/* Stacks
 * 15-122 Principles of Imperative Computation, Fall 2010
 * Frank Pfenning
 */

// type elem must be defined

/* Interface section for stacks */

struct stack;
typedef struct stack* stack;
bool is_empty(stack S);		/* O(1) */
stack s_new();			/* O(1) */
void push(elem x, stack S);	/* O(1) */
elem pop(stack S);		/* O(1) */

struct stack {
  list top;
};

bool is_stack (stack S) {
  return is_segment(S->top, NULL);
}

bool is_empty(stack S)
//@requires is_stack(S);
{
  return S->top == NULL;
}

stack s_new()
//@ensures is_stack(\result);
//@ensures is_empty(\result);
{
  stack S = alloc(struct stack);
  S->top = NULL;
  return S;
}

void push(elem x, stack S)
//@requires is_stack(S);
//@ensures !is_empty(S);
{
  list first = alloc(struct list);
  first->data = x;
  first->next = S->top;
  S->top = first;
}

elem pop(stack S)
//@requires is_stack(S);
//@requires !is_empty(S);
//@ensures is_stack(S);
{ assert(S->top != NULL, "cannot pop empty stack");
  { elem x = S->top->data;
    S->top = S->top->next;
    return x;
  }
}