[22:33:38] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > The following program is a mutual exclusion protocol for two processes due to Pnueli. There is a single shared variable s which is either 0 or 1, and initially 1. Besides, each process has a   │
           │ local Boolean variable y that initially equals 0. The program text for each process Pi (i=0,1) is as follows:  l0: loop forever do begin l1: Noncritical section l2: (yi, s) := (1, i); l3: wait   │
           │ until ((y1−i = 0) ∨ (s ̸= i)); l4: Critical section l5: yi := 0 end.  Here, the statement (yi, s) := (1, i); is a multiple assignment in which variable yi := 1 and s := i is a single, atomic      │
           │ step. Model a parallel composition of P0 and P1. Write a property that checks whether the algorithm ensures mutual exclusion and a property that checks whether the algorithm ensures starvation   │
           │ freedom. Use the variable names given in the text.                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │ Reply with your Python code inside one unique code block.                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │ ```python                                                                                                                                                                                          │
           │ class Module:                                                                                                                                                                                      │
           │     """An abstract class to represent a UCLID5 module."""                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │     def types(self):                                                                                                                                                                               │
           │         """(Optional) Defines the type declarations.                                                                                                                                               │
           │         For example, the following implementation defines a 8-bit type called T:                                                                                                                   │
           │         ```                                                                                                                                                                                        │
           │         def types(self):                                                                                                                                                                           │
           │             self.T = BitVector(8)                                                                                                                                                                  │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def locals(self):                                                                                                                                                                              │
           │         """(Optional) Defines the local variables and their types.                                                                                                                                 │
           │         For example, the following implementation defines an 8-bit variable x                                                                                                                      │
           │         and an integer variable y:                                                                                                                                                                 │
           │         ```                                                                                                                                                                                        │
           │         def locals(self):                                                                                                                                                                          │
           │             self.x = BitVector(8)                                                                                                                                                                  │
           │             self.y = Integer()                                                                                                                                                                     │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         """(Optional) Defines the input variables and their types.                                                                                                                                 │
           │         For example, the following implementation defines an input variable x,                                                                                                                     │
           │         which is an array of 8-bit bitvectors indexed by 2-bit bitvectors:                                                                                                                         │
           │         ```                                                                                                                                                                                        │
           │         def inputs(self):                                                                                                                                                                          │
           │             self.x = Array(BitVector(2), BitVector(8))                                                                                                                                             │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         """(Optional) Defines the output variables and their types.                                                                                                                                │
           │         For example, the following implementation defines an output variable y,                                                                                                                    │
           │         which is a real number:                                                                                                                                                                    │
           │         ```                                                                                                                                                                                        │
           │         def outputs(self):                                                                                                                                                                         │
           │             self.y = Real()                                                                                                                                                                        │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def shared_vars(self):                                                                                                                                                                         │
           │         """(Optional) Defines the shared variables and their types.                                                                                                                                │
           │         For example, the following implementation defines a shared variable z,                                                                                                                     │
           │         which is an array of booleans indexed by integers:                                                                                                                                         │
           │         ```                                                                                                                                                                                        │
           │         def shared_vars(self):                                                                                                                                                                     │
           │             self.z = Array(Integer(), Boolean())                                                                                                                                                   │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def instances(self):                                                                                                                                                                           │
           │         """(Optional) Defines the instances of other modules and relates their                                                                                                                     │
           │         input, output, and shared variables to local variables. Every instance                                                                                                                     │
           │         variable must be related to a local variable. For example, let M be                                                                                                                        │
           │         another module with inputs x and y, and output z. The following                                                                                                                            │
           │         implementation defines an instance of M called m, and connects M's                                                                                                                         │
