Help mate and self mate

[hgm]

As I am building a version of uMax to play with arbitrary fairy pieces (defined in a file read at startup, which the user can edit), someone asked me if it would also be able to do help mates and self mates.

As I was not familiar with these concepts, can someone tell me if the following definitions describe them correctly?

Normal mate-in-N problems are the minimax solution for the Distance-To-Mate from the given position.

Self mates are the maximin solutions, i.e. the 'losing' side (i.e. the one to be checkmated) strives for the shortest DTM, the winning side for the longest (or non-mating score). This could be obtained from normal minimax by flipping the sign of the evaluation.

Help mates are the maximax solutions, i.e. white strives for the shortest DTM, and black too (assuming it is a mate where black is checkmated). This would be obtained through 'posimax', i.e. negamax without flipping the sign.

One should be careful to apply the DTM to the actual mate, not to King capture, as voluntarily wandering in check is a form of helping that is still not allowed.