You don’t need 2 and 3. You can express them just with with T. For example, you could use an Either type for “good, here’s your value/bad, here’s your error.” If you want to get more sophisticated, you can add a type with extra error cases. In my own combinator libraries, I also include extra failure information to make diagnosing failed parses easy (and to generate pretty output). This does not change the fact that T is sufficient.

No. The parser code (in a library that everyone depends on) will branch on success/fail internally. It has nothing to branch on if it only sees T, because T may not have a success/fail nature.

You could take a step back and make sure T has a fail case, e.g. T-extends-Either<A, B>, but what is to be gained?

* Firstly, what the hell is A?

* The user would need to type Parsers of T=Cat and T=Dog instead as Parsers of T=Either<Error,Dog> and T=Either<Error,Cat>. If everyone has to do it, pull the common abstraction back into the library itself! Also the caller would receive a successful parse of T=Either and would then need to check to see if it was success(success) or success(fail).

* You also mix abstractions in the same way as newlines in string literals. You could no longer represent a successful parse of a failed Either, since the failed Either would look like a parse error.