Abstract Value Members
-
abstract
def
getClass(): Class[_]
-
abstract
def
partialActl(g: G, p: P): Opt[P]
-
abstract
def
partialActr(p: P, g: G): Opt[P]
Concrete Value Members
-
final
def
!=(arg0: Any): Boolean
-
final
def
##(): Int
-
final
def
==(arg0: Any): Boolean
-
def
actlIsDefined(g: G, p: P): Boolean
-
def
actrIsDefined(p: P, g: G): Boolean
-
final
def
asInstanceOf[T0]: T0
-
def
equals(arg0: Any): Boolean
-
def
hashCode(): Int
-
final
def
isInstanceOf[T0]: Boolean
-
def
toString(): String
A partial action is the combination of left and right partial actions, providing:
- a method
partialActl(g, p)
, org ?|+|> p
returningOpt[P]
, such that:1. for all
g
,h
inG
,p
inP
such thatg |+|? h
andh ?|+|> p
are defined,((g |+|? h).get ?|+|> p).get === (g ?|+|> (h ?|+|> p).get).get
with all operations defined.partialActr(p, g)
, orp <|+|? g
returningOpt[P]
, such that:2. for all
g
,h
inG
,p
inP
such thatg |+|? h
andp <|+|? g
are defined,(p <|+|? (g |+|? h).get).get === ((p <|+|? g).get |+|? h).get
, and all operations are defined.In addition, if
G
is a groupoid, the following relations holds:3. for all
g
inG
andp
inP
such thatg ?|+|> p
is defined:(g.rightId ?|+|> p).get === p
, the operation?|+|>
being defined.4. for all
g
inG
andp
inP
such thatp <|+|? g
is defined:(p <|+|? g.leftId).get === p
, the operation<|+|?
being defined.5. for all
g
inG
andp
inP
such thatg ?|+|> p
is defined:(g ?|+|> p).get === (p <|+|? g.inverse).get