In principle it reduces to the halting problem, but given that the domain we're discussing is real-time systems, you'd better already be dealing with programs that you know will halt (in the sense of producing an answer) in not just a finite amount of time but even below some particular bound! Once you've constrained yourself to those programs, you may well be able to get a general result... but as others have noted, really what we want is results about specific programs, and the halting problem has nothing to say there.
I don't know that there exists tooling to construct these proofs, beyond general proof-constructing support, but I'm not working in hard-realtime environments so I'm sure I'm not aware of everything going on either.
Comments
In principle it reduces to the halting problem, but given that the domain we're discussing is real-time systems, you'd better already be dealing with programs that you know will halt (in the sense of producing an answer) in not just a finite amount of time but even below some particular bound! Once you've constrained yourself to those programs, you may well be able to get a general result... but as others have noted, really what we want is results about specific programs, and the halting problem has nothing to say there.
I don't know that there exists tooling to construct these proofs, beyond general proof-constructing support, but I'm not working in hard-realtime environments so I'm sure I'm not aware of everything going on either.