PartialAction

A partial action is the combination of left and right partial actions, providing:

- a method partialActl(g, p), or g ?|+|> p returning Opt[P], such that:

1. for all g, h in G, p in P such that g |+|? h and h ?|+|> p are defined,

((g |+|? h).get ?|+|> p).get === (g ?|+|> (h ?|+|> p).get).get with all operations defined.

• a method partialActr(p, g), or p <|+|? g returning Opt[P], such that:

2. for all g, h in G, p in P such that g |+|? h and p <|+|? 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 in G and p in P such that g ?|+|> p is defined:

(g.rightId ?|+|> p).get === p, the operation ?|+|> being defined.

4. for all g in G and p in P such that p <|+|? g is defined:

(p <|+|? g.leftId).get === p, the operation <|+|? being defined.

5. for all g in G and p in P such that g ?|+|> p is defined:

(g ?|+|> p).get === (p <|+|? g.inverse).get