           │         input variable x to the local variable self.a, M's input variable y to                                                                                                                     │
           │         the local variable self.b, and M's output variable z to the local                                                                                                                          │
           │         variable self.c:                                                                                                                                                                           │
           │         ```                                                                                                                                                                                        │
           │         def instances(self):                                                                                                                                                                       │
           │             self.m = M(x=self.a, y=self.b, z=self.c)                                                                                                                                               │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         """(Optional) Defines how variables are initialized.                                                                                                                                       │
           │         For example, the following implementation initializes x to 0 if y is                                                                                                                       │
           │         greater than or equal to 20:                                                                                                                                                               │
           │         ```                                                                                                                                                                                        │
           │         def init(self):                                                                                                                                                                            │
           │             if self.y >= 20:                                                                                                                                                                       │
           │                 self.x = 0                                                                                                                                                                         │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         """(Optional) Defines the transition relation.                                                                                                                                             │
           │         For example, the following implementation increments x or decrements y                                                                                                                     │
           │         depending on z:                                                                                                                                                                            │
           │         ```                                                                                                                                                                                        │
           │         def next(self):                                                                                                                                                                            │
           │             if self.z:                                                                                                                                                                             │
           │                 self.x = self.x + 1                                                                                                                                                                │
           │             else:                                                                                                                                                                                  │
           │                 self.y = self.y - 1                                                                                                                                                                │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         """(Optional) Defines the specification in terms of invariant properties.                                                                                                                  │
           │                                                                                                                                                                                                    │
           │         Returns:                                                                                                                                                                                   │
           │             bool: True if the specification is satisfied, False otherwise.                                                                                                                         │
           │                                                                                                                                                                                                    │
           │         For example, the following implementation defines two invariants:                                                                                                                          │
           │         ```                                                                                                                                                                                        │
           │         def specification(self):                                                                                                                                                                   │
           │             return self.x < 10 and self.y > 0                                                                                                                                                      │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         """(Optional) Defines the control block.                                                                                                                                                   │
           │         For example, the following implementation uses 1-induction to prove                                                                                                                        │
           │         that the specification always holds:                                                                                                                                                       │
           │         ```                                                                                                                                                                                        │
           │         def proof(self):                                                                                                                                                                           │
           │             induction(1)                                                                                                                                                                           │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │ ```                                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │ I can definitely do that! Here is the Python code:                                                                                                                                                 │
           │ ```python                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:34:01] ╭─────────────────────────────────────────────────────────────────────────────────────────── 🧠 Response: ───────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:42
           │ ```python                                                                                                                                                                                          │
           │ class MutualExclusionModule(Module):                                                                                                                                                               │
           │     def locals(self):                                                                                                                                                                              │
           │         self.s = Integer()  # Shared variable s                                                                                                                                                    │
           │         self.y0 = Boolean()  # Local boolean variable y for process P0                                                                                                                             │
           │         self.y1 = Boolean()  # Local boolean variable y for process P1                                                                                                                             │
           │         self.pc0 = Integer()  # Program counter for P0                                                                                                                                             │
