1 files changed, 103 insertions, 0 deletions
diff --git a/Test/dafny0/MultiSets.dfy b/Test/dafny0/MultiSets.dfy
new file mode 100644
index 00000000..0bc1004f
--- /dev/null
+++ b/Test/dafny0/MultiSets.dfy
@@ -0,0 +1,103 @@
+
+method test1()
+{
+   var ms: multiset<int> := multiset{1,1,1};
+   var ms2: multiset<int> := multiset{3};
+   assert 1 in ms;
+   assert forall i :: i != 1 ==> i !in ms; // 1 is the only thing in ms.
+   
+   assert ((ms - multiset{1}) - multiset {1}) != multiset{}; // it has more than 2 ones
+   assert ((ms - multiset{1}) - multiset {1}) - multiset{1} == multiset{}; // and exactly three
+
+   assert ms2 - ms == ms2; // set difference works correctly.
+   assert ms - multiset{1} == multiset{1,1};
+   assert !(multiset{1} !! multiset{1});
+   assert exists m :: !(m !! multiset{1});
+   assert forall m :: m !! multiset{};
+
+   assert forall s :: (s == set x: int | x in ms :: x) ==> s == {1};
+}
+
+method test2(ms: multiset<int>)
+{
+   var s := set x | x in ms :: x; // seems to be a reasonable conversion
+   assert forall x :: x in s <==> x in ms;
+   assert ms !! multiset{};
+}
+
+method test3(s: set<int>)
+{
+   assert forall x :: x in s <==> x in multiset(s);
+}
+method test4(sq: seq<int>, a: array<int>)
+   requires a != null;
+   modifies a;
+{
+   assert sq == sq[..|sq|];
+   assert sq == sq[0..];
+   assert sq == sq[..];
+
+   assert a.Length >= 0;
+   var s := a[..];
+}
+
+method test5()
+{
+   assert multiset({1,1}) == multiset{1};
+   assert multiset([1,1]) == multiset{1,1};
+}
+
+method test6(a: array<int>, n: int, e: int)
+   requires a != null && 0 <= n < a.Length;
+   modifies a;
+   ensures multiset(a[..n+1]) == multiset(a[..n]) + multiset{e};
+{
+  a[n] := e;
+  assert a[..n+1] == a[..n] + [e];
+}
+method test7(a: array<int>, i: int, j: int)
+   requires a != null && 0 <= i < j < a.Length;
+   modifies a;
+   ensures old(multiset(a[..])) == multiset(a[..]);
+   ensures a[j] == old (a[i]) && a[i] == old(a[j]);
+   ensures forall k :: 0 <= k < a.Length && k !in {i, j} ==> a[k] == old(a[k]);
+{
+   ghost var s := a[..i] + [a[i]] + a[i+1 .. j] + [a[j]] + a[j+1..];
+   assert a[..] == s;
+   a[i], a[j] := a[j], a[i];
+   assert a[..] == a[..i] + [a[i]] + a[i+1 .. j] + [a[j]] + a[j+1..];
+   assert s == a[..i] + [old(a[i])] + a[i+1 .. j] + [old(a[j])] + a[j+1..];
+}
+method test8(a: array<int>, i: int, j: int)
+   requires a != null && 0 <= i < j < a.Length;
+   modifies a;
+   ensures old(multiset(a[..])) == multiset(a[..]);
+   ensures a[j] == old (a[i]) && a[i] == old(a[j]);
+   ensures forall k :: 0 <= k < a.Length && k !in {i, j} ==> a[k] == old(a[k]);
+{
+   a[i], a[j] := a[j], a[i];
+}
+method test9(a: array<int>, i: int, j: int, limit: int)
+   requires a != null && 0 <= i < j < limit <= a.Length;
+   modifies a;
+   ensures old(multiset(a[0..limit])) == multiset(a[0..limit]);
+   ensures a[j] == old (a[i]) && a[i] == old(a[j]);
+   ensures forall k :: 0 <= k < limit && k !in {i, j} ==> a[k] == old(a[k]);
+{
+   a[i], a[j] := a[j], a[i];
+}
+method test10(s: seq<int>)
+   requires |s| > 4;
+{
+   assert multiset( s[3 := 2] ) == multiset(s) - multiset{s[3]} + multiset{2};
+   assert multiset( (s[2 := 1])[3 := 2] ) == (((multiset(s) - multiset{s[2]}) + multiset{1})  - multiset{s[3]}) + multiset{2};
+   assert multiset( (s[2 := s[3]])[3 := s[2]] ) == (((multiset(s) - multiset{s[2]}) + multiset{s[3]})  - multiset{s[3]}) + multiset{s[2]};
+}
+
+method test11(a: array<int>, n: int, c: int)
+   requires a != null && 0 <= c < n <= a.Length;
+   modifies a;
+   ensures multiset(a[c..n-1]) == multiset(a[c..n]) - multiset{a[n-1]};
+{
+
+}
+\ No newline at end of file