True] =:= A

9. Annhilator for Or: ||[A, True] =:= True

10. Annhilator for And: &&[A, False] =:= False

11. Idempotence of Or: ||[A, A] =:= A

12. Idempotence of And: &&[A, A] =:= A

13. Absorption 1: &&[A, A || B] =:= A

14. Absorbtion 2: ||[A, A && B] =:= A

15. Complementation 1: &&[A, Not[A]] =:= False

16. Complementation 2: ||[A, Not[A]] =:= True

17. Double Negation: Not[Not[A]] =:= A

18. De Morgan 1: &&[Not[A], Not[B]] =:= Not[A || B]

19. De Morgan 2: ||[Not[A], Not[B]] =:= Not[A && B]

Author:

Harshad Deo

Since: 0.1

Linear Supertypes

AnyRef, Any

Type Members

type &&[A <: Bool, B <: Bool] = Bool.&&.A.If[B, False, Bool]

Type constructor for logical conjunction
Type constructor for logical conjunction
A && B =:= True if A =:= True and B =:= True
A && B =:= False otherwise

Author:

Harshad Deo

Since
0.1
type ->>[A <: Bool, B <: Bool] = Bool.->>.A.If[B, True, Bool]

Typeconstructor for material implication
Typeconstructor for material implication
If A =:= True, A ->> B =:= B
If A =:= False, the value of B is ignored and the constructor returns True

Author:

Harshad Deo

Since
0.1
final class BoolRep[B <: Bool] extends AnyVal

Provides a value for a type level boolean
Provides a value for a type level boolean

Author:

Harshad Deo

Since
0.1
type Eqv[A <: Bool, B <: Bool] = Bool.Eqv.A.If[B, Not[B], Bool]

Type constructor for logical equivalence
Type constructor for logical equivalence
A Eqv B =:= True if A =:= B
A Eqv B =:= False otherwise
Author: Harshad Deo
Since 0.1
final class False extends Bool Typelevel representation of a predicate being False Typelevel representation of a predicate being False Author: Harshad Deo Since 0.1
type Not[A <: Bool] = Bool.Not.A.If[False, True, Bool] Type constructor for logical negation Type constructor for logical negation Not[True] =:= False Not[False] =:= True Author: Harshad Deo Since 0.1
final class True extends Bool Typelevel representation of a predicate being true Typelevel representation of a predicate being true Author: Harshad Deo Since 0.1
type Xor[A <: Bool, B <: Bool] = Bool.Xor.A.If[Not[B], B, Bool] Type constructor for logical exclusive or Type constructor for logical exclusive or A Xor B =:= True if exactly one of A =:= True or B =:= True A Xor B =:= False otherwise Author: Harshad Deo Since 0.1
type ||[A <: Bool, B <: Bool] = Bool.||.A.If[True, B, Bool] Type constructor for logical disjunction Type constructor for logical disjunction A || B =:= False if A =:= False and B =:= False A || B =:= True otherwise Author: Harshad Deo Since 0.1



        

        
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        BoolRep
      
      

      
        
      
    
      Provides implicits for converting typelevel booleans to value level booleans
Provides implicits for converting typelevel booleans to value level booleans

        Author:
        Harshad Deo
      
 Since
0.1
    

      
      
      
      
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        ne(arg0: AnyRef): Boolean
      
      

      
        
      
    
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        toBoolean[B <: Bool](implicit ev: BoolRep[B]): Boolean
      
      

      
        
      
    
      Method to convert a typelevel boolean to its value representation
Method to convert a typelevel boolean to its value representation

        Author:
        Harshad Deo
      
B
Type of the boolean to be converted to a value
 Since
0.1
    

      
      
      
      
        
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Related Docs: trait Bool | package typequux

object Bool

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Type Members

type &&[A <: Bool, B <: Bool] = Bool.&&.A.If[B, False, Bool]

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type ->>[A <: Bool, B <: Bool] = Bool.->>.A.If[B, True, Bool]

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final class BoolRep[B <: Bool] extends AnyVal

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type Eqv[A <: Bool, B <: Bool] = Bool.Eqv.A.If[B, Not[B], Bool]

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final class False extends Bool

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type Not[A <: Bool] = Bool.Not.A.If[False, True, Bool]

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final class True extends Bool

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type Xor[A <: Bool, B <: Bool] = Bool.Xor.A.If[Not[B], B, Bool]

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type ||[A <: Bool, B <: Bool] = Bool.||.A.If[True, B, Bool]

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Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

object BoolRep

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final def asInstanceOf[T0]: T0

def clone(): AnyRef

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

final def ne(arg0: AnyRef): Boolean

final def notify(): Unit

final def notifyAll(): Unit

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

def toBoolean[B <: Bool](implicit ev: BoolRep[B]): Boolean

Author:

def toString(): String

final def wait(): Unit

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

final def wait(arg0: Long): Unit

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Operations

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