[22:43:21] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > Model the following feature for an automobile: A dome light that is turned on as soon as any door is opened. It stays on for 30 seconds after all doors are shut. Use the variable names         │
           │ light_on, door_open, time.                                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:43:31] ╭─────────────────────────────────────────────────────────────────────────────────────────── 🧠 Response: ───────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:42
           │ ```python                                                                                                                                                                                          │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │     def types(self):                                                                                                                                                                               │
           │         self.Boolean = bool                                                                                                                                                                        │
           │         self.Integer = int                                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │     def locals(self):                                                                                                                                                                              │
           │         self.light_on = self.Boolean                                                                                                                                                               │
           │         self.time = self.Integer                                                                                                                                                                   │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         self.door_open = self.Boolean                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         self.light_on = False                                                                                                                                                                      │
           │         self.time = 0                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         if self.door_open:                                                                                                                                                                         │
           │             self.light_on = True                                                                                                                                                                   │
           │             self.time = 30  # Reset timer to 30 seconds every time a door opens                                                                                                                    │
           │         elif self.time > 0:                                                                                                                                                                        │
           │             self.time -= 1  # Decrement the timer when door is not open                                                                                                                            │
           │             self.light_on = True                                                                                                                                                                   │
           │         else:                                                                                                                                                                                      │
           │             self.light_on = False                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         # Ensure light is on only when door is open or timer hasn't expired after door is closed.                                                                                                  │
           │         return (self.door_open or self.time > 0) == self.light_on                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         self.dome_light_status = self.light_on                                                                                                                                                     │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         # This is a hypothetical proof method demonstrating the idea; in real scenarios,                                                                                                           │
           │         # specific model checking or proof methods would be implemented.                                                                                                                           │
           │         assert self.specification(), "Light status does not match specification"                                                                                                                   │
           │         print("Specification is always satisfied based on the design.")                                                                                                                            │
           │ ```                                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │ This Python code defines a `DomeLightModule` that extends the given `Module` class. It defines the necessary variables (`light_on`, `time`, and `door_open`), implements an initialization method  │
           │ to set the initial values of variables, defines a transition function which handles the logic of the light turning on and off based on door status and a timer, defines the output variable, and   │
           │ finally, includes a very basic proof function to ensure the light behaves as expected according to the specification provided.                                                                     │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────────────────────── 🤖 Extracted: ──────────────────────────────────────────╮                                                                                                  utils.py:24
           │                                                                                                   │
           │ class DomeLightModule(Module):                                                                    │
           │     def types(self):                                                                              │
           │         self.Boolean = bool                                                                       │
           │         self.Integer = int                                                                        │
           │                                                                                                   │
           │     def locals(self):                                                                             │
           │         self.light_on = self.Boolean                                                              │
           │         self.time = self.Integer                                                                  │
           │                                                                                                   │
           │     def inputs(self):                                                                             │
           │         self.door_open = self.Boolean                                                             │
           │                                                                                                   │
           │     def init(self):                                                                               │
           │         self.light_on = False                                                                     │
           │         self.time = 0                                                                             │
           │                                                                                                   │
           │     def next(self):                                                                               │
           │         if self.door_open:                                                                        │
           │             self.light_on = True                                                                  │
           │             self.time = 30  # Reset timer to 30 seconds every time a door opens                   │
           │         elif self.time > 0:                                                                       │
           │             self.time -= 1  # Decrement the timer when door is not open                           │
           │             self.light_on = True                                                                  │
           │         else:                                                                                     │
           │             self.light_on = False                                                                 │
           │                                                                                                   │
           │     def specification(self):                                                                      │
           │         # Ensure light is on only when door is open or timer hasn't expired after door is closed. │
           │         return (self.door_open or self.time > 0) == self.light_on                                 │
           │                                                                                                   │
           │     def outputs(self):                                                                            │
           │         self.dome_light_status = self.light_on                                                    │
           │                                                                                                   │
           │     def proof(self):                                                                              │
           │         # This is a hypothetical proof method demonstrating the idea; in real scenarios,          │
           │         # specific model checking or proof methods would be implemented.                          │
           │         assert self.specification(), "Light status does not match specification"                  │
           │         print("Specification is always satisfied based on the design.")                           │
           ╰───────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────── 🤖 Repaired: ───────────────────────────╮                                                                                                                                  utils.py:24
           │ class DomeLightModule(Module):                                    │
