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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 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_interleave(s1: &Vec<i32>, s2: &Vec<i32>, s3: &Vec<i32>) -> (res: Vec<i32>)
requires
s1@.len() == s2@.len() && s2@.len() == s3@.len(),
0 <= (s1@.len() * 3) <= i32::MAX,
{
let new_seq_len = s1.len() * 3;
let mut output_seq = Vec::with_capacity(new_seq_len);
let mut index = 0;
while index < s1.len()
{
output_seq.push(s1[index]);
output_seq.push(s2[index]);
output_seq.push(s3[index]);
index += 1;
}
output_seq
}
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(str: &Vec<i32>, key: i32) -> (result: bool)
{
let mut i = 0;
while i < str.len()
{
if (str[i] == key) {
return true;
}
i += 1;
}
false
}
fn f3_remove_elements(arr1: &Vec<i32>, arr2: &Vec<i32>) -> (result: Vec<i32>)
{
let mut output_str = Vec::new();
let mut index: usize = 0;
while index < arr1.len()
{
if (!f3_contains(arr2, arr1[index])) {
output_str.push(arr1[index]);
}
index += 1;
}
output_str
}
spec fn step1(__hp0: Seq<i32>, __hp1: Seq<i32>, __hp2: Seq<i32>, outp: Seq<i32>) -> bool {
(outp.len() == __hp0.len() * 3)
&& (forall|i: int|
0 <= i < __hp0.len() ==> (outp[3 * i] == __hp0[i] && outp[3 * i + 1] == __hp1[i] && outp[3 * i + 2]
== __hp2[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(s1: &Vec<i32>, s2: &Vec<i32>, s3: &Vec<i32>, p3_key: i32) -> (r_final: bool)
requires
s1@.len() == s2@.len() && s2@.len() == s3@.len(),
0 <= (s1@.len() * 3) <= i32::MAX,
ensures
exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(s1@, s2@, s3@, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_key, r_final),
{
let x1 = f1_interleave(s1, s2, s3);
let x2 = f2_find_negative_numbers(&x1);
let x3 = f3_contains(&x2, p3_key);
proof {
assert(step1(s1@, s2@, s3@, x1@));
assert(step2(x1@, x2@));
assert(step3(x2@, p3_key, x3));
}
x3
}
} // verus!
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