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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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_remove_kth_element(list: &Vec<i32>, k: usize) -> (new_list: Vec<i32>)
requires
list.len() > 0,
0 < k < list@.len(),
{
let mut new_list = Vec::new();
let mut index = 0;
while index < (k - 1)
{
new_list.push(list[index]);
index += 1;
}
let mut index = k;
while index < list.len()
{
new_list.push(list[index]);
index += 1;
}
new_list
}
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
}
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: usize, outp: Seq<i32>) -> bool {
(outp == __hp0.subrange(0, __hp1 - 1 as int).add(
__hp0.subrange(__hp1 as int, __hp0.len() as int),
))
}
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_key: i32, outp: bool) -> bool {
(outp == (exists|i: int| 0 <= i < inp.len() && (inp[i] == p3_key)))
}
fn chain_driver(list: &Vec<i32>, k: usize, p3_key: i32) -> (r_final: bool)
requires
list.len() > 0,
0 < k < list@.len(),
ensures
exists|v1: Seq<i32>, v2: Seq<i32>| #[trigger] step1(list@, k, v1) && #[trigger] step2(v1, v2) && step3(v2, p3_key, r_final),
{
let x1 = f1_remove_kth_element(list, k);
let x2 = f2_remove_duplicates(&x1);
let x3 = f3_contains(&x2, p3_key);
proof {
assert(step1(list@, k, x1@));
assert(step2(x1@, x2@));
assert(step3(x2@, p3_key, x3));
}
x3
}
} // verus!
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