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added tests
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‎bin/alk.jar

-6.21 KB
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‎examples/analysis/tase2022/askith_assert.alk

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/*
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alki -a askith_assert.alk -s -smt="Z3"
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a |-> $a_0
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res |-> 0
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i |-> $i_0
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Path condition:
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((($a_0.size()>0)&&(0<=$i_0))&&($i_0<($a_0.size()-1))) &&
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!($a_0[$i_0]>$a_0[($i_0+1)])
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a |-> (store (store $a_0 $i_0 $a_0[($i_0+1)]) ($i_0+1) $a_0[$i_0])
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res |-> 0
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tmp |-> $a_0[$i_0]
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i |-> $i_0
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Path condition:
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((($a_0.size()>0)&&(0<=$i_0))&&($i_0<($a_0.size()-1))) &&
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($a_0[$i_0]>$a_0[($i_0+1)]) &&
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validStore($a_0, $i_0, $a_0[($i_0+1)]) &&
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validStore((store $a_0 $i_0 $a_0[($i_0+1)]), ($i_0+1), $a_0[$i_0])
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*/
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@havoc a : array<int>;
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@havoc i : int;
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@assume a.size() > 0 && 0 <= i && i < a.size() - 1;
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if (a[i] > a[i + 1])
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{
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tmp = a[i];
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a[i] = a[i + 1];
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a[i + 1] = tmp;
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res = i;
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}
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res = 0;
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@assert a[i] <= a[i + 1];
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@assert res > 0 ==> res == i;

‎examples/analysis/tase2022/askith_call.alk

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/*
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alki -a askith_call.alk -m -s -smt="Z3"
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Successfully verified: askIth
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a |-> $a_1
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last |-> $\result_0
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Path condition:
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($a.size()>3) &&
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($a_1[2]<=$a_1[3]) &&
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($\result_0>0) ==> ($\result_0==2)
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*/
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askIth(out a, i)
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@requires a : array<int>
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@requires i : int
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@requires a.size() > 0 && 0 <= i && i < a.size() - 1
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@ensures a[i] <= a[i + 1]
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@ensures \result > 0 ==> \result == i
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@ensures \result : int
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{
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if (a[i] > a[i + 1])
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{
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tmp = a[i];
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a[i] = a[i + 1];
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a[i + 1] = tmp;
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return i;
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}
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return 0;
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}
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@symbolic $a : array<int>;
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a = $a;
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@assume a.size() > 3;
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last = askIth(a, 2);

‎examples/analysis/tase2022/askith_verify.alk

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/*
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alki -a askith_verify.alk -s -smt="Z3"
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Successfully verified: askIth
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*/
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askIth(out a, i)
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@requires a : array<int>
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@requires i : int
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@requires a.size() > 0 && 0 <= i && i < a.size() - 1
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@ensures a[i] <= a[i + 1]
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@ensures \result > 0 ==> \result == i
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@ensures \result : int
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{
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if (a[i] > a[i + 1])
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{
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tmp = a[i];
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a[i] = a[i + 1];
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a[i + 1] = tmp;
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return i;
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}
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return 0;
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}

‎examples/analysis/tase2022/bubblesort.alk

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/*
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alki -a bubblesort.alk -m -i "b |-> [2, 3, 1]"
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b |-> [1, 2, 3]
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alki -a bubblesort.alk -m -i "b |-> [1.2, 1.5, 1.4]"
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b |-> [1.2, 1.4, 1.5]
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alki -a bubblesort.alk -m -i "b |-> [\"ab\", \"ac\", \"aa\"]"
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b |-> ["aa", "ab", "ac"]
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*/
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swap(out a, i, j)
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@requires 0 <= i && i < a.size()
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@requires 0 <= j && j < a.size()
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{
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temp = a[i];
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a[i] = a[j];
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a[j] = temp;
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}
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askIth(out a, i)
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@requires a.size() > 1
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@requires 0 <= i && i < a.size() - 1
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{
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if (a[i] > a[i + 1]) {
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swap(a, i, i + 1);
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return i;
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}
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return 0;
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}
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bubbleSort(out a)
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@requires a.size() > 0
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{
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last = a.size() - 1;
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while (last > 0)
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{
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n1 = last;
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for (i = 0; i < n1; ++i)
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{
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last = askIth(a, i);
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}
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}
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}
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bubbleSort(b);

‎examples/analysis/tase2022/fstalg.alk

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/*
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alki -a fstalg.alk -m -i "a |-> [1, 2, 2, 3, 3, 3]"
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a |-> [1, 2, 2, 3, 3, 3]
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slp |-> 3
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i |-> 6
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*/
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slp = 1;
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i = 1;
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while (i < a.size())
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{
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if (a[i] == a[i - slp])
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slp = slp + 1;
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i = i + 1;
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}

