1 files changed, 30 insertions, 0 deletions
diff --git a/Test/dafny1/FindZero.dfy b/Test/dafny1/FindZero.dfy
new file mode 100644
index 00000000..cff8b934
--- /dev/null
+++ b/Test/dafny1/FindZero.dfy
@@ -0,0 +1,30 @@
+method FindZero(a: array<int>) returns (r: int)
+  requires a != null && forall i :: 0 <= i && i < a.Length ==> 0 <= a[i];
+  requires forall i :: 0 <= i && i+1 < a.Length ==> a[i]-1 <= a[i+1];
+  ensures 0 <= r ==> r < a.Length && a[r] == 0;
+  ensures r < 0 ==> forall i :: 0 <= i && i < a.Length ==> a[i] != 0;
+{
+  var n := 0;
+  while (n < a.Length)
+    invariant forall i :: 0 <= i && i < n && i < a.Length ==> a[i] != 0;
+  {
+    if (a[n] == 0) { r := n; return; }
+    call Lemma(a, n, a[n]);
+    n := n + a[n];
+  }
+  r := -1;
+}
+
+ghost method Lemma(a: array<int>, k: int, m: int)
+  requires a != null && forall i :: 0 <= i && i < a.Length ==> 0 <= a[i];
+  requires forall i :: 0 <= i && i+1 < a.Length ==> a[i]-1 <= a[i+1];
+  requires 0 <= k;
+  requires k < a.Length ==> m <= a[k];
+  ensures forall i :: k <= i && i < k+m && i < a.Length ==> a[i] != 0;
+  decreases m;
+{
+  if (0 < m && k < a.Length) {
+    assert a[k] != 0;
+    call Lemma(a, k+1, m-1);
+  }
+}