           │   def locals(self):                                               │
           │     self.?? = bool                                                │
           │     self.time = int                                               │
           │                                                                   │
           │   def inputs(self):                                               │
           │     self.door_open = bool                                         │
           │                                                                   │
           │   def outputs(self):                                              │
           │     self.dome_light_status = self.light_on                        │
           │                                                                   │
           │   def init(self):                                                 │
           │     self.light_on = False                                         │
           │     self.time = 0                                                 │
           │                                                                   │
           │   def next(self):                                                 │
           │     if self.door_open:                                            │
           │       self.light_on = True                                        │
           │       self.time = 30                                              │
           │     else:                                                         │
           │       if (self.time > 0):                                         │
           │         self.time = (self.time - 1)                               │
           │         self.light_on = True                                      │
           │       else:                                                       │
           │         self.light_on = False                                     │
           │                                                                   │
           │   def specification(self):                                        │
           │     return ((self.door_open or (self.time > 0)) == self.light_on) │
           │                                                                   │
           │   def proof(self):                                                │
           │     ??                                                            │
           │     ??                                                            │
           │                                                                   │
           │                                                                   │
           ╰───────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │   def locals(self):                                                                                                                                                                                │
           │     self.?? = bool                                                                                                                                                                                 │
           │     self.time = int                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.door_open = bool                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.dome_light_status = self.light_on                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.light_on = False                                                                                                                                                                          │
           │     self.time = 0                                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if self.door_open:                                                                                                                                                                             │
           │       self.light_on = True                                                                                                                                                                         │
           │       self.time = 30                                                                                                                                                                               │
           │     else:                                                                                                                                                                                          │
           │       if (self.time > 0):                                                                                                                                                                          │
           │         self.time = (self.time - 1)                                                                                                                                                                │
           │         self.light_on = True                                                                                                                                                                       │
           │       else:                                                                                                                                                                                        │
           │         self.light_on = False                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ((self.door_open or (self.time > 0)) == self.light_on)                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def proof(self):                                                                                                                                                                                 │
           │     ??                                                                                                                                                                                             │
           │     ??                                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Model the following feature for an automobile: A dome light that is turned on as soon as any door is opened. It stays on for 30 seconds after all doors are shut. Use the variable names         │
           │ light_on, door_open, time.                                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:43:39] ╭──────────────────────────────────────────────────── 🧠 Response: ────────────────────────────────────────────────────╮                                                                               utils.py:42
           │ ```python                                                                                                            │
           │ class DomeLightModule(Module):                                                                                       │
           │     def types(self):                                                                                                 │
           │         pass  # No specific types needed for the variables used                                                      │
           │                                                                                                                      │
           │     def locals(self):                                                                                                │
           │         self.light_on = bool  # Corrected attribute name                                                             │
           │         self.time = int                                                                                              │
           │                                                                                                                      │
           │     def inputs(self):                                                                                                │
           │         self.door_open = bool                                                                                        │
           │                                                                                                                      │
           │     def outputs(self):                                                                                               │
           │         self.dome_light_status = self.light_on                                                                       │
           │                                                                                                                      │
           │     def init(self):                                                                                                  │
           │         self.light_on = False                                                                                        │
           │         self.time = 0                                                                                                │
           │                                                                                                                      │
           │     def next(self):                                                                                                  │
           │         if self.door_open:                                                                                           │
           │             self.light_on = True                                                                                     │
           │             self.time = 30                                                                                           │
           │         else:                                                                                                        │
           │             if self.time > 0:                                                                                        │
           │                 self.time -= 1  # Incremented using a shorthand operator                                             │
           │                 self.light_on = True                                                                                 │
           │             else:                                                                                                    │
           │                 self.light_on = False                                                                                │
           │                                                                                                                      │
           │     def specification(self):                                                                                         │
           │         return (self.door_open or self.time > 0) == self.dome_light_status                                           │
           │                                                                                                                      │
           │     def proof(self):                                                                                                 │