           │         self.pc1 = Integer()  # Program counter for P1                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │     def shared_vars(self):                                                                                                                                                                         │
           │         self.s = Integer()  # Shared between processes P0 and P1                                                                                                                                   │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         self.s = 1   # Initially, s is 1                                                                                                                                                           │
           │         self.y0 = False  # Initially, y0 is 0 (False)                                                                                                                                              │
           │         self.y1 = False  # Initially, y1 is 0 (False)                                                                                                                                              │
           │         self.pc0 = 0    # Initial location in the program for P0                                                                                                                                   │
           │         self.pc1 = 0    # Initial location in the program for P1                                                                                                                                   │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         self.pc0 = If(self.pc0 == 0, 1,                                                                                                                                                            │
           │                       If(self.pc0 == 1, 2,                                                                                                                                                         │
           │                          If(self.pc0 == 2, 3,                                                                                                                                                      │
           │                             If(And(self.y1 == False, Or(self.s != 0, self.y1 == False)), 4, 3),                                                                                                    │
           │                             If(self.pc0 == 4, 5, 0))))                                                                                                                                             │
           │         self.pc1 = If(self.pc1 == 0, 1,                                                                                                                                                            │
           │                       If(self.pc1 == 1, 2,                                                                                                                                                         │
           │                          If(self.pc1 == 2, 3,                                                                                                                                                      │
           │                             If(And(self.y0 == False, Or(self.s != 1, self.y0 == False)), 4, 3),                                                                                                    │
           │                             If(self.pc1 == 4, 5, 0))))                                                                                                                                             │
           │         self.y0 = If(self.pc0 == 2, True, If(self.pc0 == 5, False, self.y0))                                                                                                                       │
           │         self.y1 = If(self.pc1 == 2, True, If(self.pc1 == 5, False, self.y1))                                                                                                                       │
           │         self.s = If(self.pc0 == 2, 0, If(self.pc1 == 2, 1, self.s))                                                                                                                                │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         # Mutual exclusion check: Both processes can't be in their critical sections simultaneously.                                                                                               │
           │         mutual_exclusion = Not(And(self.pc0 == 4, self.pc1 == 4))                                                                                                                                  │
           │         # Starvation freedom check: Assuming that the system continues running,                                                                                                                    │
           │         # each process will eventually leave its noncritical section.                                                                                                                              │
           │         starvation_freedom_p0 = Always(Eventually(self.pc0 == 4))                                                                                                                                  │
           │         starvation_freedom_p1 = Always(Eventually(self.pc1 == 4))                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │         # Return true if both properties hold                                                                                                                                                      │
           │         return And(mutual_exclusion, starvation_freedom_p0, starvation_freedom_p1)                                                                                                                 │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         self.prove(self.specification())                                                                                                                                                           │
           │ ```                                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │ This Python code provides an extension to the abstract `Module` class that models two processes accessing shared critical resources using Pnueli's mutual exclusion protocol. The                  │
           │ `MutualExclusionModule` overrides necessary methods to define the shared variable `s`, the per-process local variable `y`, and program counters to manage states. It then offers a specification   │
           │ with a proof that checks for mutual exclusion and starvation freedom properties as indicated in the problem statement. Please note the code structure assumes external symbolic verification       │
           │ capabilities similar to those found in DSLs like UCLID5.                                                                                                                                           │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭─────────────────────────────────────────── 🤖 Extracted: ────────────────────────────────────────────╮                                                                                               utils.py:24
           │                                                                                                      │
           │ class MutualExclusionModule(Module):                                                                 │
           │     def locals(self):                                                                                │
           │         self.s = Integer()  # Shared variable s                                                      │
           │         self.y0 = Boolean()  # Local boolean variable y for process P0                               │
           │         self.y1 = Boolean()  # Local boolean variable y for process P1                               │
           │         self.pc0 = Integer()  # Program counter for P0                                               │
           │         self.pc1 = Integer()  # Program counter for P1                                               │
           │                                                                                                      │
           │     def shared_vars(self):                                                                           │
           │         self.s = Integer()  # Shared between processes P0 and P1                                     │
           │                                                                                                      │
           │     def init(self):                                                                                  │
           │         self.s = 1   # Initially, s is 1                                                             │
           │         self.y0 = False  # Initially, y0 is 0 (False)                                                │
           │         self.y1 = False  # Initially, y1 is 0 (False)                                                │
           │         self.pc0 = 0    # Initial location in the program for P0                                     │
           │         self.pc1 = 0    # Initial location in the program for P1                                     │
           │                                                                                                      │
           │     def next(self):                                                                                  │
           │         self.pc0 = If(self.pc0 == 0, 1,                                                              │
