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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_add_list(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_find_negative_numbers(arr: &Vec<i32>) -> (negative_list: Vec<i32>)
{
let mut negative_list: Vec<i32> = Vec::new();
let input_len = arr.len();
let mut index = 0;
while index < arr.len()
{
if (arr[index] < 0) {
negative_list.push(arr[index]);
}
index += 1;
}
negative_list
}
proof fn f3_lemma_vec_push<T>(vec: Seq<T>, i: T, l: usize)
requires
l == vec.len(),
ensures
forall|k: int| 0 <= k < vec.len() ==> #[trigger] vec[k] == vec.push(i)[k],
vec.push(i).index(l as int) == i,
{
}
fn f3_contains(arr: &Vec<i32>, key: i32) -> (result: bool)
{
let mut index = 0;
while index < arr.len()
{
if (arr[index] == key) {
return true;
}
index += 1;
}
false
}
fn f3_difference(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
let mut result = Vec::new();
let mut index = 0;
while index < arr1.len()
{
if (!f3_contains(arr2, arr1[index]) && !f3_contains(&result, arr1[index])) {
result.push(arr1[index]);
}
index += 1;
}
index = 0;
while index < arr2.len()
{
if (!f3_contains(arr1, arr2[index]) && !f3_contains(&result, arr2[index])) {
result.push(arr2[index]);
}
index += 1;
}
result
}
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: Seq<i32>) -> bool {
(outp == inp.filter(|x: i32| x < 0))
}
spec fn step3(inp: Seq<i32>, p3_key: i32, outp: bool) -> bool {
(outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p3_key)))
}
fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>, p3_key: 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>, v2: Seq<i32>| #[trigger] step1(arr1@, arr2@, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_key, r_final),
{
let x1 = f1_add_list(arr1, arr2);
let x2 = f2_find_negative_numbers(&x1);
let x3 = f3_contains(&x2, p3_key);
proof {
assert(step1(arr1@, arr2@, x1@));
assert(step2(x1@, x2@));
assert(step3(x2@, p3_key, x3));
}
x3
}
} // verus!
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