           │         # The proof method is typically used to verify specifications                                                │
           │         # Since no specific verification logic is provided, we will assume it validates the specification            │
           │         assert self.specification() == True                                                                          │
           │         # Additional proof mechanisms could be added here if needed                                                  │
           │ ```                                                                                                                  │
           │ This completes the necessary code and corrects the use of variables and methods as required by the task description. │
           ╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────────────────────────── 🤖 Extracted: ──────────────────────────────────────────────╮                                                                                          utils.py:24
           │                                                                                                           │
           │ class DomeLightModule(Module):                                                                            │
           │     def types(self):                                                                                      │
           │         pass  # No specific types needed for the variables used                                           │
           │                                                                                                           │
           │     def locals(self):                                                                                     │
           │         self.light_on = bool  # Corrected attribute name                                                  │
           │         self.time = int                                                                                   │
           │                                                                                                           │
           │     def inputs(self):                                                                                     │
           │         self.door_open = bool                                                                             │
           │                                                                                                           │
           │     def outputs(self):                                                                                    │
           │         self.dome_light_status = self.light_on                                                            │
           │                                                                                                           │
           │     def init(self):                                                                                       │
           │         self.light_on = False                                                                             │
           │         self.time = 0                                                                                     │
           │                                                                                                           │
           │     def next(self):                                                                                       │
           │         if self.door_open:                                                                                │
           │             self.light_on = True                                                                          │
           │             self.time = 30                                                                                │
           │         else:                                                                                             │
           │             if self.time > 0:                                                                             │
           │                 self.time -= 1  # Incremented using a shorthand operator                                  │
           │                 self.light_on = True                                                                      │
           │             else:                                                                                         │
           │                 self.light_on = False                                                                     │
           │                                                                                                           │
           │     def specification(self):                                                                              │
           │         return (self.door_open or self.time > 0) == self.dome_light_status                                │
           │                                                                                                           │
           │     def proof(self):                                                                                      │
           │         # The proof method is typically used to verify specifications                                     │
           │         # Since no specific verification logic is provided, we will assume it validates the specification │
           │         assert self.specification() == True                                                               │
           │         # Additional proof mechanisms could be added here if needed                                       │
           ╰───────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭─────────────────────────────── 🤖 Repaired: ───────────────────────────────╮                                                                                                                         utils.py:24
           │ class DomeLightModule(Module):                                             │
           │   def locals(self):                                                        │
           │     self.?? = bool                                                         │
           │     self.time = int                                                        │
           │                                                                            │
           │   def inputs(self):                                                        │
           │     self.door_open = bool                                                  │
           │                                                                            │
           │   def outputs(self):                                                       │
           │     self.dome_light_status = self.light_on                                 │
           │                                                                            │
           │   def init(self):                                                          │
           │     self.light_on = False                                                  │
           │     self.time = 0                                                          │
           │                                                                            │
           │   def next(self):                                                          │
           │     if self.door_open:                                                     │
           │       self.light_on = True                                                 │
           │       self.time = 30                                                       │
           │     else:                                                                  │
           │       if (self.time > 0):                                                  │
           │         self.time = (self.time - 1)                                        │
           │         self.light_on = True                                               │
           │       else:                                                                │
           │         self.light_on = False                                              │
           │                                                                            │
           │   def specification(self):                                                 │
           │     return ((self.door_open or (self.time > 0)) == self.dome_light_status) │
           │                                                                            │
           │   def proof(self):                                                         │
           │     ??                                                                     │
           │                                                                            │
           │                                                                            │
           ╰────────────────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │   def locals(self):                                                                                                                                                                                │
           │     self.?? = bool                                                                                                                                                                                 │
           │     self.time = int                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.door_open = bool                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.dome_light_status = self.light_on                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.light_on = False                                                                                                                                                                          │
           │     self.time = 0                                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if self.door_open:                                                                                                                                                                             │
           │       self.light_on = True                                                                                                                                                                         │
           │       self.time = 30                                                                                                                                                                               │
           │     else:                                                                                                                                                                                          │
           │       if (self.time > 0):                                                                                                                                                                          │