           │                       If(self.pc0 == 1, 2,                                                           │
           │                          If(self.pc0 == 2, 3,                                                        │
           │                             If(And(self.y1 == False, Or(self.s != 0, self.y1 == False)), 4, 3),      │
           │                             If(self.pc0 == 4, 5, 0))))                                               │
           │         self.pc1 = If(self.pc1 == 0, 1,                                                              │
           │                       If(self.pc1 == 1, 2,                                                           │
           │                          If(self.pc1 == 2, 3,                                                        │
           │                             If(And(self.y0 == False, Or(self.s != 1, self.y0 == False)), 4, 3),      │
           │                             If(self.pc1 == 4, 5, 0))))                                               │
           │         self.y0 = If(self.pc0 == 2, True, If(self.pc0 == 5, False, self.y0))                         │
           │         self.y1 = If(self.pc1 == 2, True, If(self.pc1 == 5, False, self.y1))                         │
           │         self.s = If(self.pc0 == 2, 0, If(self.pc1 == 2, 1, self.s))                                  │
           │                                                                                                      │
           │     def specification(self):                                                                         │
           │         # Mutual exclusion check: Both processes can't be in their critical sections simultaneously. │
           │         mutual_exclusion = Not(And(self.pc0 == 4, self.pc1 == 4))                                    │
           │         # Starvation freedom check: Assuming that the system continues running,                      │
           │         # each process will eventually leave its noncritical section.                                │
           │         starvation_freedom_p0 = Always(Eventually(self.pc0 == 4))                                    │
           │         starvation_freedom_p1 = Always(Eventually(self.pc1 == 4))                                    │
           │                                                                                                      │
           │         # Return true if both properties hold                                                        │
           │         return And(mutual_exclusion, starvation_freedom_p0, starvation_freedom_p1)                   │
           │                                                                                                      │
           │     def proof(self):                                                                                 │
           │         self.prove(self.specification())                                                             │
           ╰──────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:34:02] ╭──────────────────────────────────── 🤖 Repaired: ────────────────────────────────────╮                                                                                                               utils.py:24
           │ class MutualExclusionModule(Module):                                                 │
           │   def locals(self):                                                                  │
           │     self.s = int                                                                     │
           │     self.y0 = bool                                                                   │
           │     self.y1 = bool                                                                   │
           │     self.pc0 = int                                                                   │
           │     self.pc1 = int                                                                   │
           │                                                                                      │
           │   def init(self):                                                                    │
           │     self.s = 1                                                                       │
           │     self.y0 = False                                                                  │
           │     self.y1 = False                                                                  │
           │     self.pc0 = 0                                                                     │
           │     self.pc1 = 0                                                                     │
           │                                                                                      │
           │   def next(self):                                                                    │
           │     self.pc0 = (1 if (self.pc0 == 0) else (2 if (self.pc0 == 1) else ??))            │
           │     self.pc1 = (1 if (self.pc1 == 0) else (2 if (self.pc1 == 1) else ??))            │
           │     self.y0 = (True if (self.pc0 == 2) else (False if (self.pc0 == 5) else self.y0)) │
           │     self.y1 = (True if (self.pc1 == 2) else (False if (self.pc1 == 5) else self.y1)) │
           │     self.s = (0 if (self.pc0 == 2) else (1 if (self.pc1 == 2) else self.s))          │
           │                                                                                      │
           │   def proof(self):                                                                   │
           │     ??                                                                               │
           │     ??                                                                               │
           │                                                                                      │
           │                                                                                      │
           ╰──────────────────────────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class MutualExclusionModule(Module):                                                                                                                                                               │
           │   def locals(self):                                                                                                                                                                                │
           │     self.s = int                                                                                                                                                                                   │
           │     self.y0 = bool                                                                                                                                                                                 │
           │     self.y1 = bool                                                                                                                                                                                 │
           │     self.pc0 = int                                                                                                                                                                                 │
           │     self.pc1 = int                                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.s = 1                                                                                                                                                                                     │
           │     self.y0 = False                                                                                                                                                                                │
           │     self.y1 = False                                                                                                                                                                                │
           │     self.pc0 = 0                                                                                                                                                                                   │
           │     self.pc1 = 0                                                                                                                                                                                   │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.pc0 = (1 if (self.pc0 == 0) else (2 if (self.pc0 == 1) else ??))                                                                                                                          │
           │     self.pc1 = (1 if (self.pc1 == 0) else (2 if (self.pc1 == 1) else ??))                                                                                                                          │
           │     self.y0 = (True if (self.pc0 == 2) else (False if (self.pc0 == 5) else self.y0))                                                                                                               │
           │     self.y1 = (True if (self.pc1 == 2) else (False if (self.pc1 == 5) else self.y1))                                                                                                               │
           │     self.s = (0 if (self.pc0 == 2) else (1 if (self.pc1 == 2) else self.s))                                                                                                                        │
           │                                                                                                                                                                                                    │
           │   def proof(self):                                                                                                                                                                                 │
