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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 | use vstd::prelude::*;
fn main() {}
verus!{
spec fn f1_seq_to_set_rec<A>(seq: Seq<A>) -> Set<A>
decreases seq.len()
{
if seq.len() == 0 {
Set::empty()
} else {
f1_seq_to_set_rec(seq.drop_last()).insert(seq.last())
}
}
/// helper function showing that the resulting set contains all elements of the sequence
proof fn f1_seq_to_set_rec_contains<A>(seq: Seq<A>)
ensures forall |a| #[trigger] seq.contains(a) <==> f1_seq_to_set_rec(seq).contains(a)
decreases seq.len()
{
if seq.len() > 0 {
assert(forall |a| #[trigger] seq.drop_last().contains(a) <==> f1_seq_to_set_rec(seq.drop_last()).contains(a)) by {
f1_seq_to_set_rec_contains(seq.drop_last());
}
assert(seq =~= (seq.drop_last().push(seq.last())));
assert forall |a| #[trigger] seq.contains(a) <==> f1_seq_to_set_rec(seq).contains(a) by {
if !seq.drop_last().contains(a) {
if a == seq.last() {
assert(seq.contains(a));
assert(f1_seq_to_set_rec(seq).contains(a));
} else {
assert(!f1_seq_to_set_rec(seq).contains(a));
}
}
}
}
}
/// helper function showing that the recursive definition matches the set comprehension one
proof fn f1_seq_to_set_equal_rec<A>(seq: Seq<A>)
ensures seq.to_set() == f1_seq_to_set_rec(seq)
{
assert(forall |n| #[trigger] seq.contains(n) <==> f1_seq_to_set_rec(seq).contains(n)) by {
f1_seq_to_set_rec_contains(seq);
}
assert(forall |n| #[trigger] seq.contains(n) <==> seq.to_set().contains(n));
assert(seq.to_set() =~= f1_seq_to_set_rec(seq));
}
proof fn f1_lemma_seq_push_to_set_insert<T>(s: Seq<T>, val: T)
ensures
s.push(val).to_set() === s.to_set().insert(val),
{
f1_seq_to_set_equal_rec(s.push(val));
assert(s =~= s.push(val).drop_last());
f1_seq_to_set_equal_rec(s);
assert(s.push(val).to_set() === f1_seq_to_set_rec(s.push(val)));
assert(s.push(val).to_set() === f1_seq_to_set_rec(s.push(val).drop_last()).insert(val));
}
fn f1_remove_duplicates(nums: Vec<i32>) -> (res: Vec<i32>)
{
let mut res = Vec::new();
let mut i = 0;
while i < nums.len()
{
let mut found = false;
let mut j = 0;
while j < res.len()
invariant_except_break
!found
{
if nums[i] == res[j] {
found = true;
break;
}
j += 1;
}
if !found {
res.push(nums[i]);
}
i += 1;
}
res
}
spec fn step1(__hp0: Seq<i32>, outp: Seq<i32>) -> bool {
(outp.no_duplicates())
&& (__hp0.to_set() =~= (outp.to_set()))
}
fn chain_driver(nums: Vec<i32>) -> (r_final: Vec<i32>)
ensures
step1(nums@, r_final@),
{
let x1 = f1_remove_duplicates(nums);
proof {
assert(step1(nums@, x1@));
}
x1
}
} // verus!
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