Add Dafny submission

dafny/submission.dfy

@@ -0,0 +1,120 @@
+// Dafny coursework tasks
+// Autumn term, 2022
+//
+// Authors: John Wickerson
+
+method countsquares(n:nat) returns (result:nat)
+  //ensures result == ...
+{
+  var i := 0;
+  result := 0;
+  while i < n {
+    i := i + 1;
+    result := result + i * i;
+  }
+}
+
+method countsquares2(n:nat) returns (result:nat)
+  // ensures result == ...
+{
+  var i := n;
+  result := 0;
+  while i > 0 {
+    result := result + i * i;
+    i := i - 1;
+  }
+}
+
+predicate sorted(A:array<int>)
+  reads A
+{
+	forall m,n :: 0 <= m < n < A.Length ==> A[m] <= A[n]
+}
+
+method binarysearch_between(A:array<int>, v:int, lo:int, hi:int) returns (result:bool)
+  requires false // Please remove this line.
+{
+  if lo == hi {
+    return false;
+  }
+  var mid:int := (lo + hi) / 2;
+  if v == A[mid] {
+    return true;
+  }
+  if v < A[mid] {
+    result := binarysearch_between(A, v, lo, mid);
+  }
+  if v > A[mid] {
+    result := binarysearch_between(A, v, mid+1, hi);
+  }
+}
+
+method binarysearch(A:array<int>, v:int) returns (result:bool)
+  requires false // Please remove this line.
+{
+  result := binarysearch_between(A, v, 0, A.Length);
+}
+
+method binarysearch_iter(A:array<int>, v:int) returns (result:bool)
+{
+  // Please provide an implementation of this method.
+}
+
+method partition(A:array<int>, lo:int, hi:int) returns (pivot:int)
+  requires 0 <= lo < hi <= A.Length
+  ensures 0 <= lo <= pivot < hi
+  ensures forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
+  modifies A
+{
+  pivot := lo;
+  var i := lo+1;
+  while i < hi
+    invariant 0 <= lo <= pivot < i <= hi
+    invariant forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
+    decreases hi - i
+  {
+    if A[i] < A[pivot] {
+      var j := i-1;
+      var tmp := A[i];
+      A[i] := A[j];
+      while pivot < j
+        invariant forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
+        decreases j
+      {
+        A[j+1] := A[j];
+        j := j-1;
+      }
+      A[pivot+1] := A[pivot];
+      A[pivot] := tmp;
+      pivot := pivot+1;
+    }
+    i := i+1;
+  }
+}
+
+method quicksort_between(A:array<int>, lo:int, hi:int)
+  requires 0 <= lo <= hi <= A.Length
+  ensures forall k :: (0 <= k < lo || hi <= k < A.Length) ==> old(A[k]) == A[k]
+  modifies A
+  decreases hi - lo
+{
+  if lo+1 >= hi { return; }
+  var pivot := partition(A, lo, hi);
+  quicksort_between(A, lo, pivot);
+  quicksort_between(A, pivot+1, hi);
+}
+
+method quicksort(A:array<int>)
+	modifies A
+{
+  quicksort_between(A, 0, A.Length);
+}
+
+method Main() {
+  var A:array<int> := new int[7] [4,0,1,9,7,1,2];
+  print "Before: ", A[0], A[1], A[2], A[3],
+        A[4], A[5], A[6], "\n";
+  quicksort(A);
+  print "After:  ", A[0], A[1], A[2], A[3],
+        A[4], A[5], A[6], "\n";
+}