In XBetza notation all captures are written as normal (i.e. replacement) captures, where you specify a multi-leg move that makes a detour over the victim square when they are not. So for withdrawer capture as in Ultima you would specify a trajectory that first takes a step in the opposit direction of how you want to move, and then reverts direction to move with a non-capture to the destination. This has a much larger expressive power than introducing a new letter for each type of capture.
There are two caveats in the withdrawer case, though:
To exclude plain rifle capture, the piece would have to move at least two steps after making the capture. So you must make it a 3-leg move, where the first leg steps to capture, (i.e. K if you want it to go in all 8 directions), the second leg steps back, and a third leg then continues with a slide in that derection (and so needs to toggle the range by usin ya in stead of a for connecting the legs).
The detour must not be blocked by a board edge or an own piece, while it must be mandarory. (So you cannot add a separate mQ for the non-captures, or the capture would be optional if there is something to capture). So the first leg must also be able to leave the board (o) or hop over a friend (but not an enemy). Unfortunately there does not exist a letter for 'friendly hop', so this must be improvised through 'friendly capture' (d) + 'unload (u) on the next leg. Because of the unload this cannot be contracted with the 'mco part' and has to be specified as a second move.
That finally gives mcoabyafmKdaubyafmK for the Ultima Withdrawer. The new 'bracket notation' for multi-leg moves, which is supposed to be more intuitive because in explicitly indicates direction type and range for every leg, instead of having to reconstruct it through range toggling and atom rotation, would be [mcoK-bK-fmQ][dK-buK-fmQ].
I agree that this is rather cumbersome, compared to, say, wmQ. But that is the tradeoff you will always have in using a completely general system over a system taylored to one application. There is in principle an infinity of capture modes, and by giving each mode its dedicated letter you will run out of letters pretty quickly, and then there is no room for further expansion. And even if there was (e.g. by using the Chinese character set), it would be impossible to remember all the meanings. Having a separate letter for 'friendly hop' would have helped here, but then you would still not have something for 'enemy-only hop'.
It is true that the combination "capture if there is something to capture, but do not block if there isn't" is relatively common amongst the cumbersome combinations of modes. It could be an idea to use cc for that (i.e. move, enemy capture, friendly hop or over the edge). That would simplify the Withdrawer case to [ccK-bK-fmQ]. It might even be better to give cc the meaning of a "rifle capture if possible", to remove the need for the extra backward step before you start sliding. Then the Withdrawer would become [ccK-bmQ]. And an Advancer would be [mQ-fccK]: move to an empty square as Queen, and from there rifle-capture the next square along the path if there is an enemy there (but never mind if there isn't one).
In XBetza notation all captures are written as normal (i.e. replacement) captures, where you specify a multi-leg move that makes a detour over the victim square when they are not. So for withdrawer capture as in Ultima you would specify a trajectory that first takes a step in the opposit direction of how you want to move, and then reverts direction to move with a non-capture to the destination. This has a much larger expressive power than introducing a new letter for each type of capture.
There are two caveats in the withdrawer case, though:
That finally gives mcoabyafmKdaubyafmK for the Ultima Withdrawer. The new 'bracket notation' for multi-leg moves, which is supposed to be more intuitive because in explicitly indicates direction type and range for every leg, instead of having to reconstruct it through range toggling and atom rotation, would be [mcoK-bK-fmQ][dK-buK-fmQ].
I agree that this is rather cumbersome, compared to, say, wmQ. But that is the tradeoff you will always have in using a completely general system over a system taylored to one application. There is in principle an infinity of capture modes, and by giving each mode its dedicated letter you will run out of letters pretty quickly, and then there is no room for further expansion. And even if there was (e.g. by using the Chinese character set), it would be impossible to remember all the meanings. Having a separate letter for 'friendly hop' would have helped here, but then you would still not have something for 'enemy-only hop'.
It is true that the combination "capture if there is something to capture, but do not block if there isn't" is relatively common amongst the cumbersome combinations of modes. It could be an idea to use cc for that (i.e. move, enemy capture, friendly hop or over the edge). That would simplify the Withdrawer case to [ccK-bK-fmQ]. It might even be better to give cc the meaning of a "rifle capture if possible", to remove the need for the extra backward step before you start sliding. Then the Withdrawer would become [ccK-bmQ]. And an Advancer would be [mQ-fccK]: move to an empty square as Queen, and from there rifle-capture the next square along the path if there is an enemy there (but never mind if there isn't one).