various fixes

Author: llalexandru00

bin/alk.jar

@@ -0,0 +1,16 @@
+symbolic $a:array<int>;
+a = $a;
+assume a.size() < 2;
+min = a[0];
+i = 1;
+while (i < a.size())
+invariant a
+invariant b
+invariant c
+modifies i
+{
+    if (a[i] < min) min = a[i];
+    i = i+1;
+
+    assert d;
+}

input/symb/test0.alk

@@ -0,0 +1,23 @@
+plateau(a: array<int>)
+requires forall i:int :: 0 <= i && i < a.size() - 1 ==> a[i] <= a[i+1]
+ensures (forall k:int :: forall l:int :: 0 <= k && k <= l && l < a.size() && a[k] == a[l] ==> (l-k) <= result)
+{
+    lg = 1;
+    i = 1;
+    while (i < a.size())
+    invariant (forall k:int :: forall l:int ::
+        0 <= k && k <= l && l < i && a[k] == a[l]
+        ==>
+        (l-k) <= lg)
+    modifies lg
+    {
+        if (a[i] == a[i - lg]) lg = lg+1;
+        i = i + 1;
+    }
+}
+
+symbolic $a: array<int>;
+a = $a;
+assume a.size() < 4;
+assume forall i:int :: 0 <= i && i < a.size()-1 ==> a[i] <= a[i+1];
+x = plateau(a);

input/symb/test1.alk

@@ -0,0 +1,38 @@
+plateau(a: array<int>) : int
+requires forall i:int :: 0 <= i && i < a.size()-1 ==> a[i] <= a[i+1]
+ensures (forall k:int :: forall l:int ::
+    0 <= k && k <= l && l < a.size() && a[k] == a[l]
+    ==>
+    (l-k) <= result)
+{
+    lg = 1;
+    i = 1;
+    while (i < a.size())
+    invariant (forall k:int :: forall l:int ::
+        0 <= k && k <= l && l < i && a[k] == a[l]
+        ==>
+        (l-k) <= lg)
+    modifies lg
+    {
+        if (a[i] == a[i - lg]) lg = lg+1;
+        i = i + 1;
+    }
+    return lg;
+}
+
+symbolic $a: array<int>;
+a = $a;
+//assume a.size() < 4;
+assume forall i:int :: 0 <= i && i < a.size()-1 ==> a[i] <= a[i+1];
+//x = plateau(a);
+for (i = 0; i < 4; ++i)
+{
+    havoc a;
+    assume a.size() == i;
+    x[i] = plateau(a);
+}
+
+assert x[0] <= x[1] && x[1] <= x[2] && x[2] <= x[3];
+
+Internal error [0:0]
+Unknown Z3 check! [5:3]

input/symb/test2.alk

@@ -0,0 +1,11 @@
+symbolic $n: int;
+n = $n;
+sum = 0;
+i = 1;
+
+while (i <= n)
+invariant sum == (i-1)*i/2
+{
+    sum = sum + i;
+    i = i + 1;
+}

input/symb/test3.alk

@@ -0,0 +1,18 @@
+alg12(a: array<int>) : int
+{
+    lg = 1;
+    i = 1;
+    while (i < a.size())
+    {
+        if (a[i] == a[i - lg]) lg = lg+1;
+        i = i + 1;
+    }
+    return lg;
+}
+
+symbolic $a: array<int>;
+a = $a;
+assume forall i:int :: 0 <= i && i < a.size()-1 ==> a[i] <= a[i+1];
+assume a.size() == 3;
+
+x = alg12(a);

input/symb/test4.alk

@@ -0,0 +1,36 @@
+askIth(out a:array<int>, i:int) : int
+requires a.size() > 0 && 0 <= i && i < a.size()-1
+ensures a[i] <= a[i+1]
+ensures result > 0 ==> result == i
+{
+    if (a[i] > a[i+1]) {
+        temp = a[i];
+        a[i] = a[i+1];
+        a[i+1] = temp;
+        return i;
+    }
+    return 0;
+}
+
+sorted(out a) {
+    return forall j:int :: forall k:int ::
+           0 <= j && j <= last && last < k &&
+           k < a.size() ==> a[j] <= a[k];
+}
+
+bubbleSort(out a: array<int>) {
+    last = a.size()-1;
+    while (last > 0)
+    invariant sorted(a)
+    {
+        n1 = last;
+        i = 0;
+        while (i < n1)
+        invariant forall j:int ::
+        0 <= j && j < i ==> a[j] <= a[i]
+        {
+            last = askIth(a, i);
+            i = i + 1;
+        }
+    }
+}

input/symb/test5.alk

@@ -0,0 +1,17 @@
+@symbolic $a: array<int>;
+a = $a;
+@assume forall i:int :: 0 <= i && i < a.size()-1 ==> a[i] <= a[i+1];
+slp = 1;
+i = 1;
+while (i < a.size())
+@invariant i <= a.size()
+@invariant (forall k:int :: forall l:int ::
+    0 <= k && k <= l && l < i && a[k] == a[l]
+    ==>
+    (l-k) <= slp)
+@modifies slp
+@modifies i
+{
+    if (a[i] == a[i - slp]) slp = slp+1;
+    i = i + 1;
+}

input/symb/test6.alk

@@ -0,0 +1,16 @@
+@symbolic $a: array<int>;
+a = $a;
+@assume forall i:int :: 0 <= i && i < a.size()-1 ==> a[i] <= a[i+1];
+slp = 1;
+i = 1;
+while (i < a.size())
+@invariant slp <= i
+@invariant (forall k:int :: forall l:int ::
+    0 <= k && k <= l && l < i && a[k] == a[l]
+    ==>
+    (l-k) <= slp)
+@modifies slp, i
+{
+    if (a[i] == a[i - slp]) slp = slp+1;
+    i = i + 1;
+}

input/symb/test7.alk

@@ -1,17 +1,7 @@
-a = { "a" |-> 5 };
-
-{} x = a.keys()
-
-// map-uri (keys)
-// invariantii trebuie procesati intr-o singura executie (nu o executie pentru fiecare invariant)
-
-// apel conditional la Z3 (-pr)
-// dataflow -> cautare secventiala si minim in tablou
-// conversia structurilor si a map-urilor in Z3
-
-// redenumit keyword-urile assert, assume, requires, ensures, symbolic, modifies -> @
-// operatorul : pentru apartenenta la un tip de date:
-    // @requires a : array<int> && x : int;  -> din gramatica
-    // @ensures  result : int;               -> din gramatica
-    // type assertions
-// @Trusted
+@symbolic $a : array<int>, $i : int;
+a = $a;
+@assume a.size() == 8;
+a.pushFront($i);
+@assert a.topFront() == $i;
+b = $a;
+@assert b.topFront() == b[0];