Multidimensional decreases clauses

Author: Long Pham

regression/contracts/variant_missing_invariant_warning/test.desc

@@ -1,10 +1,7 @@
 CORE
 main.c
 --apply-loop-contracts
-activate-multi-line-match
 ^The loop at file main.c line 4 function main does not have a loop invariant, but has a decreases clause. Hence, a default loop invariant \('true'\) is being used.$
-^\[main.1\].*Check loop invariant before entry: SUCCESS$
-^\[main.2\].*Check that loop invariant is preserved: SUCCESS$
 ^\[main.3\].*Check decreases clause on loop iteration: SUCCESS$
 ^EXIT=0$
 ^SIGNAL=0$

regression/contracts/variant_multidimensional_ackermann/main.c

@@ -0,0 +1,40 @@
+#include <stdio.h>
+
+int ackermann(int m, int n);
+
+int main()
+{
+  int m = 3;
+  int n = 5;
+  int result = ackermann(m, n);
+
+  printf("Result of the Ackermann function: %d\n", result);
+  return 0;
+}
+
+int ackermann(int m, int n)
+  // clang-format off
+__CPROVER_requires(0 <= m && 0 <= n)
+__CPROVER_ensures(__CPROVER_return_value >= 0)
+// clang-format on
+{
+  while(m > 0)
+    // clang-format off
+    __CPROVER_loop_invariant(0 <= m && 0 <= n)
+    __CPROVER_decreases(m, n)
+    // clang-format on
+    {
+      if(n == 0)
+      {
+        m--;
+        n = 1;
+      }
+      else
+      {
+        n = ackermann(m, n - 1);
+        m--;
+      }
+    }
+
+  return n + 1;
+}

regression/contracts/variant_multidimensional_ackermann/test.desc

@@ -0,0 +1,29 @@
+CORE
+main.c
+--apply-loop-contracts --replace-all-calls-with-contracts
+^\[ackermann.3\] .* Check decreases clause on loop iteration: SUCCESS$
+^EXIT=0$
+^SIGNAL=0$
+--
+--
+This test succeeds. It tests whether we can prove (only partially) the 
+termination of the Ackermann function using a multidimensional decreases clause. 
+
+Note that this particular implementation of the Ackermann function contains
+both a while-loop and recursion. Therefore, to fully prove the termination of 
+the Ackermann function, we must prove both 
+(i) the termination of the while-loop and
+(ii) the termination of the recursion. 
+Because CBMC does not support termination proofs of recursions (yet), we cannot
+prove the latter, but the former. Hence, the termination proof in the code is
+only "partial."
+
+Furthermore, the Ackermann function has a function contract that the result
+is always non-negative. This post-condition is necessary for establishing
+the loop invariant. However, in this test, we do not enforce the function
+contract. Instead, we assume that the function contract is correct and use it
+(i.e. replace a recursive call of the Ackermann function with its contract). 
+
+We cannot verify/enforce the function contract of the Ackermann function, since
+CBMC does not support function contracts for recursively defined functions.
+As of now, CBMC only supports function contracts for non-recursive functions. 

regression/contracts/variant_multidimensional_not_decreasing_fail1/main.c

@@ -0,0 +1,23 @@
+
+int main()
+{
+  int i = 0;
+  int j = 0;
+  int N = 10;
+  while(i < N)
+    // clang-format off
+    __CPROVER_loop_invariant(0 <= i && i <= N && 0 <= j && j <= N)
+    __CPROVER_decreases(N - i, j)
+    // clang-format on
+    {
+      if(j < N)
+      {
+        j++;
+      }
+      else
+      {
+        i++;
+        j = 0;
+      }
+    }
+}

regression/contracts/variant_multidimensional_not_decreasing_fail1/test.desc

@@ -0,0 +1,11 @@
+CORE
+main.c
+--apply-loop-contracts
+^\[main.3\] .* Check decreases clause on loop iteration: FAILURE$
+^EXIT=10$
+^SIGNAL=0$
+--
+--
+This test fails because the given multidimensional decreases clause does not 
+monotonically decrease. A mistake is in the second component of the
+decreases clause: j. It should instead be N - j. 

regression/contracts/variant_multidimensional_not_decreasing_fail2/main.c

@@ -0,0 +1,23 @@
+
+int main()
+{
+  int i = 0;
+  int j = 0;
+  int N = 10;
+  while(i < N)
+    // clang-format off
+    __CPROVER_loop_invariant(0 <= i && i <= N && 0 <= j && j <= N)
+    __CPROVER_decreases(i, N - j)
+    // clang-format on
+    {
+      if(j < N)
+      {
+        j++;
+      }
+      else
+      {
+        i++;
+        j = 0;
+      }
+    }
+}

regression/contracts/variant_multidimensional_not_decreasing_fail2/test.desc

@@ -0,0 +1,11 @@
+CORE
+main.c
+--apply-loop-contracts
+^\[main.3\] .* Check decreases clause on loop iteration: FAILURE$
+^EXIT=10$
+^SIGNAL=0$
+--
+--
+This test fails because the given multidimensional decreases clause does not 
+monotonically decrease. A mistake is in the first component of the
+decreases clause: i. It should instead be N - i. 

regression/contracts/variant_multidimensional_two_index_variables/main.c

@@ -0,0 +1,23 @@
+
+int main()
+{
+  int i = 0;
+  int j = 0;
+  int N = 10;
+  while(i < N)
+    // clang-format off
+    __CPROVER_loop_invariant(0 <= i && i <= N && 0 <= j && j <= N)
+    __CPROVER_decreases(N - i, N - j)
+    // clang-format on
+    {
+      if(j < N)
+      {
+        j++;
+      }
+      else
+      {
+        i++;
+        j = 0;
+      }
+    }
+}

regression/contracts/variant_multidimensional_two_index_variables/test.desc

@@ -0,0 +1,10 @@
+CORE
+main.c
+--apply-loop-contracts
+^\[main.3\].*Check decreases clause on loop iteration: SUCCESS$
+^EXIT=0$
+^SIGNAL=0$
+--
+--
+This test succeeds. It tests whether a multidimensional decreases clause works
+properly. 

regression/contracts/variant_not_decreasing_fail/test.desc

@@ -1,12 +1,7 @@
 CORE
 main.c
 --apply-loop-contracts
-^main.c function main$
-^\[main.1\] .* Check loop invariant before entry: SUCCESS$
-^\[main.2\] .* Check that loop invariant is preserved: SUCCESS$
 ^\[main.3\] .* Check decreases clause on loop iteration: FAILURE$
-^.* 1 of 3 failed \(2 iterations\)$
-^VERIFICATION FAILED$
 ^EXIT=10$
 ^SIGNAL=0$
 --