Groupoid

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

Abstract Value Members

abstract def getClass(): Class[_]

Definition Classes
Any
abstract def inverse(a: A): A

Returns the inverse element of a such that (a |+|? a.inverse).get is an identity.
abstract def partialOp(x: A, y: A): Opt[A]

Definition Classes
Semigroupoid

Concrete Value Members

final def !=(arg0: Any): Boolean

Definition Classes
Any
final def ##(): Int

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

Definition Classes
Any
final def asInstanceOf[T0]: T0

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

Definition Classes
Any
def hashCode(): Int

Definition Classes
Any
def isId(a: A)(implicit ev: Eq[A]): Boolean

Tests if a is an identity.
final def isInstanceOf[T0]: Boolean

Definition Classes
Any
def leftId(a: A): A

Returns the left identity of a.
def opInverseIsDefined(x: A, y: A): Boolean
def opIsDefined(x: A, y: A): Boolean

Definition Classes
Semigroupoid
def partialOpInverse(x: A, y: A): Opt[A]
def rightId(a: A): A

Returns the right identity of a.
def toString(): String

Definition Classes
Any

Related Docs: object Groupoid | package partial

trait Groupoid[A] extends Semigroupoid[A]

Abstract Value Members

abstract def getClass(): Class[_]

abstract def inverse(a: A): A

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

Concrete Value Members

final def !=(arg0: Any): Boolean

final def ##(): Int

final def ==(arg0: Any): Boolean

final def asInstanceOf[T0]: T0

def equals(arg0: Any): Boolean

def hashCode(): Int

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

final def isInstanceOf[T0]: Boolean

def leftId(a: A): A

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

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

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

def rightId(a: A): A

def toString(): String

Inherited from Semigroupoid[A]

Inherited from Any

Ungrouped