10_rec.c

//@ logic integer sum_upto(integer n) = n*(n+1) / 2;

/*@ lemma sum_rec: \forall integer n; n >=0 ==>
  @     sum_upto(n+1) == sum_upto(n)+n+1;
  @*/

/*@ requires x >= 0;
  @ requires x <= 1000;
  @ decreases x;
  @ ensures \result == sum_upto(x);
  @*/
long sum(int x) {
  if (x == 0) return 0;
  else return x + sum (x-1);
}


/*@ ensures \result == 36; 
  @*/
long main () {
  long i = sum(8);
  return i;
}