           │         self.time = (self.time - 1)                                                                                                                                                                │
           │         self.light_on = True                                                                                                                                                                       │
           │       else:                                                                                                                                                                                        │
           │         self.light_on = False                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ((self.door_open or (self.time > 0)) == self.dome_light_status)                                                                                                                         │
           │                                                                                                                                                                                                    │
           │   def proof(self):                                                                                                                                                                                 │
           │     ??                                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Model the following feature for an automobile: A dome light that is turned on as soon as any door is opened. It stays on for 30 seconds after all doors are shut. Use the variable names         │
           │ light_on, door_open, time.                                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:43:52] ╭─────────────────────────────────────────────────────────────────────────────────────────── 🧠 Response: ───────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:42
           │ ```python                                                                                                                                                                                          │
           │ class Module:                                                                                                                                                                                      │
           │     """An abstract class to represent a UCLID5 module."""                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │     def types(self):                                                                                                                                                                               │
           │         """(Optional) Defines the type declarations."""                                                                                                                                            │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def locals(self):                                                                                                                                                                              │
           │         """(Optional) Defines the local variables and their types."""                                                                                                                              │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         """(Optional) Defines the input variables and their types."""                                                                                                                              │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         """(Optional) Defines the output variables and their types."""                                                                                                                             │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def shared_vars(self):                                                                                                                                                                         │
           │         """(Optional) Defines the shared variables and their types."""                                                                                                                             │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def instances(self):                                                                                                                                                                           │
           │         """(Optional) Defines the instances of other modules."""                                                                                                                                   │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         """(Optional) Defines how variables are initialized."""                                                                                                                                    │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         """(Optional) Defines the transition relation."""                                                                                                                                          │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         """(Optional) Defines the specification in terms of invariant properties.                                                                                                                  │
           │                                                                                                                                                                                                    │
           │         Returns:                                                                                                                                                                                   │
           │             bool: True if the specification is satisfied, False otherwise.                                                                                                                         │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         """(Optional) Defines the control block."""                                                                                                                                                │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │     def locals(self):                                                                                                                                                                              │
           │         self.light_on = bool                                                                                                                                                                       │
           │         self.time = int                                                                                                                                                                            │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         self.door_open = bool                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         self.dome_light_status = bool                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         self.light_on = False                                                                                                                                                                      │
           │         self.time = 0                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         if self.door_open:                                                                                                                                                                         │
           │             self.light_on = True                                                                                                                                                                   │
           │             self.time = 30                                                                                                                                                                         │
           │         else:                                                                                                                                                                                      │
           │             if self.time > 0:                                                                                                                                                                      │
           │                 self.time = self.time - 1                                                                                                                                                          │
           │                 self.light_on = True                                                                                                                                                               │
           │             else:                                                                                                                                                                                  │
           │                 self.light_on = False                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         return (self.door_open or (self.time > 0)) == self.light_on                                                                                                                                │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         pass  # As proof() is optional and specific implementation would be domain-specific                                                                                                        │
           │ ```                                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │ This code adjusts the DomeLightModule to inherit correctly from the abstract `Module` class provided, and rectifies logical components such as tracking the light status, time decrement, and      │
           │ logic handling for when doors are opened or closed. This should now correctly model the automobile’s dome light behavior.                                                                          │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭─────────────────────────────────────── 🤖 Extracted: ───────────────────────────────────────╮                                                                                                        utils.py:24
           │                                                                                             │
           │ class Module:                                                                               │
           │     """An abstract class to represent a UCLID5 module."""                                   │
           │                                                                                             │
           │     def types(self):                                                                        │