‎examples/analysis/tase2022/fstalg_assert.alk

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/*
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alki -a fstalg_assert.alk -m -s -smt="Z3"
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a |-> $a_0
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slp |-> $slp_0
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i |-> ($i_1+1)
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Path condition:
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($a_0.size()>0) &&
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forall $i_0 : int :: ((0<=$i_0)&&($i_0<($a_0.size()-1))) ==> ($a_0[$i_0]<=$a_0[($i_0+1)]) &&
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exists $k_0 : int :: (((($slp_0-1)<=$k_0)&&($k_0<$i_1))&&($a_0[$k_0]==$a_0[(($k_0-$slp_0)+1)])) &&
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!($a_0[$i_1]==$a_0[($i_1-$slp_0)])
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a |-> $a_0
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slp |-> ($slp_0+1)
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i |-> ($i_1+1)
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Path condition:
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($a_0.size()>0) &&
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forall $i_0 : int :: ((0<=$i_0)&&($i_0<($a_0.size()-1))) ==> ($a_0[$i_0]<=$a_0[($i_0+1)]) &&
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exists $k_0 : int :: (((($slp_0-1)<=$k_0)&&($k_0<$i_1))&&($a_0[$k_0]==$a_0[(($k_0-$slp_0)+1)])) &&
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($a_0[$i_1]==$a_0[($i_1-$slp_0)])
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*/
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@havoc a : array<int>;
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slp = 1;
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i = 1;
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@assume a.size() > 0;
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@assume forall i : int :: 0 <= i && i < a.size() - 1 ==> a[i] <= a[i + 1];
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@havoc i : int;
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@havoc slp : int;
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@assume exists k:int :: slp - 1 <= k && k < i && a[k] == a[k - slp + 1];
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if (a[i] == a[i - slp])
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slp = slp + 1;
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i = i + 1;
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@assert exists k:int :: slp - 1 <= k && k < i && a[k] == a[k - slp + 1];

‎examples/analysis/tase2022/fstalg_assume.alk

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/*
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alki -a fstalg_assume.alk -m -s -smt="Z3"
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a |-> $a_0
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slp |-> 2
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i |-> 3
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a |-> $a_0
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slp |-> 3
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i |-> 3
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a |-> $a_0
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slp |-> 2
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i |-> 3
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a |-> $a_0
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slp |-> 1
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i |-> 3
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*/
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@havoc a : array<int>;
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@assume forall i : int :: 0 <= i && i < a.size() - 1 ==> a[i] <= a[i + 1];
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@assume a.size() == 3;
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slp = 1;
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i = 1;
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while (i < a.size())
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{
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if (a[i] == a[i - slp])
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slp = slp + 1;
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i = i + 1;
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}

‎examples/analysis/tase2022/fstalg_inv.alk

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/*
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alki -a fstalg_inv.alk -m -s -smt="Z3"
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a |-> $a_0
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slp |-> $slp_0
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i |-> $i_1
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[13:11] Loop invariant was verified!
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[14:12] Loop invariant was verified!
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[13:11] Loop invariant was verified!
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[14:12] Loop invariant was verified!
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*/
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@havoc a : array<int>;
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slp = 1;
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i = 1;
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@assume a.size() > 0;
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@assume forall i : int :: 0 <= i && i < a.size() - 1 ==> a[i] <= a[i + 1];
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while (i < a.size())
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@invariant 1 <= slp && i <= a.size();
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@invariant (exists k:int :: slp - 1 <= k && k < i && a[k] == a[k - slp + 1]);
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// @invariant (forall k:int :: slp <= k && k < i ==> a[k] != a[k - slp]);
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// Z3 TIMEOUT, Dafny TIMEOUT; Why3 with Alt-Ergo WORKS FINE
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@modifies slp, i;
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{
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if (a[i] == a[i - slp])
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slp = slp + 1;
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i = i + 1;
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}

‎examples/analysis/tase2022/fstalg_loopassert.alk

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/*
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alki -a fstalg_loopassert.alk -m -s -smt="Z3"
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a |-> $a_0
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slp |-> 1
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i |-> 3
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a |-> $a_0
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slp |-> 2
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i |-> 3
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a |-> $a_0
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slp |-> 3
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i |-> 3
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a |-> $a_0
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slp |-> 2
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i |-> 3
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*/
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@havoc a : array<int>;
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slp = 1;
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i = 1;
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@assume a.size() == 3;
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@assume forall i : int :: 0 <= i && i < a.size() - 1 ==> a[i] <= a[i + 1];
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while (i < a.size())
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@modifies slp, i;
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{
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if (a[i] == a[i - slp])
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slp = slp + 1;
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i = i + 1;
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}
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@loopassert 1 <= slp && i <= a.size() && (exists k:int :: slp - 1 <= k && k < i && a[k] == a[k - slp + 1]);

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