Fact actr_is_action : is_action 'N(A) actr.
Canonical actr_action := Action actr_is_action.
Notation "''M'" := actr_action (at level 8) : action_scope.

Lemma act0r x : 0 ^@ x = 0.
Definition actr_sum x := big_morph _ (actAr x) (act0r x).