> monadic combinators are more powerful [than context free parsers]
Monadic parsers can do context-sensitive things that context free parsers can't, but they can't have unordered options which context free parsers can. So really monadic parsers have different powers to context-free.
> do monads warn the user when there is an ambiguity in the "grammar"?
You don't have ambiguity in the grammar because monadic parsers only provide ordered options.
> You don't have ambiguity in the grammar because monadic parsers only provide ordered options.
Oh, but you do have ambiguity in the grammar, except that parser
returns one of the possible parse trees deterministically and thus doesn't
warn you that the input could be parsed differently. This leads to the false
impression that your grammar is unambiguous.
> Further, do monads warn the user when there is an ambiguity in the "grammar"?
I'm not aware of a parser combinator library that does this. The way you build parser combinators in Haskell doesn't exactly preclude it from being done but it wouldn't be totally trivial either.
Googling for it didn't turn up much that wasn't a veiled reference to this paper:
If you mean big O efficiency, it doesn't make any difference if you are creating a monad, applicative, or an state machine. Complexity comes explicitly in the parser construction, so if you write a monadic parser using only LR(k) combinators, you will get an LR(k) parser. If you write some backtracking, you will get worse complexity.
Further, do monads warn the user when there is an ambiguity in the "grammar"?