           │     ??                                                                                                                                                                                             │
           │     ??                                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > The following program is a mutual exclusion protocol for two processes due to Pnueli. There is a single shared variable s which is either 0 or 1, and initially 1. Besides, each process has a   │
           │ local Boolean variable y that initially equals 0. The program text for each process Pi (i=0,1) is as follows:  l0: loop forever do begin l1: Noncritical section l2: (yi, s) := (1, i); l3: wait   │
           │ until ((y1−i = 0) ∨ (s ̸= i)); l4: Critical section l5: yi := 0 end.  Here, the statement (yi, s) := (1, i); is a multiple assignment in which variable yi := 1 and s := i is a single, atomic      │
           │ step. Model a parallel composition of P0 and P1. Write a property that checks whether the algorithm ensures mutual exclusion and a property that checks whether the algorithm ensures starvation   │
           │ freedom. Use the variable names given in the text.                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │ Reply with your Python code inside one unique code block.                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │ ```python                                                                                                                                                                                          │
           │ class Module:                                                                                                                                                                                      │
           │     """An abstract class to represent a UCLID5 module."""                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │     def types(self):                                                                                                                                                                               │
           │         """(Optional) Defines the type declarations.                                                                                                                                               │
           │         For example, the following implementation defines a 8-bit type called T:                                                                                                                   │
           │         ```                                                                                                                                                                                        │
           │         def types(self):                                                                                                                                                                           │
           │             self.T = BitVector(8)                                                                                                                                                                  │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def locals(self):                                                                                                                                                                              │
           │         """(Optional) Defines the local variables and their types.                                                                                                                                 │
           │         For example, the following implementation defines an 8-bit variable x                                                                                                                      │
           │         and an integer variable y:                                                                                                                                                                 │
           │         ```                                                                                                                                                                                        │
           │         def locals(self):                                                                                                                                                                          │
           │             self.x = BitVector(8)                                                                                                                                                                  │
           │             self.y = Integer()                                                                                                                                                                     │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         """(Optional) Defines the input variables and their types.                                                                                                                                 │
           │         For example, the following implementation defines an input variable x,                                                                                                                     │
           │         which is an array of 8-bit bitvectors indexed by 2-bit bitvectors:                                                                                                                         │
           │         ```                                                                                                                                                                                        │
           │         def inputs(self):                                                                                                                                                                          │
           │             self.x = Array(BitVector(2), BitVector(8))                                                                                                                                             │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         """(Optional) Defines the output variables and their types.                                                                                                                                │
           │         For example, the following implementation defines an output variable y,                                                                                                                    │
           │         which is a real number:                                                                                                                                                                    │
           │         ```                                                                                                                                                                                        │
           │         def outputs(self):                                                                                                                                                                         │
           │             self.y = Real()                                                                                                                                                                        │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def shared_vars(self):                                                                                                                                                                         │
           │         """(Optional) Defines the shared variables and their types.                                                                                                                                │
           │         For example, the following implementation defines a shared variable z,                                                                                                                     │
           │         which is an array of booleans indexed by integers:                                                                                                                                         │
           │         ```                                                                                                                                                                                        │
           │         def shared_vars(self):                                                                                                                                                                     │
           │             self.z = Array(Integer(), Boolean())                                                                                                                                                   │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def instances(self):                                                                                                                                                                           │
           │         """(Optional) Defines the instances of other modules and relates their                                                                                                                     │
           │         input, output, and shared variables to local variables. Every instance                                                                                                                     │
           │         variable must be related to a local variable. For example, let M be                                                                                                                        │
           │         another module with inputs x and y, and output z. The following                                                                                                                            │
