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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 | 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
}
pub open spec fn count_frequency_rcr(seq: Seq<i32>, key: i32) -> int
decreases seq.len(),
{
if seq.len() == 0 {
0
} else {
count_frequency_rcr(seq.drop_last(), key) + if (seq.last() == key) {
1 as int
} else {
0 as int
}
}
}
fn f2_count_frequency(arr: &Vec<i32>, key: i32) -> (frequency: usize)
{
let mut index = 0;
let mut counter = 0;
while index < arr.len()
{
if (arr[index] == key) {
counter += 1;
}
index += 1;
}
counter
}
fn f2_remove_duplicates(arr: &Vec<i32>) -> (unique_arr: Vec<i32>)
{
let mut unique_arr: Vec<i32> = Vec::new();
let input_len = arr.len();
let mut index = 0;
while index < arr.len()
{
if f2_count_frequency(&arr, arr[index]) == 1 {
unique_arr.push(arr[index]);
}
index += 1;
}
unique_arr
}
fn f3_insert_before_each(arr: &Vec<i32>, elem: i32) -> (result: Vec<i32>)
{
let mut result: Vec<i32> = Vec::new();
let mut index = 0;
while index < arr.len()
{
result.push(elem);
result.push(arr[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| count_frequency_rcr(inp, x) == 1))
}
spec fn step3(inp: Seq<i32>, p3_elem: i32, outp: Seq<i32>) -> bool {
(outp.len() == (2 * inp.len()))
&& (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k] == p3_elem)
&& (forall|k: int| 0 <= k < inp.len() ==> #[trigger] outp[2 * k + 1] == inp[k])
}
fn chain_driver(arr1: &Vec<i32>, arr2: &Vec<i32>, p3_elem: i32) -> (r_final: Vec<i32>)
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_elem, r_final@),
{
let x1 = f1_element_wise_subtract(arr1, arr2);
let x2 = f2_remove_duplicates(&x1);
let x3 = f3_insert_before_each(&x2, p3_elem);
proof {
assert(step1(arr1@, arr2@, x1@));
assert(step2(x1@, x2@));
assert(step3(x2@, p3_elem, x3@));
}
x3
}
} // verus!
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