If your language is TC and thus supports general recursion, no algorithm can possibly exist for deciding whether a function is in fact total in the general case

If your language is TC and thus supports general recursion, no algorithm can possibly exist for deciding whether a function is in fact total in the general case. As all primitive recursive functions are provably total, that is a place a compiler can work. But just using for loops gets you there too. Total functions that are also pure functions are a pretty small set so there may be other reductions like the above. But don't depend on the compiler. But I agree writing total functions from the start is the ideal if possible.