So will you admit that the first example has been sufficiently addressed? Because I was commenting on the problem involving the Collatz conjecture.
> It's safety also "depends on the semantics of C and how they've been used in a function", specifically on the fact that accessing an array is safe if and only if the index is in bounds. Out of bounds accesses to memory are probably the most common critical vulnerability in C programs, so it is essential that Xr0 prevents them.
True. As you said earlier:
> The safety of this program requires you to prove that `generate_random_planar_graph` always returns a planar graph, that `compute_chromatic_number` correctly identifies the chromatic number and that the chromatic number of every planar graph is less than 5.
This can obviously only be proven if we have the bodies of `generate_random_planar_graph` and `compute_chromatic_number`. Please provide these, and then I can attempt to answer. Because our whole point in Xr0 is that safety comes down to formalising interfaces – without interfaces for these functions we cannot investigate the safety of `main`.
> So will you admit that the first example has been sufficiently addressed? Because I was commenting on the problem involving the Collatz conjecture.
In that this specific program is obviously designed to be extremely hard to prove correct? Yeah. In that most real programs will be easier to prove correct automatically? No.
> This can obviously only be proven if we have the bodies of `generate_random_planar_graph` and `compute_chromatic_number`. Please provide these, and then I can attempt to answer. Because our whole point in Xr0 is that safety comes down to formalising interfaces – without interfaces for these functions we cannot investigate the safety of `main`.
What would be the point of that exactly? We both know that those functions would contain loops and as such Xr0 would be completely unable to verify them. We also know that Xr0 isn't actually able to state that `generate_random_planar_graph` generates a planar graph (other than completely repeating the body in the annotations, I guess). We also both know that Xr0 would not be able to deduce that the chromatic number of planar graphs is less than five.
I already provided two examples of programs the safety of which Xr0 will not be able to verify. I think it's your turn to produce a non-trivial C program that Xr0 will be able to handle.
This discussion really isn't all that enlightening, sadly. Xr0 can't currently handle loops and you haven't produced a single technical argument as to why I should expect Xr0 to be able to handle non-trivial loops in the future.
You also haven't produced a single technical argument as to why Xr0 should succeed where Frama-C failed. The argument that Frama-C is more general while Xr0 is specialized on safety is refuted easily as it is easy to come up with C programs the safety of which depends on arbitrary properties (and I would argue that many if not most real world C programs fall into this category).
So will you admit that the first example has been sufficiently addressed? Because I was commenting on the problem involving the Collatz conjecture.
> It's safety also "depends on the semantics of C and how they've been used in a function", specifically on the fact that accessing an array is safe if and only if the index is in bounds. Out of bounds accesses to memory are probably the most common critical vulnerability in C programs, so it is essential that Xr0 prevents them.
True. As you said earlier:
> The safety of this program requires you to prove that `generate_random_planar_graph` always returns a planar graph, that `compute_chromatic_number` correctly identifies the chromatic number and that the chromatic number of every planar graph is less than 5.
This can obviously only be proven if we have the bodies of `generate_random_planar_graph` and `compute_chromatic_number`. Please provide these, and then I can attempt to answer. Because our whole point in Xr0 is that safety comes down to formalising interfaces – without interfaces for these functions we cannot investigate the safety of `main`.