           │         """(Optional) Defines the type declarations."""                                     │
           │         pass                                                                                │
           │                                                                                             │
           │     def locals(self):                                                                       │
           │         """(Optional) Defines the local variables and their types."""                       │
           │         pass                                                                                │
           │                                                                                             │
           │     def inputs(self):                                                                       │
           │         """(Optional) Defines the input variables and their types."""                       │
           │         pass                                                                                │
           │                                                                                             │
           │     def outputs(self):                                                                      │
           │         """(Optional) Defines the output variables and their types."""                      │
           │         pass                                                                                │
           │                                                                                             │
           │     def shared_vars(self):                                                                  │
           │         """(Optional) Defines the shared variables and their types."""                      │
           │         pass                                                                                │
           │                                                                                             │
           │     def instances(self):                                                                    │
           │         """(Optional) Defines the instances of other modules."""                            │
           │         pass                                                                                │
           │                                                                                             │
           │     def init(self):                                                                         │
           │         """(Optional) Defines how variables are initialized."""                             │
           │         pass                                                                                │
           │                                                                                             │
           │     def next(self):                                                                         │
           │         """(Optional) Defines the transition relation."""                                   │
           │         pass                                                                                │
           │                                                                                             │
           │     def specification(self):                                                                │
           │         """(Optional) Defines the specification in terms of invariant properties.           │
           │                                                                                             │
           │         Returns:                                                                            │
           │             bool: True if the specification is satisfied, False otherwise.                  │
           │         """                                                                                 │
           │         pass                                                                                │
           │                                                                                             │
           │     def proof(self):                                                                        │
           │         """(Optional) Defines the control block."""                                         │
           │         pass                                                                                │
           │                                                                                             │
           │ class DomeLightModule(Module):                                                              │
           │     def locals(self):                                                                       │
           │         self.light_on = bool                                                                │
           │         self.time = int                                                                     │
           │                                                                                             │
           │     def inputs(self):                                                                       │
           │         self.door_open = bool                                                               │
           │                                                                                             │
           │     def outputs(self):                                                                      │
           │         self.dome_light_status = bool                                                       │
           │                                                                                             │
           │     def init(self):                                                                         │
           │         self.light_on = False                                                               │
           │         self.time = 0                                                                       │
           │                                                                                             │
           │     def next(self):                                                                         │
           │         if self.door_open:                                                                  │
           │             self.light_on = True                                                            │
           │             self.time = 30                                                                  │
           │         else:                                                                               │
           │             if self.time > 0:                                                               │
           │                 self.time = self.time - 1                                                   │
           │                 self.light_on = True                                                        │
           │             else:                                                                           │
           │                 self.light_on = False                                                       │
           │                                                                                             │
           │     def specification(self):                                                                │
           │         return (self.door_open or (self.time > 0)) == self.light_on                         │
           │                                                                                             │
           │     def proof(self):                                                                        │
           │         pass  # As proof() is optional and specific implementation would be domain-specific │
           ╰─────────────────────────────────────────────────────────────────────────────────────────────╯
[22:43:53] ╭────────────────────────── 🤖 Repaired: ───────────────────────────╮                                                                                                                                  utils.py:24
           │ class Module(Module):                                             │
           │   def next(self):                                                 │
           │     ??                                                            │
           │                                                                   │
           │ class DomeLightModule(Module):                                    │
           │   def locals(self):                                               │
           │     self.light_on = bool                                          │
           │     self.time = int                                               │
           │                                                                   │
           │   def inputs(self):                                               │
           │     self.door_open = bool                                         │
           │                                                                   │
           │   def outputs(self):                                              │
           │     self.dome_light_status = bool                                 │
           │                                                                   │
           │   def init(self):                                                 │
           │     self.light_on = False                                         │
           │     self.time = 0                                                 │
           │                                                                   │
           │   def next(self):                                                 │
           │     if self.door_open:                                            │
           │       self.light_on = True                                        │
           │       self.time = 30                                              │
           │     else:                                                         │
           │       if (self.time > 0):                                         │
           │         self.time = (self.time - 1)                               │
           │         self.light_on = True                                      │
           │       else:                                                       │
           │         self.light_on = False                                     │
           │                                                                   │
           │   def specification(self):                                        │
           │     return ((self.door_open or (self.time > 0)) == self.light_on) │
           │                                                                   │
           │                                                                   │
           ╰───────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class Module(Module):                                                                                                                                                                              │
