Datasets:
File size: 1,719 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 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_element_wise_subtract(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
requires
arr1.len() == arr2.len(),
forall|i: int|
(0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] - arr2[i]) <= i32::MAX),
{
let mut output_arr = Vec::with_capacity(arr1.len());
let mut index = 0;
while index < arr1.len()
{
output_arr.push((arr1[index] - arr2[index]));
index += 1;
}
output_arr
}
fn f2_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>, __hp1: Seq<i32>, outp: Seq<i32>) -> bool {
(outp.len() == __hp0.len())
&& (forall|i: int|
0 <= i < outp.len() ==> #[trigger] outp[i] == #[trigger] (__hp0[i] - __hp1[i]))
}
spec fn step2(inp: Seq<i32>, outp: bool) -> bool {
(outp == (forall|i: int| 1 <= i < inp.len() ==> inp[0] == #[trigger] inp[i]))
}
fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (r_final: bool)
requires
arr1.len() == arr2.len(),
forall|i: int|
(0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] - arr2[i]) <= i32::MAX),
ensures
exists|v1: Seq<i32>| #[trigger] step1(arr1@, arr2@, v1) && step2(v1, r_final),
{
let x1 = f1_element_wise_subtract(arr1, arr2);
let x2 = f2_has_only_one_distinct_element(&x1);
proof {
assert(step1(arr1@, arr2@, x1@));
assert(step2(x1@, x2));
}
x2
}
} // verus!
|