           │         implementation defines an instance of M called m, and connects M's                                                                                                                         │
           │         input variable x to the local variable self.a, M's input variable y to                                                                                                                     │
           │         the local variable self.b, and M's output variable z to the local                                                                                                                          │
           │         variable self.c:                                                                                                                                                                           │
           │         ```                                                                                                                                                                                        │
           │         def instances(self):                                                                                                                                                                       │
           │             self.m = M(x=self.a, y=self.b, z=self.c)                                                                                                                                               │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         """(Optional) Defines how variables are initialized.                                                                                                                                       │
           │         For example, the following implementation initializes x to 0 if y is                                                                                                                       │
           │         greater than or equal to 20:                                                                                                                                                               │
           │         ```                                                                                                                                                                                        │
           │         def init(self):                                                                                                                                                                            │
           │             if self.y >= 20:                                                                                                                                                                       │
           │                 self.x = 0                                                                                                                                                                         │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         """(Optional) Defines the transition relation.                                                                                                                                             │
           │         For example, the following implementation increments x or decrements y                                                                                                                     │
           │         depending on z:                                                                                                                                                                            │
           │         ```                                                                                                                                                                                        │
           │         def next(self):                                                                                                                                                                            │
           │             if self.z:                                                                                                                                                                             │
           │                 self.x = self.x + 1                                                                                                                                                                │
           │             else:                                                                                                                                                                                  │
           │                 self.y = self.y - 1                                                                                                                                                                │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         """(Optional) Defines the specification in terms of invariant properties.                                                                                                                  │
           │                                                                                                                                                                                                    │
           │         Returns:                                                                                                                                                                                   │
           │             bool: True if the specification is satisfied, False otherwise.                                                                                                                         │
           │                                                                                                                                                                                                    │
           │         For example, the following implementation defines two invariants:                                                                                                                          │
           │         ```                                                                                                                                                                                        │
           │         def specification(self):                                                                                                                                                                   │
           │             return self.x < 10 and self.y > 0                                                                                                                                                      │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         """(Optional) Defines the control block.                                                                                                                                                   │
           │         For example, the following implementation uses 1-induction to prove                                                                                                                        │
           │         that the specification always holds:                                                                                                                                                       │
           │         ```                                                                                                                                                                                        │
           │         def proof(self):                                                                                                                                                                           │
           │             induction(1)                                                                                                                                                                           │
           │         ```                                                                                                                                                                                        │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │ ```                                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │ I can definitely do that! Here is the fixed Python code:                                                                                                                                           │
           │ ```python                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:34:17] ╭─────────────────────────────────────────────────────────────────────────────────────────── 🧠 Response: ───────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:42
           │ ```python                                                                                                                                                                                          │
           │ class MutualExclusionModule(Module):                                                                                                                                                               │
           │     def locals(self):                                                                                                                                                                              │
           │         self.s = int                                                                                                                                                                               │
           │         self.y0 = bool                                                                                                                                                                             │
