File: simple.mlw

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let sqrt (n:int) =
  { n >= 0 } 
  let count = ref 0 in
  let sum = ref 1 in
  while !sum <= n do
    { invariant count >= 0 and n >= count*count 
            and sum = (count+1)*(count+1)
      variant n - sum }
    count := !count + 1;
    sum := !sum + 2 * !count + 1
  done;
  !count
  { result >= 0 and 
    result * result <= n < (result+1)*(result+1) }