Datasets:
File size: 1,847 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 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_element_wise_divide(arr1: &Vec<u32>, arr2: &Vec<u32>) -> (result: Vec<u32>)
requires
arr1.len() == arr2.len(),
forall|i: int| 0 <= i < arr2.len() ==> arr2[i] != 0,
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_find_odd_numbers(arr: &Vec<u32>) -> (odd_numbers: Vec<u32>)
{
let mut odd_numbers: Vec<u32> = Vec::new();
let input_len = arr.len();
let mut index = 0;
while index < arr.len()
{
if (arr[index] % 2 != 0) {
odd_numbers.push(arr[index]);
}
index += 1;
}
odd_numbers
}
spec fn step1(__hp0: Seq<u32>, __hp1: Seq<u32>, outp: Seq<u32>) -> 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<u32>, outp: Seq<u32>) -> bool {
(outp == inp.filter(|x: u32| x % 2 != 0))
}
fn chain_driver(arr1: &Vec<u32>, arr2: &Vec<u32>) -> (r_final: Vec<u32>)
requires
arr1.len() == arr2.len(),
forall|i: int| 0 <= i < arr2.len() ==> arr2[i] != 0,
forall|i: int|
(0 <= i < arr1.len()) ==> (i32::MIN <= #[trigger] (arr1[i] / arr2[i]) <= i32::MAX),
ensures
exists|v1: Seq<u32>| #[trigger] step1(arr1@, arr2@, v1) && step2(v1, r_final@),
{
let x1 = f1_element_wise_divide(arr1, arr2);
let x2 = f2_find_odd_numbers(&x1);
proof {
assert(step1(arr1@, arr2@, x1@));
assert(step2(x1@, x2@));
}
x2
}
} // verus!
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