           │         self.y1 = bool                                                                                                                                                                             │
           │         self.pc0 = int                                                                                                                                                                             │
           │         self.pc1 = int                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         self.s = 1                                                                                                                                                                                 │
           │         self.y0 = False                                                                                                                                                                            │
           │         self.y1 = False                                                                                                                                                                            │
           │         self.pc0 = 0                                                                                                                                                                               │
           │         self.pc1 = 0                                                                                                                                                                               │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         # Transitions for pc0                                                                                                                                                                      │
           │         self.pc0 = (1 if (self.pc0 == 0) else                                                                                                                                                      │
           │                     2 if (self.pc0 == 1) else                                                                                                                                                      │
           │                     3 if ((self.pc0 == 2) and ((not self.y1) or self.s != 0)) else                                                                                                                 │
           │                     4 if (self.pc0 == 3) else                                                                                                                                                      │
           │                     5 if (self.pc0 == 4) else                                                                                                                                                      │
           │                     0)                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │         # Transitions for pc1                                                                                                                                                                      │
           │         self.pc1 = (1 if (self.pc1 == 0) else                                                                                                                                                      │
           │                     2 if (self.pc1 == 1) else                                                                                                                                                      │
           │                     3 if ((self.pc1 == 2) and ((not self.y0) or self.s != 1)) else                                                                                                                 │
           │                     4 if (self.pc1 == 3) else                                                                                                                                                      │
           │                     5 if (self.pc1 == 4) else                                                                                                                                                      │
           │                     0)                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │         # Transitions for y0 and y1 based on pc values                                                                                                                                             │
           │         self.y0 = (True if (self.pc0 == 2) else                                                                                                                                                    │
           │                    False if (self.pc0 == 5) else                                                                                                                                                   │
           │                    self.y0)                                                                                                                                                                        │
           │         self.y1 = (True if (self.pc1 == 2) else                                                                                                                                                    │
           │                    False if (self.pc1 == 5) else                                                                                                                                                   │
           │                    self.y1)                                                                                                                                                                        │
           │                                                                                                                                                                                                    │
           │         # Transition for s                                                                                                                                                                         │
           │         self.s = (0 if (self.pc0 == 2) else                                                                                                                                                        │
           │                   1 if (self.pc1 == 2) else                                                                                                                                                        │
           │                   self.s)                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         # Mutual Exclusion                                                                                                                                                                         │
           │         assert not (self.pc0 == 4 and self.pc1 == 4)                                                                                                                                               │
           │                                                                                                                                                                                                    │
           │         # Starvation Freedom                                                                                                                                                                       │
           │         assert not (self.pc0 == 2 and self.pc1 == 2 and self.s == 0 and self.s == 1)                                                                                                               │
           │ ```                                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │ This code models the mutual exclusion protocol and also includes assertions to ensure that the protocol meets its requirements for mutual exclusion and starvation freedom. The `proof` method     │
           │ asserts property checks:                                                                                                                                                                           │
           │ 1. Mutual Exclusion: No two processes can be in their critical section (`pc4`) simultaneously.                                                                                                     │
           │ 2. Starvation Freedom: Whenever a process is ready to enter its critical section by setting its `y` flag, it must eventually be able to proceed (not perpetually blocked despite satisfying        │
           │ conditions to proceed into the critical section).                                                                                                                                                  │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭─────────────────────────────────── 🤖 Extracted: ────────────────────────────────────╮                                                                                                               utils.py:24
           │                                                                                      │
           │ class MutualExclusionModule(Module):                                                 │
           │     def locals(self):                                                                │
           │         self.s = int                                                                 │
           │         self.y0 = bool                                                               │
           │         self.y1 = bool                                                               │
           │         self.pc0 = int                                                               │
           │         self.pc1 = int                                                               │
