What is loop invariant for this loop?

Question

As far as i understand all loops have a loop invariants. My understanding is that loop invariant is an argument that is true at the beginning of the loop block as well as at the end of the loop. For example:

while(P) {
  //predicate is true here
  body of the loop
  //predicate still true here
}

But let`s say i have the following loop (the code is in Java):

while(stack.size() > 0 && stack.peek() < 0) {
   stack.pop();
}

What i am trying to do here is to pop all negative numbers from the top of the stack - so at the end of the loop at the beginning of the stack will be a positive number or we have an empty stack. It is not clear from this loop what its invariant? What technic we can use to get loop invariant. In general, i would like to use loop invariants for validation of program correctness.

Answer 1

"
    Pre: stack is empty or contains only integers
    Post: Stack top is non-negative Integer
    P:  Stack top is an Integer   ( P is the invariant )
    BB: Stack top is negative
    T:  Stack size
"

" Establish P "
stack size > 0 or: [stack push: 0].
[ stack top negative
] whileTrue:
    [ " reduce T "
      stack pop. 
      " restore P "
      stack size > 0 or: [stack push: 0]
    ]
" P && non BB => Post "