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PV-Bench / benchmarks /Algorithms /lcs_n /lean /solution_annotated.c
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cielseven
add benchmark corpora, groundtruth, symexec scripts and coverage docs
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/*@ Import Lean
import Algorithms.lcs_n.lean.helper_lib
open scoped SimpleC
*/
/*@ Extern Coq
(LCSNTableResult : list Z -> list Z -> Z -> list Z -> Prop)
(IntArray::mixed_full : Z -> Z -> list (option Z) -> Assertion)
(LCSNColumnProgress : list (option Z) -> list Z -> Z -> Z -> Prop)
(LCSNBoundaryProgress : list (option Z) -> list Z -> Z -> Z -> Prop)
(LCSNRowsProgress : list Z -> list Z -> list (option Z) -> list Z -> Z -> Z -> Prop)
(LCSNRowProgress : list Z -> list Z -> list (option Z) -> list Z -> Z -> Z -> Z -> Prop)
*/
int lcs_n(int *x, int *y, int n, int *table)
/*@ With (xs ys : list Z)
Require
0 <= n && n <= 1000 &&
Zlength(xs) == n && Zlength(ys) == n &&
IntArray::full(x, n, xs) *
IntArray::full(y, n, ys) *
IntArray::undef_full(table, (n + 1) * (n + 1))
Ensure
exists table_l,
LCSNTableResult(xs, ys, n, table_l) &&
__return == Znth((n + 1) * n + n, table_l, 0) &&
IntArray::full(x, n, xs) *
IntArray::full(y, n, ys) *
IntArray::full(table, (n + 1) * (n + 1), table_l)
*/
{
int stride;
int i;
int j;
int above;
int left;
stride = n + 1;
i = 0;
/*@ Inv Assert
exists mixed_table table_l,
x == x@pre && y == y@pre && table == table@pre &&
n == n@pre && stride == n@pre + 1 &&
0 <= n@pre && n@pre <= 1000 &&
Zlength(xs) == n@pre && Zlength(ys) == n@pre &&
0 <= i && i <= n@pre + 1 &&
0 <= stride * i &&
stride * i <= (n@pre + 1) * (n@pre + 1) &&
LCSNColumnProgress(mixed_table, table_l, n@pre, i) &&
IntArray::full(x, n@pre, xs) *
IntArray::full(y, n@pre, ys) *
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table) *
has_int_permission(&j) *
has_int_permission(&above) *
has_int_permission(&left)
*/
while (i <= n) {
/*@ 0 <= stride * i &&
stride * i < (n@pre + 1) * (n@pre + 1) by local */
table[stride * i] = 0;
i = i + 1;
}
j = 1;
/*@ Inv Assert
exists mixed_table table_l,
x == x@pre && y == y@pre && table == table@pre &&
n == n@pre && stride == n@pre + 1 &&
0 <= n@pre && n@pre <= 1000 &&
Zlength(xs) == n@pre && Zlength(ys) == n@pre &&
1 <= j && j <= n@pre + 1 &&
LCSNBoundaryProgress(mixed_table, table_l, n@pre, j) &&
IntArray::full(x, n@pre, xs) *
IntArray::full(y, n@pre, ys) *
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table) *
has_int_permission(&i) *
has_int_permission(&above) *
has_int_permission(&left)
*/
while (j <= n) {
/*@ 0 <= j &&
j < (n@pre + 1) * (n@pre + 1) by local */
table[j] = 0;
j = j + 1;
}
i = 1;
/*@ Inv Assert
exists mixed_table table_l,
x == x@pre && y == y@pre && table == table@pre &&
n == n@pre && stride == n@pre + 1 &&
0 <= n@pre && n@pre <= 1000 &&
