org.scalactic.algebra

Monoid

trait Monoid[A] extends Associative[A]

Typeclass trait representing a binary operation that obeys the associative law and an identity element that obeys the left and right identity laws.

The associative law states that given values a, b, and c of type A (and implicit Monoid.adapters imported):

((a combine b) combine c) === (a combine (b combine c))

The left identity law states that given the identity value, z, and any other value, a, of type A (and implicit Monoid.adapters imported):

(z combine a) === a

An similarly, the right identity law states that given the same values and implicit:

(a combine z) === a

Source
Monoid.scala
Linear Supertypes
Associative[A], AnyRef, Any
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Abstract Value Members

  1. abstract def combine(a1: A, a2: A): A

    A binary operation that obeys the associative law.

    A binary operation that obeys the associative law.

    See the main documentation for this trait for more detail.

    Definition Classes
    Associative

  2. abstract def z: A

    The identity element.

    The identity element.

    Passing the identity element, z, to combine along with any other value, a, of type A will result in the same value, a. See the main documentation for this trait for more detail.

Concrete Value Members

  1. final def !=(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  2. final def !=(arg0: Any): Boolean

    Definition Classes
    Any

  3. final def ##(): Int

    Definition Classes
    AnyRef → Any

  4. final def ==(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  5. final def ==(arg0: Any): Boolean

    Definition Classes
    Any

  6. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  7. def clone(): AnyRef

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  8. final def eq(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  9. def equals(arg0: Any): Boolean

    Definition Classes
    AnyRef → Any

  10. def finalize(): Unit

    Attributes
    protected[java.lang]
    Definition Classes
    AnyRef
    Annotations
    @throws( classOf[java.lang.Throwable] )

  11. final def getClass(): Class[_]

    Definition Classes
    AnyRef → Any

  12. def hashCode(): Int

    Definition Classes
    AnyRef → Any

  13. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  14. final def ne(arg0: AnyRef): Boolean

    Definition Classes
    AnyRef

  15. final def notify(): Unit

    Definition Classes
    AnyRef

  16. final def notifyAll(): Unit

    Definition Classes
    AnyRef

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

    Definition Classes
    AnyRef

  18. def toString(): String

    Definition Classes
    AnyRef → Any

  19. final def wait(): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

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

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

  21. final def wait(arg0: Long): Unit

    Definition Classes
    AnyRef
    Annotations
    @throws( ... )

Inherited from Associative[A]

Inherited from AnyRef

Inherited from Any

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