Datasets:
File size: 1,244 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 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_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 f2_is_even(n: u32) -> bool {
(n % 2) == 0
}
fn f2_is_product_even(arr: &Vec<u32>) -> (result: bool)
{
let mut index = 0;
while index < arr.len()
{
if (arr[index] % 2 == 0) {
return true;
}
index += 1;
}
false
}
spec fn step1(__hp0: Seq<u32>, outp: Seq<u32>) -> bool {
(outp == __hp0.filter(|x: u32| x % 2 != 0))
}
spec fn step2(inp: Seq<u32>, outp: bool) -> bool {
(outp <==> (exists|k: int| 0 <= k < inp.len() && f2_is_even(#[trigger] inp[k])))
}
fn chain_driver(arr: &Vec<u32>) -> (r_final: bool)
ensures
exists|v1: Seq<u32>| #[trigger] step1(arr@, v1) && step2(v1, r_final),
{
let x1 = f1_find_odd_numbers(arr);
let x2 = f2_is_product_even(&x1);
proof {
assert(step1(arr@, x1@));
assert(step2(x1@, x2));
}
x2
}
} // verus!
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