Datasets:
File size: 1,668 Bytes
c62beea | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_split_and_append(list: &Vec<i32>, n: usize) -> (new_list: Vec<i32>)
requires
list@.len() > 0,
0 < n < list@.len(),
{
let mut new_list = Vec::new();
let mut index = n;
while index < list.len()
{
new_list.push(list[index]);
index += 1;
}
let mut index = 0;
while index < n
{
new_list.push(list[index]);
index += 1;
}
new_list
}
fn f2_insert_before_each(arr: &Vec<i32>, elem: i32) -> (result: Vec<i32>)
{
let mut result: Vec<i32> = Vec::new();
let mut index = 0;
while index < arr.len()
{
result.push(elem);
result.push(arr[index]);
index += 1;
}
result
}
spec fn step1(__hp0: Seq<i32>, __hp1: usize, outp: Seq<i32>) -> bool {
(outp == __hp0.subrange(__hp1 as int, __hp0.len() as int).add(__hp0.subrange(0, __hp1 as int)))
}
spec fn step2(inp: Seq<i32>, p2_elem: i32, outp: Seq<i32>) -> bool {
(outp.len() == (2 * inp.len()))
&& (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k] == p2_elem)
&& (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k + 1] == inp[k])
}
fn chain_driver(list: &Vec<i32>, n: usize, p2_elem: i32) -> (r_final: Vec<i32>)
requires
list@.len() > 0,
0 < n < list@.len(),
ensures
exists|v1: Seq<i32>| #[trigger] step1(list@, n, v1) && step2(v1, p2_elem, r_final@),
{
let x1 = f1_split_and_append(list, n);
let x2 = f2_insert_before_each(&x1, p2_elem);
proof {
assert(step1(list@, n, x1@));
assert(step2(x1@, p2_elem, x2@));
}
x2
}
} // verus!
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