Tagging std::function with a name?

I'm working on a parser combinator library, and I'd really like my parser to simply be some callable object:

typedef std::function<parse_result(parse_stream)> parser;

Which makes the parser combinators nice, eg:

parser operator &(parser a, parser b) { return both(a,b); }

but I'd like two features:

1) I'd like string literals to get promoted to a parser automatically so you can do things like:

parser option = "<" & regexp("[^+>]+");

2) I'd like a parser to have a name that I can use for error formatting. In the case of the "both" parser above, I could print that I expected a.name() and b.name() for example.

The two options I've tried so far are

1. a parser class that's callable, this lets me build from strings and std::function instances but a general callable has to be converted to a std::function first and from there to a parser, and C++ won't do two implicit conversions

2. Inheriting from std::function so I can implicitly convert the functions, but this seems to have a lot of gotchas in terms of only converting callables into a parser.

Does anyone have any thoughts on how to structure this?