mode 4 with cheating checks

prompts/humaneval-nagini-few-shot/produce.txt

@@ -4,11 +4,43 @@ Even if you think some invariant is not totally necessary, better add it than no
 Don't add any additional text comments, your response must contain only program with invariants.
 Do not provide ANY explanations. Don't include markdown backticks. Respond only in Python code, nothing else.
 
-Pay attention to important details of Nagini syntax:
-1. You should use only single inequalities of type `a <= b` or equalities `a == b`
-2. Use `Acc(list_pred(x))` invariants for variables of type List[] (for example, if x is of type List[int], add `Acc(list_pred(x))` invariants to all cycles in the scope of variable x)
-3. Try to reuse the invariants, encountered as preconditions and postconditions, if these invariants hold during cycle execution
-4. Don't use any built-in functions
+You remember the following aspects of Nagini syntax:
+
+1. Nagini DOES NOT SUPPORT some Python features as list comprehensions (k + 1 for k in range(5)), as double inequalities (a <= b <= c).
+Instead of double inequalities it's customary to use two separate inequalities (a <= b and b <= c).
+
+2. In Nagini method preconditions (Requires) and postconditions (Ensures) placed right after method signature, like here:
+"
+def Sum(a : List[int], s : int, t : int) -> int :
+    Requires(Acc(list_pred(a)))
+    Requires(((0) <= (s)) and ((s) <= (t)) and ((t) <= (len(a))))
+    Ensures(Acc(list_pred(a)))
+    ...
+"
+
+3. Invariant are placed right after `while` statement and before the code of `while` body:
+"
+    while i < len(numbers):
+        Invariant(Acc(list_pred(numbers)))
+        Invariant(0 <= i and i <= len(numbers))
+        s = s + numbers[i]
+"
+Invariants CANNOT be placed in any other position.
+You remember that each invariant (and each expression) should contain equal number of opening and closing brackets, so that it is valid.
+You should sustain balanced parentheses.
+
+4. Nagini requires special annotations for working with lists `Acc(list_pred(..))`. You can use these constructs only inside `Invariant`,
+anywhere else you should not use `Acc()` or `list_pred()`:
+"
+    while i < len(numbers):
+        Invariant(Acc(list_pred(numbers)))
+"
+
+5. Nagini contains `Forall` and `Exists` constructs that can be used in invariants. First argument of Forall/Exists is typically a type (i.e `int`),
+second argument is a lambda. `Forall(type, lambda x : a)` denotes that assertion `a` is true for every element `x` of type `type`.
+
+6. In Nagini `Implies(e1, a2)` plays role of implication. `Implies(e1, a2)` denotes that assertion a2 holds if boolean expression e1 is true.
+You can use it inside invariants and asserts.
 
