[dbaupp]

If you're narrowly interpreting an API to mean just the function signature, then sure, if your type system is appropriately restricted then it is computable (although many type systems are Turing complete, meaning this won't be computable in all cases, for the same reasons). This is, in fact, something my comment explicitly called out.

Having signature compatibility is an important prerequisite, but I think it's possible worse to have code that compiles but does the wrong thing than to have code that doesn't compile (at least it's obvious to the developer that something needs to be fixed, in the latter case).