diff options
| author |  mikebarnett <unknown> | 2009-07-15 21:03:41 +0000 |
|---|---|---|
| committer | mikebarnett <unknown> | 2009-07-15 21:03:41 +0000 |
| commit | ce1c2de044c91624370411e23acab13b0381949b (patch) | |
| tree | 592539996fe08050ead5ee210c973801611dde40 /Test/textbook/Bubble.bpl | |
Initial set of files.
Diffstat (limited to 'Test/textbook/Bubble.bpl')
| -rw-r--r-- | Test/textbook/Bubble.bpl | 66 |
1 files changed, 66 insertions, 0 deletions
diff --git a/Test/textbook/Bubble.bpl b/Test/textbook/Bubble.bpl new file mode 100644 index 00000000..51a8cefa --- /dev/null +++ b/Test/textbook/Bubble.bpl @@ -0,0 +1,66 @@ +// Bubble sort, where specification says the output is a permutation of its input
+// Rustan Leino, 30 April 2009
+
+const N: int;
+axiom 0 <= N;
+
+var a: [int]int;
+
+procedure BubbleSort() returns (perm: [int]int)
+ modifies a;
+ // array is sorted
+ ensures (forall i, j: int :: 0 <= i && i <= j && j < N ==> a[i] <= a[j]);
+ // perm is a permutation
+ ensures (forall i: int :: 0 <= i && i < N ==> 0 <= perm[i] && perm[i] < N);
+ ensures (forall i, j: int :: 0 <= i && i < j && j < N ==> perm[i] != perm[j]);
+ // the final array is that permutation of the input array
+ ensures (forall i: int :: 0 <= i && i < N ==> a[i] == old(a)[perm[i]]);
+{
+ var n, p, tmp: int;
+
+ n := 0;
+ while (n < N)
+ invariant n <= N;
+ invariant (forall i: int :: 0 <= i && i < n ==> perm[i] == i);
+ {
+ perm[n] := n;
+ n := n + 1;
+ }
+
+ while (true)
+ invariant 0 <= n && n <= N;
+ // array is sorted from n onwards
+ invariant (forall i, k: int :: n <= i && i < N && 0 <= k && k < i ==> a[k] <= a[i]);
+ // perm is a permutation
+ invariant (forall i: int :: 0 <= i && i < N ==> 0 <= perm[i] && perm[i] < N);
+ invariant (forall i, j: int :: 0 <= i && i < j && j < N ==> perm[i] != perm[j]);
+ // the current array is that permutation of the input array
+ invariant (forall i: int :: 0 <= i && i < N ==> a[i] == old(a)[perm[i]]);
+ {
+ n := n - 1;
+ if (n < 0) {
+ break;
+ }
+
+ p := 0;
+ while (p < n)
+ invariant p <= n;
+ // array is sorted from n+1 onwards
+ invariant (forall i, k: int :: n+1 <= i && i < N && 0 <= k && k < i ==> a[k] <= a[i]);
+ // perm is a permutation
+ invariant (forall i: int :: 0 <= i && i < N ==> 0 <= perm[i] && perm[i] < N);
+ invariant (forall i, j: int :: 0 <= i && i < j && j < N ==> perm[i] != perm[j]);
+ // the current array is that permutation of the input array
+ invariant (forall i: int :: 0 <= i && i < N ==> a[i] == old(a)[perm[i]]);
+ // a[p] is at least as large as any of the first p elements
+ invariant (forall k: int :: 0 <= k && k < p ==> a[k] <= a[p]);
+ {
+ if (a[p+1] < a[p]) {
+ tmp := a[p]; a[p] := a[p+1]; a[p+1] := tmp;
+ tmp := perm[p]; perm[p] := perm[p+1]; perm[p+1] := tmp;
+ }
+
+ p := p + 1;
+ }
+ }
+}
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