Let me start this post with some definitions taken from The Retrograde Analysis Corner:
Retrograde Analysis is a genre of chess problems where the legality of the position is a key element. A position is legal if it can be reached through a legal chess game (no matter how weird).
Retractors are problems where it is asked to retract some "last" moves. A typical stipulation being "White retracts his last move and then mate in one". This is more than just asking for the last move because there can be a forward play and/or some retro-strategy. (...) These problems have a retro-flavor because only legal last moves can be retracted, but they also have the usual, forward, combinatorial flavor because you have to pick the right retraction, the one that will allow e.g. to mate in one.
Defensive Retractors. In these problems, you retract both white and black moves. Black is defending by trying to retract the moves that will forbid (or delay) the achievement of White's goal. The canonical example of a defensive retractor is the Proca-retractor stipulation.
Proca Retractor. Named after Zeno Proca (1906-1936). A Proca-retractor in 5 (say) asks for White to retract 5 moves and then mate in 1 with a forward move. After every White retraction (but the last) Black retracts what he wants, trying to defend against the forward mate. White retractions must end in a forward mate against any retractive defense by Black. As in direct problems, White is allowed to mate forward in 1 at any time (after a retraction) and this may happen if Black picks a poor defense. Also, Black may defend by mating White through a forward move if such an opportunity exists after one of his retractions.
Below you can find an example of Orthodox (without fairy units or conditions) Defensive (Black has the chance to defend against White with the same stipulation after any of its retractions) Proca (both sides are allowed to retract legal captures and the side that uncaptures decides which unit is resurrected) Retractor -n (if n=1 Black has no defensive moves) & #m (the stipulation is a direct mate).
Die Schwalbe 1980
-1.Rb4-b7 Qc4-e6 -2.Rb3-b4 Sc3-a4 -3.Rb3-b5 Sd5-c3 -4.Rb8-b5 and 1.Rxg8#
Notice that there are no duals because all captures (both by Black and White) were made by pawns (the wPs g2 and h2 had to promote).