step 2: loop detection

prompts/humaneval-dafny-cot/steps/001/examples/001/question.txt

@@ -15,17 +15,10 @@ lemma sum_prop(s: seq<int>)
 method sum_loop(numbers: seq<int>) returns (s: int)
     ensures s == sum(numbers)
 {
-    assert numbers[..|numbers|] == numbers;
     s := 0;
     var i := 0;
     while (i < |numbers|)
-        invariant 0 <= i <= |numbers|
-        invariant s == sum(numbers[..i])
     {
-        assert sum(numbers[..i + 1]) == sum(numbers[..i]) + numbers[i] by {
-            assert numbers[..i+1][..i] == numbers[..i];
-            sum_prop(numbers[..i + 1]);
-        }
         s := s + numbers[i];
 
         i := i + 1;

prompts/humaneval-dafny-cot/steps/002/examples/002/answer.txt

@@ -0,0 +1,6 @@
+Looking at the functions, we can see that the 'sum' function uses recursion and thus contains no loops. The 'sum_prop' lemma, in the same way, does not contain any loops, as evidenced by the absence of 'while' and 'for' keywords.
+Now, let's examine the 'sum_loop' method. This method contains a while loop that iterates through the elements of the 'numbers' sequence. The loop starts with 's' and 'i' initialized to 0, and continues as long as 'i' is less than the length of 'numbers'. Let's try to understand what 's' and 'i' represent in this context.
+
+Looking at the body of the loop, we can see that it adds the current element of 'numbers' to 's'. This means that 's' is the running sum of the elements in 'numbers', namely 's = sum(numbers[..i])'. 'i' is easier to analyze. It is the index of the current element being processed. In each iteration of the loop, 'i' is incremented by 1, so 'i' represents the index of the next element to be processed.
+
+Each iteration of the loop adds the current element to 's', and then increments 'i' to move to the next element. This process continues until 'i' reaches the length of 'numbers', at which point the loop terminates and 's' holds the final sum of the elements in 'numbers'.

prompts/humaneval-dafny-cot/steps/002/examples/002/question.txt

@@ -0,0 +1,28 @@
+Now we are finished with the specifications. Let's move onto the loops.
+Given the following program, for each function, determine if it has loops. If it does, try to determine what the loop does in detail.
+```dafny
+function sum(s: seq<int>) : int {
+    if |s| == 0 then 0 else s[0] + sum(s[1..])
+}
+
+lemma sum_prop(s: seq<int>)
+    requires |s| > 0
+    ensures sum(s) == sum(s[..|s| - 1]) + s[ |s| - 1 ]
+{
+    if (|s| > 1) {
+        assert (s[1..][..|s[1..]| - 1]) == s[1..|s| - 1];
+    }
+}
+method sum_loop(numbers: seq<int>) returns (s: int)
+    ensures s == sum(numbers)
+{
+    s := 0;
+    var i := 0;
+    while (i < |numbers|)
+    {
+        s := s + numbers[i];
+
+        i := i + 1;
+    }
+}
+```

prompts/humaneval-dafny-cot/steps/002/question.txt

@@ -0,0 +1,4 @@
+Given the following program, for each function, determine if it has loops. If it does, try to determine what the loop does in detail.
+```dafny
+{program}
+```