No, you can parse SML without doing type inference. The (only) tricky part of SML parsing is operator fixity, which doesn't depend on types at all.
And yes, SML type inference is superexponential, but only for contrived examples. So for "any practical reasons", it's not even remotely close to undecidability.
in reply to Re: Perl Cannot Be Parsed: A Formal Proof
in thread Perl Cannot Be Parsed: A Formal Proof