Zlength(xs) == n@pre && Zlength(ys) == n@pre &&
1 <= i && i <= n@pre + 1 &&
0 <= stride * i &&
stride * i <= (n@pre + 1) * (n@pre + 1) &&
LCSNRowsProgress(xs, ys, mixed_table, table_l, n@pre, i) &&
IntArray::full(x, n@pre, xs) *
IntArray::full(y, n@pre, ys) *
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table) *
has_int_permission(&j) *
has_int_permission(&above) *
has_int_permission(&left)
*/
while (i <= n) {
j = 1;
/*@ Inv Assert
exists mixed_table table_l,
x == x@pre && y == y@pre && table == table@pre &&
n == n@pre && stride == n@pre + 1 &&
0 <= n@pre && n@pre <= 1000 &&
Zlength(xs) == n@pre && Zlength(ys) == n@pre &&
1 <= i && i <= n@pre &&
1 <= j && j <= n@pre + 1 &&
0 <= stride * i + j &&
stride * i + j <= (n@pre + 1) * (n@pre + 1) &&
LCSNRowProgress(
xs, ys, mixed_table, table_l, n@pre, i, j) &&
IntArray::full(x, n@pre, xs) *
IntArray::full(y, n@pre, ys) *
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table) *
has_int_permission(&above) *
has_int_permission(&left)
*/
while (j <= n) {
/*@ 0 <= i - 1 && i - 1 < n@pre &&
0 <= j - 1 && j - 1 < n@pre &&
0 <= stride * i + j &&
stride * i + j < (n@pre + 1) * (n@pre + 1) &&
0 <= stride * (i - 1) + (j - 1) &&
stride * (i - 1) + (j - 1) <
(n@pre + 1) * (n@pre + 1) &&
0 <= stride * (i - 1) + j &&
stride * (i - 1) + j <
(n@pre + 1) * (n@pre + 1) &&
0 <= stride * i + (j - 1) &&
stride * i + (j - 1) <
(n@pre + 1) * (n@pre + 1) by local */
if (x[i - 1] == y[j - 1]) {
/*@ exists mixed_table table_l,
1 <= i && i <= n@pre &&
1 <= j && j <= n@pre &&
LCSNRowProgress(
xs, ys, mixed_table, table_l, n@pre, i, j) &&
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table)
which implies
exists mixed_table table_l,
1 <= i && i <= n@pre &&
1 <= j && j <= n@pre &&
LCSNRowProgress(
xs, ys, mixed_table, table_l, n@pre, i, j) &&
Znth(
(n@pre + 1) * i + j, mixed_table, None) == None &&
Znth(
(n@pre + 1) * (i - 1) + (j - 1), mixed_table, None) ==
Some(Znth(
(n@pre + 1) * (i - 1) + (j - 1), table_l, 0)) &&
0 <= Znth(
(n@pre + 1) * (i - 1) + (j - 1), table_l, 0) &&
Znth(
(n@pre + 1) * (i - 1) + (j - 1), table_l, 0) <= n@pre &&
IntArray::mixed_seg(
table, 0,
(n@pre + 1) * (i - 1) + (j - 1),
sublist(0,
(n@pre + 1) * (i - 1) + (j - 1), mixed_table)) *
store(
table +
(((n@pre + 1) * (i - 1) + (j - 1)) * sizeof(int)),
int,
Znth(
(n@pre + 1) * (i - 1) + (j - 1), table_l, 0)) *
IntArray::mixed_seg(
table,
(n@pre + 1) * (i - 1) + (j - 1) + 1,
(n@pre + 1) * i + j,
sublist(
(n@pre + 1) * (i - 1) + (j - 1) + 1,
(n@pre + 1) * i + j, mixed_table)) *
IntArray::undef_seg(
table,
(n@pre + 1) * i + j,
(n@pre + 1) * i + j + 1) *
IntArray::mixed_seg(
table,
(n@pre + 1) * i + j + 1,
(n@pre + 1) * (n@pre + 1),
sublist(
(n@pre + 1) * i + j + 1,
(n@pre + 1) * (n@pre + 1), mixed_table))
*/
table[stride * i + j] =
table[stride * (i - 1) + (j - 1)] + 1;
} else {
/*@ exists mixed_table table_l,