           │                                                                                      │
           │     def init(self):                                                                  │
           │         self.s = 1                                                                   │
           │         self.y0 = False                                                              │
           │         self.y1 = False                                                              │
           │         self.pc0 = 0                                                                 │
           │         self.pc1 = 0                                                                 │
           │                                                                                      │
           │     def next(self):                                                                  │
           │         # Transitions for pc0                                                        │
           │         self.pc0 = (1 if (self.pc0 == 0) else                                        │
           │                     2 if (self.pc0 == 1) else                                        │
           │                     3 if ((self.pc0 == 2) and ((not self.y1) or self.s != 0)) else   │
           │                     4 if (self.pc0 == 3) else                                        │
           │                     5 if (self.pc0 == 4) else                                        │
           │                     0)                                                               │
           │                                                                                      │
           │         # Transitions for pc1                                                        │
           │         self.pc1 = (1 if (self.pc1 == 0) else                                        │
           │                     2 if (self.pc1 == 1) else                                        │
           │                     3 if ((self.pc1 == 2) and ((not self.y0) or self.s != 1)) else   │
           │                     4 if (self.pc1 == 3) else                                        │
           │                     5 if (self.pc1 == 4) else                                        │
           │                     0)                                                               │
           │                                                                                      │
           │         # Transitions for y0 and y1 based on pc values                               │
           │         self.y0 = (True if (self.pc0 == 2) else                                      │
           │                    False if (self.pc0 == 5) else                                     │
           │                    self.y0)                                                          │
           │         self.y1 = (True if (self.pc1 == 2) else                                      │
           │                    False if (self.pc1 == 5) else                                     │
           │                    self.y1)                                                          │
           │                                                                                      │
           │         # Transition for s                                                           │
           │         self.s = (0 if (self.pc0 == 2) else                                          │
           │                   1 if (self.pc1 == 2) else                                          │
           │                   self.s)                                                            │
           │                                                                                      │
           │     def proof(self):                                                                 │
           │         # Mutual Exclusion                                                           │
           │         assert not (self.pc0 == 4 and self.pc1 == 4)                                 │
           │                                                                                      │
           │         # Starvation Freedom                                                         │
           │         assert not (self.pc0 == 2 and self.pc1 == 2 and self.s == 0 and self.s == 1) │
           ╰──────────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────────────────────────────────────────────────────────────────────── 🤖 Repaired: ───────────────────────────────────────────────────────────────────────────────────────────╮  utils.py:24
           │ class MutualExclusionModule(Module):                                                                                                                                                              │
           │   def locals(self):                                                                                                                                                                               │
           │     self.s = int                                                                                                                                                                                  │
           │     self.y0 = bool                                                                                                                                                                                │
           │     self.y1 = bool                                                                                                                                                                                │
           │     self.pc0 = int                                                                                                                                                                                │
           │     self.pc1 = int                                                                                                                                                                                │
           │                                                                                                                                                                                                   │
           │   def init(self):                                                                                                                                                                                 │
           │     self.s = 1                                                                                                                                                                                    │
           │     self.y0 = False                                                                                                                                                                               │
           │     self.y1 = False                                                                                                                                                                               │
           │     self.pc0 = 0                                                                                                                                                                                  │
           │     self.pc1 = 0                                                                                                                                                                                  │
           │                                                                                                                                                                                                   │
           │   def next(self):                                                                                                                                                                                 │
           │     self.pc0 = (1 if (self.pc0 == 0) else (2 if (self.pc0 == 1) else (3 if ((self.pc0 == 2) and (not self.y1 or (self.s != 0))) else (4 if (self.pc0 == 3) else (5 if (self.pc0 == 4) else 0))))) │
           │     self.pc1 = (1 if (self.pc1 == 0) else (2 if (self.pc1 == 1) else (3 if ((self.pc1 == 2) and (not self.y0 or (self.s != 1))) else (4 if (self.pc1 == 3) else (5 if (self.pc1 == 4) else 0))))) │
           │     self.y0 = (True if (self.pc0 == 2) else (False if (self.pc0 == 5) else self.y0))                                                                                                              │
           │     self.y1 = (True if (self.pc1 == 2) else (False if (self.pc1 == 5) else self.y1))                                                                                                              │
           │     self.s = (0 if (self.pc0 == 2) else (1 if (self.pc1 == 2) else self.s))                                                                                                                       │
           │                                                                                                                                                                                                   │
           │                                                                                                                                                                                                   │
           ╰───────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────── 🤖 Stats: ───────╮                                                                                                                                                                             utils.py:24
           │ Original Lines: 47     │
           │ Final Lines:    22     │
           │ LLM Calls:      2      │
           │ LLM Time:       37.30s │
           │ Repair Time:    1.70s  │
           ╰────────────────────────╯
