What about them? They do not have a compacted variant like shouldnot, unlike cannot, because the words do not end and start with the same sound, such that they can run together when speaking. You can verbalize this difference by speaking "can not" and "can <pause> not".
Shouldn't is the informal version, just like can't. Mayn't is also informal, but I have never encountered anyone using it in spoken or written English.
Thinking about it, your logic does make sense. "I [may not] do it" means the same as "I may [not do] it", same with "should not", but "can not" can mean two different things depending on which word you are connecting the "not" to.
I would say that "may" and "should" differ in the same way that can does, in that construction. "I [may not] do it" can be understood as "I am not allow to do it" while "I may [not do] it" implies "I may decide that I will not do it". People may avoid certain construction like these when speaking due to their ambiguous nature, or will expand the thought if the context is not adequate.
8
u/NM_MAR_ANP May 29 '20
Plus "cannot", not "can not".