1 <= i && i <= n@pre &&
1 <= j && j <= n@pre &&
LCSNRowProgress(
xs, ys, mixed_table, table_l, n@pre, i, j) &&
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table)
which implies
exists mixed_table table_l,
1 <= i && i <= n@pre &&
1 <= j && j <= n@pre &&
LCSNRowProgress(
xs, ys, mixed_table, table_l, n@pre, i, j) &&
Znth(
(n@pre + 1) * i + j, mixed_table, None) == None &&
Znth(
(n@pre + 1) * (i - 1) + j, mixed_table, None) ==
Some(Znth(
(n@pre + 1) * (i - 1) + j, table_l, 0)) &&
Znth(
(n@pre + 1) * i + (j - 1), mixed_table, None) ==
Some(Znth(
(n@pre + 1) * i + (j - 1), table_l, 0)) &&
IntArray::mixed_seg(
table, 0,
(n@pre + 1) * (i - 1) + j,
sublist(0,
(n@pre + 1) * (i - 1) + j, mixed_table)) *
store(
table + (((n@pre + 1) * (i - 1) + j) * sizeof(int)),
int, Znth(
(n@pre + 1) * (i - 1) + j, table_l, 0)) *
IntArray::mixed_seg(
table,
(n@pre + 1) * (i - 1) + j + 1,
(n@pre + 1) * i + (j - 1),
sublist(
(n@pre + 1) * (i - 1) + j + 1,
(n@pre + 1) * i + (j - 1), mixed_table)) *
store(
table + (((n@pre + 1) * i + (j - 1)) * sizeof(int)),
int, Znth(
(n@pre + 1) * i + (j - 1), table_l, 0)) *
IntArray::undef_seg(
table,
(n@pre + 1) * i + j,
(n@pre + 1) * i + j + 1) *
IntArray::mixed_seg(
table,
(n@pre + 1) * i + j + 1,
(n@pre + 1) * (n@pre + 1),
sublist(
(n@pre + 1) * i + j + 1,
(n@pre + 1) * (n@pre + 1), mixed_table))
*/
above = table[stride * (i - 1) + j];
left = table[stride * i + (j - 1)];
if (above >= left) {
table[stride * i + j] = above;
} else {
table[stride * i + j] = left;
}
}
/*@ Assert
exists mixed_table table_l,
x == x@pre && y == y@pre && table == table@pre &&
n == n@pre && stride == n@pre + 1 &&
0 <= n@pre && n@pre <= 1000 &&
Zlength(xs) == n@pre && Zlength(ys) == n@pre &&
1 <= i && i <= n@pre &&
1 <= j && j <= n@pre &&
1 <= j + 1 && j + 1 <= n@pre + 1 &&
0 <= stride * i + (j + 1) &&
stride * i + (j + 1) <=
(n@pre + 1) * (n@pre + 1) &&
LCSNRowProgress(
xs, ys, mixed_table, table_l, n@pre, i, j + 1) &&
IntArray::full(x, n@pre, xs) *
IntArray::full(y, n@pre, ys) *
IntArray::mixed_full(
table, (n@pre + 1) * (n@pre + 1), mixed_table) *
has_int_permission(&above) *
has_int_permission(&left)
*/
j = j + 1;
}
i = i + 1;
}
/*@ Assert
exists mixed_table table_l,
x == x@pre && y == y@pre && table == table@pre &&
n == n@pre && stride == n@pre + 1 &&
0 <= n@pre && n@pre <= 1000 &&
Zlength(xs) == n@pre && Zlength(ys) == n@pre &&
LCSNRowsProgress(
xs, ys, mixed_table, table_l, n@pre, n@pre + 1) &&
LCSNTableResult(xs, ys, n@pre, table_l) &&
IntArray::full(x, n@pre, xs) *
IntArray::full(y, n@pre, ys) *
IntArray::full(
table, (n@pre + 1) * (n@pre + 1), table_l) *
has_int_permission(&i) *
has_int_permission(&j) *
has_int_permission(&above) *
has_int_permission(&left)
*/
/*@ 0 <= stride * n + n &&
stride * n + n < (n@pre + 1) * (n@pre + 1) by local */
return table[stride * n + n];
}