spire.algebra.partial

Groupoid

trait Groupoid[A] extends Semigroupoid[A]

A groupoid is a semigroupoid where inverse are defined for all elements, and thus left and right identity elements such that:

(i) (leftId(g) |+|? g).get === g (ii) (g |+|? rightId(g)).get === g (iii) a.inverse |+|? a and a |+|? a.inverse are always defined (iv) if a |+|? b, then ((a |+|? b).get |+|? b.inverse).get === a and ((a.inverse |+|? a).get |+|? b) === b

Linear Supertypes
Semigroupoid[A], Any
Known Subclasses
IterableGroupoid
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  2. Semigroupoid
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Abstract Value Members

  1. abstract def getClass(): Class[_]

    Definition Classes
    Any

  2. abstract def inverse(a: A): A

    Returns the inverse element of a such that (a |+|? a.inverse).get is an identity.

  3. abstract def partialOp(x: A, y: A): Opt[A]

    Definition Classes
    Semigroupoid

Concrete Value Members

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

    Definition Classes
    Any

  2. final def ##(): Int

    Definition Classes
    Any

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

    Definition Classes
    Any

  4. final def asInstanceOf[T0]: T0

    Definition Classes
    Any

  5. def equals(arg0: Any): Boolean

    Definition Classes
    Any

  6. def hashCode(): Int

    Definition Classes
    Any

  7. def isId(a: A)(implicit ev: Eq[A]): Boolean

    Tests if a is an identity.

  8. final def isInstanceOf[T0]: Boolean

    Definition Classes
    Any

  9. def leftId(a: A): A

    Returns the left identity of a.

  10. def opInverseIsDefined(x: A, y: A): Boolean

  11. def opIsDefined(x: A, y: A): Boolean

    Definition Classes
    Semigroupoid

  12. def partialOpInverse(x: A, y: A): Opt[A]

  13. def rightId(a: A): A

    Returns the right identity of a.

  14. def toString(): String

    Definition Classes
    Any

Inherited from Semigroupoid[A]

Inherited from Any

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