Datasets:
File size: 2,125 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 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 | use vstd::prelude::*;
fn main() {}
verus!{
fn f1_square_nums(nums: &Vec<i32>) -> (squared: Vec<i32>)
requires
forall|k: int|
0 <= k < nums.len() ==> (0 <= #[trigger] nums[k] * #[trigger] nums[k] < i32::MAX),
{
let mut result: Vec<i32> = Vec::new();
let mut index = 0;
while index < nums.len()
{
result.push(nums[index] * nums[index]);
index += 1
}
result
}
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
}
spec fn step1(__hp0: Seq<i32>, outp: Seq<i32>) -> bool {
(__hp0.len() == outp.len())
&& (forall|k: int| 0 <= k < __hp0.len() ==> (#[trigger] outp[k] == __hp0[k] * __hp0[k]))
}
spec fn step2(inp: Seq<i32>, outp: Seq<i32>) -> bool {
(outp == inp.filter(|x: i32| count_frequency_rcr(inp, x) == 1))
}
fn chain_driver(nums: &Vec<i32>) -> (r_final: Vec<i32>)
requires
forall|k: int|
0 <= k < nums.len() ==> (0 <= #[trigger] nums[k] * #[trigger] nums[k] < i32::MAX),
ensures
exists|v1: Seq<i32>| #[trigger] step1(nums@, v1) && step2(v1, r_final@),
{
let x1 = f1_square_nums(nums);
let x2 = f2_remove_duplicates(&x1);
proof {
assert(step1(nums@, x1@));
assert(step2(x1@, x2@));
}
x2
}
} // verus!
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