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`.
- Companion:
- object