Dafny: updated test files (will soon update Answer files as well)

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;

+}