 Here are some examples of verified Python cycles with Nagini invariants:
 ```

prompts/humaneval-nagini-few-shot/rewrite.txt

@@ -5,11 +5,43 @@ Even if you think some invariant is not totally necessary, better add it than no
 Don't add any additional text comments, your response must contain only program with invariants.
 Do not provide ANY explanations. Don't include markdown backticks. Respond only in Python code, nothing else.
 
-Pay attention to important details of Nagini syntax:
-1. You should use only single inequalities of type `a <= b` or equalities `a == b`
-2. Use `Acc(list_pred(x))` invariants for variables of type List[] (for example, if x is of type List[int], add `Acc(list_pred(x))` invariants to all cycles in the scope of variable x)
-3. Try to reuse the invariants, encountered as preconditions and postconditions, if these invariants hold during cycle execution
-4. Don't use any built-in functions
+You remember the following aspects of Nagini syntax:
+
+1. Nagini DOES NOT SUPPORT some Python features as list comprehensions (k + 1 for k in range(5)), as double inequalities (a <= b <= c).
+Instead of double inequalities it's customary to use two separate inequalities (a <= b and b <= c).
+
+2. In Nagini method preconditions (Requires) and postconditions (Ensures) placed right after method signature, like here:
+"
+def Sum(a : List[int], s : int, t : int) -> int :
+    Requires(Acc(list_pred(a)))
+    Requires(((0) <= (s)) and ((s) <= (t)) and ((t) <= (len(a))))
+    Ensures(Acc(list_pred(a)))
+    ...
+"
+
+3. Invariant are placed right after `while` statement and before the code of `while` body:
+"
+    while i < len(numbers):
+        Invariant(Acc(list_pred(numbers)))
+        Invariant(0 <= i and i <= len(numbers))
+        s = s + numbers[i]
+"
+Invariants CANNOT be placed in any other position.
+You remember that each invariant (and each expression) should contain equal number of opening and closing brackets, so that it is valid.
+You should sustain balanced parentheses.
+
+4. Nagini requires special annotations for working with lists `Acc(list_pred(..))`. You can use these constructs only inside `Invariant`,
+anywhere else you should not use `Acc()` or `list_pred()`:
+"
+    while i < len(numbers):
+        Invariant(Acc(list_pred(numbers)))
+"
+
+5. Nagini contains `Forall` and `Exists` constructs that can be used in invariants. First argument of Forall/Exists is typically a type (i.e `int`),
+second argument is a lambda. `Forall(type, lambda x : a)` denotes that assertion `a` is true for every element `x` of type `type`.
+
+6. In Nagini `Implies(e1, a2)` plays role of implication. `Implies(e1, a2)` denotes that assertion a2 holds if boolean expression e1 is true.
+You can use it inside invariants and asserts.
 
 You might need to work with accumulating functions, such as sum, so here's an example of how to do that:
 ```

prompts/humaneval-nagini-without-impls-few-shot/ask_for_fixed.txt

@@ -0,0 +1,6 @@
+The following errors occurred during verification:
+{error}
+
+Please fix the error by adding, removing or modifying the implementation, invariants or assertions and return the fixed program.
+Don't add any additional text comments, your response must contain only program with invariants.
+Do not provide ANY explanations. Don't include markdown backticks. Respond only in Python code, nothing else.

prompts/humaneval-nagini-without-impls-few-shot/ask_for_fixed_had_errors.txt

@@ -0,0 +1,6 @@
+There are still some errors:
+{error}
+
+Could you please fix them?
+Don't add any additional text comments, your response must contain only program with invariants.
+Do not provide ANY explanations. Don't include markdown backticks. Respond only in Python code, nothing else.

prompts/humaneval-nagini-without-impls-few-shot/helpers.txt

@@ -0,0 +1,3 @@
+Generally, you should use helper functions (marked with @Pure annotation) only in invariants, asserts and conditions (in `if` or `while` conditions), not in the plain code.
+But, the following helper functions you can use anywhere: {helpers}.
+Do not change helper functions.

prompts/humaneval-nagini-without-impls-few-shot/invalid_helpers.txt

@@ -0,0 +1,9 @@
+We detected an improper usage of helper functions. Here is the list of helper functions used in a wrong way:
+{invalid_helpers}
+You should use helper functions only in invariants, asserts and conditions (in `if` or `while` conditions), not in the plain code.
+The following helper functions you can use anywhere: {helpers}.
+We replaced all improper usages with `invalid_call()` and got the following program:
+{program}
+You should rewrite this program without changing pre/postconditions and helper functions (denoted with @Pure).
+After rewriting your code should verify.
+Your code should not contain any `invalid_call()` invocations.

