Aspects of functional paradigms are good for safety critical systems, e.g., using pure functions when possible, when it leads to more predictable and testable systems. Recursion and non-strict evaluation, however, are clearly problematic viz. stack consumption, system load, and execution time; ditto for purely functional data structures and associated functions.
[0] I'm hedging here with frequently, but I'm having trouble thinking of safety critical systems that aren't hard real-time off the cuff… perhaps supervised expert systems, say an automated pathology platform, might count?
What you'd want is not a Turing complete language by default, but one that's guaranteed to halt. (And only have Turing complete bits as a fallback, just like unsafePerformIO today.)
Primitive Recursion might be a good limited but useful model of computation. Or something along the lines of Agda.
With such a more restricted notion, recursion doesn't necessarily have to be compiled to a stack.
Not if one codes towards TCO (Tail Call Optimization): http://stackoverflow.com/questions/310974/what-is-tail-call-...
also there is always state. look at the io front there your application needs to deal with state, if you are using fp your program maybe doesn't contain state. but the public api mostly deals with it.
There are lots of useful stateless services. But that's the nirvana, and not possible with all things you might want to offer.
In the second example, you stand on firmer ground though.