This is problematic even in dependently-typed languages like Idris, because while you can require a proof that something is not (or does not contain) NaN, it's

This is problematic even in dependently-typed languages like Idris, because while you can require a proof that something is not (or does not contain) NaN, it's pretty easy to call a function that is allowed to return NaN, which means that you actually cannot satisfy that proof after calling one of those functions unless you actually check again.