prompts/humaneval-nagini-without-impls-few-shot/rewrite.txt

@@ -0,0 +1,82 @@
+Rewrite the following Nagini code with implementations of some functions missing. While rewriting it, ensure that it verifies. Include invariants and assertions. Don't remove any helper functions (they are marked with @Pure annotation), they are there to help you. Prefer loops to recursion.
+Use helper functions only in invariants, asserts and conditions (in `if` or `while` conditions). Don't use helpers in the plain code.
+Do not change helper functions.
+Add code and invariants to other functions.
+Ensure that the invariants are as comprehensive as they can be.
+Even if you think some invariant is not totally necessary, better add it than not.
+Don't add any additional text comments, your response must contain only program with invariants.
+Do not provide ANY explanations. Don't include markdown backticks. Respond only in Python code, nothing else.
+
+
+You remember the following aspects of Nagini syntax:
+
+1. Nagini DOES NOT SUPPORT some Python features as list comprehensions (k + 1 for k in range(5)), as double inequalities (a <= b <= c).
+Instead of double inequalities it's customary to use two separate inequalities (a <= b and b <= c).
+
+2. In Nagini method preconditions (Requires) and postconditions (Ensures) placed right after method signature, like here:
+"
+def Sum(a : List[int], s : int, t : int) -> int :
+    Requires(Acc(list_pred(a)))
+    Requires(((0) <= (s)) and ((s) <= (t)) and ((t) <= (len(a))))
+    Ensures(Acc(list_pred(a)))
+    ...
+"
+
+3. Invariant are placed right after `while` statement and before the code of `while` body:
+"
+    while i < len(numbers):
+        Invariant(Acc(list_pred(numbers)))
+        Invariant(0 <= i and i <= len(numbers))
+        s = s + numbers[i]
+"
+Invariants CANNOT be placed in any other position.
+You remember that each invariant (and each expression) should contain equal number of opening and closing brackets, so that it is valid.
+You should sustain balanced parentheses.
+
+4. Nagini requires special annotations for working with lists `Acc(list_pred(..))`. You can use these constructs only inside `Invariant`,
+anywhere else you should not use `Acc()` or `list_pred()`:
+"
+    while i < len(numbers):
+        Invariant(Acc(list_pred(numbers)))
+"
+
+5. Nagini contains `Forall` and `Exists` constructs that can be used in invariants. First argument of Forall/Exists is typically a type (i.e `int`),
+second argument is a lambda. `Forall(type, lambda x : a)` denotes that assertion `a` is true for every element `x` of type `type`.
+
+6. In Nagini `Implies(e1, a2)` plays role of implication. `Implies(e1, a2)` denotes that assertion a2 holds if boolean expression e1 is true.
+You can use it inside invariants and asserts.
+
+You might need to work with accumulating functions, such as sum, so here's an example of how to do that:
+```
+from typing import cast, List, Dict, Set, Optional, Union
+from nagini_contracts.contracts import *
+
+@Pure
+def Sum(a : List[int], s : int, t : int) -> int :
+    Requires(Acc(list_pred(a)))
+    Requires(((0) <= (s)) and ((s) <= (t)) and ((t) <= (len(a))))
+
+    if s == t:
+        return 0
+    else:
+        return (a)[t - 1] + (Sum(a, s, t - 1))
+
+def sum_loop(numbers: List[int]) -> int:
+    Requires(Acc(list_pred(numbers)))
+    Ensures(Acc(list_pred(numbers)))
+    Ensures(Result() == Sum(numbers, 0, len(numbers)))
+    s = int(0)
+    i = int(0)
+    while (i) < (len(numbers)):
+        Invariant(Acc(list_pred(numbers)))
+        Invariant(0 <= i and i <= len(numbers))
+        Invariant(Forall(int, lambda d_1_p_:
+            (Implies(0 <= d_1_p_ and d_1_p_ < len(numbers), Sum(numbers, 0, d_1_p_ + 1) == Sum(numbers, 0, d_1_p_) + numbers[d_1_p_]), [[Sum(numbers, 0, d_1_p_ + 1)]])))
+        Invariant(s == Sum(numbers, 0, i))
+        Assert(Sum(numbers, 0, i + 1) == Sum(numbers, 0, i) + numbers[i])
+        s = s + (numbers)[i]
+        i = i + 1
+    return s
+```
+The program:
+{program}

prompts/humaneval-nagini-without-impls-few-shot/sys.txt

@@ -0,0 +1,4 @@
+You are an expert in a Python verification framework Nagini.
+You will be given tasks dealing with Python programs including precise annotations.
+Do not provide ANY explanations. Don't include markdown backticks. Respond only in Python code, nothing else.
+You respond only with code blocks.

prompts/humaneval-nagini-without-impls-few-shot/timeout.txt

@@ -0,0 +1,3 @@
+The verifier timed out during the verification.
+This usually means that the provided invariants were too broad or were difficult to check.
+Could you please try to improve the invariants and try again?