1 files changed, 51 insertions, 5 deletions
diff --git a/Test/dafny1/FindZero.dfy b/Test/dafny1/FindZero.dfy
index 76e67205..c92dd065 100644
--- a/Test/dafny1/FindZero.dfy
+++ b/Test/dafny1/FindZero.dfy
@@ -1,12 +1,12 @@
 method FindZero(a: array<int>) returns (r: int)
-  requires a != null && forall i :: 0 <= i && i < a.Length ==> 0 <= a[i];
+  requires a != null && forall i :: 0 <= 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;
+  ensures r < 0 ==> forall i :: 0 <= 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;
+    invariant forall i :: 0 <= i < n && i < a.Length ==> a[i] != 0;
   {
     if (a[n] == 0) { r := n; return; }
     Lemma(a, n, a[n]);
@@ -16,11 +16,11 @@ method FindZero(a: array<int>) returns (r: int)
 }
 
 ghost method Lemma(a: array<int>, k: int, m: int)
-  requires a != null && forall i :: 0 <= i && i < a.Length ==> 0 <= a[i];
+  requires a != null && forall i :: 0 <= 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;
+  ensures forall i :: k <= i < k+m && i < a.Length ==> a[i] != 0;
   decreases m;
 {
   if (0 < m && k < a.Length) {
@@ -28,3 +28,49 @@ ghost method Lemma(a: array<int>, k: int, m: int)
     Lemma(a, k+1, m-1);
   }
 }
+
+// -----------------------------------------------------------------
+
+method FindZero_GhostLoop(a: array<int>) returns (r: int)
+  requires a != null && forall i :: 0 <= 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 < a.Length ==> a[i] != 0;
+{
+  var n := 0;
+  while (n < a.Length)
+    invariant forall i :: 0 <= i < n && i < a.Length ==> a[i] != 0;
+  {
+    if (a[n] == 0) { return n; }
+    ghost var m := n;
+    while (m < n + a[n])
+      invariant m <= n + a[n] && m < a.Length;
+      invariant n + a[n] - m <= a[m];
+      invariant forall i :: 0 <= i < m && i < a.Length ==> a[i] != 0;
+    {
+      m := m + 1;
+      if (m == a.Length) { break; }
+    }
+    n := n + a[n];
+  }
+  return -1;
+}
+
+// -----------------------------------------------------------------
+
+method FindZero_Assert(a: array<int>) returns (r: int)
+  requires a != null && forall i :: 0 <= i < a.Length ==> 0 <= a[i];
+  requires forall i :: 0 <= i-1 && i < a.Length ==> a[i-1]-1 <= a[i];
+  ensures 0 <= r ==> r < a.Length && a[r] == 0;
+  ensures r < 0 ==> forall i :: 0 <= i < a.Length ==> a[i] != 0;
+{
+  var n := 0;
+  while (n < a.Length)
+    invariant forall i :: 0 <= i < n && i < a.Length ==> a[i] != 0;
+  {
+    if (a[n] == 0) { return n; }
+    assert forall m {:induction} :: n <= m < n + a[n] && m < a.Length ==> n+a[n]-m <= a[m];
+    n := n + a[n];
+  }
+  return -1;
+}