Comment by skybrian

Further nit-picking: even if there are no errors, I don't think it's an isomorphism unless the parser preserves all information? Usually parsers treat some input strings as equivalent (by stripping whitespace and comments), so there are fewer outputs than valid inputs.

I can't think of an easy way to make string splitting an isomorphism in both directions. You can serialize any list of strings to a comma-separated list, but only if you use escape sequences or encode the length of each item, and then there are some input strings that are errors.

I guess you could define a type as the set of all valid strings in the input language, but that's going out of your way to make sure parsing has to be done more than once.

Parsers that report no errors don't seem desirable anyway; error-checking is usually good.