Packages

trait Inverse[A] extends Identity[A]

The Inverse type class describes an associative binary operator for a type A that has an identity element and an inverse binary operator. Combining any value with itself with the inverse operator must return the identity element. For example, for integer addition zero is an identity element and subtraction is an inverse operation, because subtracting any value from itself always returns zero.

Because Inverse defines a binary rather than a unary operator it can be used to describe inverse operations for types that do not have inverse values. For example, the natural numbers do not have inverses because the set of natural numbers does not include negative numbers. But we can still define a subtraction operation that is the inverse of addition for the natural numbers, since subtracting a number from itself always returns zero.

Linear Supertypes
Identity[A], Associative[A], AnyRef, Any
Known Subclasses
EqualInverse
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Inherited
  1. Inverse
  2. Identity
  3. Associative
  4. AnyRef
  5. Any
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Visibility
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Abstract Value Members

  1. abstract def combine(l: ⇒ A, r: ⇒ A): A
    Definition Classes
    Associative
  2. abstract def identity: A

    The identity element.

    The identity element.

    Definition Classes
    Identity
  3. abstract def inverse(l: ⇒ A, r: ⇒ A): A

Concrete Value Members

  1. final def !=(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  2. final def ##(): Int
    Definition Classes
    AnyRef → Any
  3. final def ==(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  4. final def asInstanceOf[T0]: T0
    Definition Classes
    Any
  5. def clone(): AnyRef
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()
  6. final def eq(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  7. def equals(arg0: Any): Boolean
    Definition Classes
    AnyRef → Any
  8. def finalize(): Unit
    Attributes
    protected[lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )
  9. final def getClass(): Class[_]
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  10. def hashCode(): Int
    Definition Classes
    AnyRef → Any
    Annotations
    @native()
  11. final def intersperse(middle: A): Associative[A]
    Definition Classes
    Associative
  12. final def isInstanceOf[T0]: Boolean
    Definition Classes
    Any
  13. def multiply(n: Int)(a: A): A
  14. def multiplyOption(n: Int)(a: A): Some[A]
    Definition Classes
    Inverse → Identity → Associative
  15. final def ne(arg0: AnyRef): Boolean
    Definition Classes
    AnyRef
  16. final def notify(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  17. final def notifyAll(): Unit
    Definition Classes
    AnyRef
    Annotations
    @native()
  18. final def repeat(a: A)(n: Int): A
    Definition Classes
    Associative
  19. final def synchronized[T0](arg0: ⇒ T0): T0
    Definition Classes
    AnyRef
  20. def toString(): String
    Definition Classes
    AnyRef → Any
  21. final def wait(): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  22. final def wait(arg0: Long, arg1: Int): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )
  23. final def wait(arg0: Long): Unit
    Definition Classes
    AnyRef
    Annotations
    @throws( ... ) @native()

Inherited from Identity[A]

Inherited from Associative[A]

Inherited from AnyRef

Inherited from Any

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