Datasets:
File size: 2,626 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 99 100 101 102 103 104 105 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_cube_element(nums: &Vec<i32>) -> (cubed: Vec<i32>)
requires
forall|k: int|
0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k]
<= i32::MAX),
forall|k: int|
0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k]
* #[trigger] nums[k] <= i32::MAX),
{
let mut cubed_array: Vec<i32> = Vec::new();
let mut i = 0;
while i < nums.len()
{
cubed_array.push(nums[i] * nums[i] * nums[i]);
i += 1;
}
cubed_array
}
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_has_only_one_distinct_element(arr: &Vec<i32>) -> (result: bool)
{
if arr.len() <= 1 {
return true;
}
let mut index = 1;
while index < arr.len()
{
if arr[0] != arr[index] {
return false;
}
index += 1;
}
true
}
spec fn step1(__hp0: Seq<i32>, outp: Seq<i32>) -> bool {
(forall|i: int|
0 <= i < __hp0.len() ==> outp[i] == #[trigger] __hp0[i] * #[trigger] __hp0[i]
* #[trigger] __hp0[i])
}
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>, outp: bool) -> bool {
(outp == (forall|i: int| 1 <= i < inp.len() ==> inp[0] == #[trigger] inp[i]))
}
fn chain_driver(nums: &Vec<i32>, p2_elem: i32) -> (r_final: bool)
requires
forall|k: int|
0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k]
<= i32::MAX),
forall|k: int|
0 <= k < nums.len() ==> (i32::MIN <= #[trigger] nums[k] * #[trigger] nums[k]
* #[trigger] nums[k] <= i32::MAX),
ensures
exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(nums@, v1) && #[trigger] step2(v1, p2_elem, v2) && step3(v2, r_final),
{
let x1 = f1_cube_element(nums);
let x2 = f2_insert_before_each(&x1, p2_elem);
let x3 = f3_has_only_one_distinct_element(&x2);
proof {
assert(step1(nums@, x1@));
assert(step2(x1@, p2_elem, x2@));
assert(step3(x2@, x3));
}
x3
}
} // verus!
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