Datasets:
File size: 2,247 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 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_replace_last_element(first: &Vec<i32>, second: &Vec<i32>) -> (replaced_list: Vec<i32>)
requires
first.len() > 0,
{
let mut replaced_list = Vec::new();
let first_end = first.len() - 1;
let mut index = 0;
while index < first_end
{
replaced_list.push(first[index]);
index += 1;
}
index = 0;
while index < second.len()
{
replaced_list.push(second[index]);
index += 1;
}
replaced_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
}
fn f3_all_elements_equals(arr: &Vec<i32>, element: i32) -> (result: bool)
{
let mut index = 0;
while index < arr.len()
{
if arr[index] != element {
return false;
}
index += 1;
}
true
}
spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, outp: Seq<i32>) -> bool {
(outp == __hp0.subrange(0, __hp0.len() - 1).add(__hp1))
}
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])
}
spec fn step3(inp: Seq<i32>, p3_element: i32, outp: bool) -> bool {
(outp == (forall|i: int| 0 <= i < inp.len() ==> (inp[i] == p3_element)))
}
fn chain_driver(first: &Vec<i32>, second: &Vec<i32>, p2_elem: i32, p3_element: i32) -> (r_final: bool)
requires
first.len() > 0,
ensures
exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(first@, second@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, p3_element, r_final),
{
let x1 = f1_replace_last_element(first, second);
let x2 = f2_insert_before_each(&x1, p2_elem);
let x3 = f3_all_elements_equals(&x2, p3_element);
proof {
assert(step1(first@, second@, x1@));
assert(step2(x1@, p2_elem, x2@));
assert(step3(x2@, p3_element, x3));
}
x3
}
} // verus!
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