Action

A semigroup/monoid/group action of G on P is the combination of compatible left and right actions, providing:

• the implementation of a method actl(g, p), or g |+|> p, such that:

1. (g |+| h) |+|> p === g |+|> (h |+|> p) for all g, h in G and p in P.

2. id |+|> p === p for all p in P (if id is defined)

• the implementation of a method actr(p, g), or p <|+| g, such that:

3. p <|+| (g |+| h) === (p <|+| g) <|+| h for all g, h in G and p in P.

4. p <|+| id === p for all p in P (if id is defined)

In addition, if G is a group, left and right actions are compatible:

5. g |+|> p === p <|+| g.inverse.