[black_knight]

Rice theorem is not really applicative here. It is a beautiful theorem, but it has to do with what we can compute, while "safe" has to do with what one can access.

A function taking Integers to Integers in a pure language cannot do I/O, and thus is "safe" to run, in the sense that I can be guaranteed it does not contain a trojan making my computer into a peer on a botnet. This is true, even if I allow it to compute any computable function.

Computational expressiveness and "safeness" are in a sense orthogonal. And just as I don't think it is always appropriate for any function to do I/O, I am not convinced all functions should be able to perform any computation. But that's a different discussion.

Regarding definedness of the term "safe", I would say it is defined by your threat model. It not an absolute term, but dependent on context.