File size: 3,938 Bytes
bff4ec7 | 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 | /*@ Extern Coq (sll :: *) */
/*@ Extern Coq
(stack_capacity : Z)
(sll_empty : sll)
(sll_cons : Z -> sll -> sll)
(sll_from_array : list Z -> sll)
(store_stack : Z -> sll -> Z -> Assertion)
(BuildStackPrefix : sll -> list Z -> Z -> Prop)
(StackConcreteView : sll -> list Z -> Z -> Prop)
*/
/*@ Import Coq Require Import PVbench.Data_structures.stack.rocq.spec_lib */
void push(int *stack, int n, int x)
/*@ With (before : sll)
Require
n < stack_capacity &&
store_stack(stack, before, n) *
IntArray::undef_seg(stack, n, n + 1)
Ensure
store_stack(stack, sll_cons(x, before), n + 1)
*/
{
/*@ Assert
exists concrete,
stack == stack@pre && n == n@pre && x == x@pre &&
0 <= n@pre && n@pre < stack_capacity &&
StackConcreteView(before, concrete, n@pre) &&
IntArray::full(stack, n@pre, concrete) *
IntArray::undef_seg(stack, n@pre, n@pre + 1)
*/
stack[n] = x;
/*@ Assert
stack == stack@pre && n == n@pre && x == x@pre &&
0 <= n@pre && n@pre < stack_capacity &&
store_stack(stack, sll_cons(x@pre, before), n@pre + 1)
*/
}
int pop(int *stack, int n)
/*@ With (top : Z) (rest : sll)
Require
1 <= n &&
store_stack(stack, sll_cons(top, rest), n)
Ensure
__return == top &&
store_stack(stack, rest, n - 1) *
IntArray::undef_seg(stack, n - 1, n)
*/
{
/*@ Assert
exists concrete,
stack == stack@pre && n == n@pre &&
1 <= n@pre && n@pre <= stack_capacity &&
StackConcreteView(
sll_cons(top, rest), concrete, n@pre
) &&
IntArray::full(stack, n@pre, concrete)
*/
int ret = stack[n - 1];
/*@ Assert
stack == stack@pre && n == n@pre &&
1 <= n@pre && n@pre <= stack_capacity &&
ret == top &&
store_stack(stack, rest, n@pre - 1) *
IntArray::undef_seg(stack, n@pre - 1, n@pre)
*/
return ret;
}
void build(int *stack, int n)
/*@ With (input : list Z)
Require
0 <= n &&
n <= stack_capacity &&
Zlength(input) == n &&
IntArray::full(stack, n, input)
Ensure
store_stack(stack, sll_from_array(input), n)
*/
{
/*@ Inv Assert
(stack == stack@pre && n == n@pre &&
n@pre == 0 && i == 1 &&
Zlength(input) == n@pre &&
IntArray::full(stack, n@pre, input))
||
(exists prefix,
stack == stack@pre && n == n@pre &&
1 <= n@pre && n@pre <= stack_capacity &&
1 <= i && i <= n@pre &&
Zlength(input) == n@pre &&
BuildStackPrefix(prefix, input, i) &&
store_stack(stack, prefix, i) *
IntArray::seg(stack, i, n@pre,
sublist(i, n@pre, input)))
*/
for (int i = 1; i < n; ++i) {
int x = stack[i];
/*@ Assert
exists prefix,
stack == stack@pre && n == n@pre &&
1 <= n@pre && n@pre <= stack_capacity &&
1 <= i && i < n@pre &&
x == input[i] &&
Zlength(input) == n@pre &&
BuildStackPrefix(prefix, input, i) &&
store_stack(stack, prefix, i) *
IntArray::undef_seg(stack, i, i + 1) *
IntArray::seg(stack, i + 1, n@pre,
sublist(i + 1, n@pre, input))
*/
push(stack, i, x);
/*@ Assert
exists next,
stack == stack@pre && n == n@pre &&
1 <= n@pre && n@pre <= stack_capacity &&
1 <= i && i < n@pre &&
x == input[i] &&
Zlength(input) == n@pre &&
BuildStackPrefix(next, input, i + 1) &&
store_stack(stack, next, i + 1) *
IntArray::seg(stack, i + 1, n@pre,
sublist(i + 1, n@pre, input))
*/
}
/*@ Assert
stack == stack@pre && n == n@pre &&
0 <= n@pre && n@pre <= stack_capacity &&
Zlength(input) == n@pre &&
store_stack(stack, sll_from_array(input), n@pre)
*/
}
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