           │   def next(self):                                                                                                                                                                                  │
           │     ??                                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │   def locals(self):                                                                                                                                                                                │
           │     self.light_on = bool                                                                                                                                                                           │
           │     self.time = int                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.door_open = bool                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.dome_light_status = bool                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.light_on = False                                                                                                                                                                          │
           │     self.time = 0                                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if self.door_open:                                                                                                                                                                             │
           │       self.light_on = True                                                                                                                                                                         │
           │       self.time = 30                                                                                                                                                                               │
           │     else:                                                                                                                                                                                          │
           │       if (self.time > 0):                                                                                                                                                                          │
           │         self.time = (self.time - 1)                                                                                                                                                                │
           │         self.light_on = True                                                                                                                                                                       │
           │       else:                                                                                                                                                                                        │
           │         self.light_on = False                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ((self.door_open or (self.time > 0)) == self.light_on)                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Model the following feature for an automobile: A dome light that is turned on as soon as any door is opened. It stays on for 30 seconds after all doors are shut. Use the variable names         │
           │ light_on, door_open, time.                                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:44:04] ╭─────────────────────────────────────────────────────────────────────────────────────────── 🧠 Response: ───────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:42
           │ ```python                                                                                                                                                                                          │
           │ class Module:                                                                                                                                                                                      │
           │     """An abstract class to represent a UCLID5 module."""                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │     def types(self):                                                                                                                                                                               │
           │         """(Optional) Defines the type declarations."""                                                                                                                                            │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def locals(self):                                                                                                                                                                              │
           │         """(Optional) Defines the local variables and their types."""                                                                                                                              │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         """(Optional) Defines the input variables and their types."""                                                                                                                              │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         """(Optional) Defines the output variables and their types."""                                                                                                                             │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def shared_vars(self):                                                                                                                                                                         │
           │         """(Optional) Defines the shared variables and their types."""                                                                                                                             │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def instances(self):                                                                                                                                                                           │
           │         """(Optional) Defines the instances of other modules."""                                                                                                                                   │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         """(Optional) Defines how variables are initialized."""                                                                                                                                    │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         """(Optional) Defines the transition relation."""                                                                                                                                          │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         """(Optional) Defines the specification in terms of invariant properties.                                                                                                                  │
           │                                                                                                                                                                                                    │
           │         Returns:                                                                                                                                                                                   │
           │             bool: True if the specification is satisfied, False otherwise.                                                                                                                         │
           │         """                                                                                                                                                                                        │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │     def proof(self):                                                                                                                                                                               │
           │         """(Optional) Defines the control block."""                                                                                                                                                │
           │         pass                                                                                                                                                                                       │
           │                                                                                                                                                                                                    │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │     def locals(self):                                                                                                                                                                              │
           │         self.light_on = bool                                                                                                                                                                       │
           │         self.time = int                                                                                                                                                                            │
           │                                                                                                                                                                                                    │
           │     def inputs(self):                                                                                                                                                                              │
           │         self.door_open = bool                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │     def outputs(self):                                                                                                                                                                             │
           │         self.dome_light_status = bool                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def init(self):                                                                                                                                                                                │
           │         self.light_on = False                                                                                                                                                                      │
           │         self.time = 0                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def next(self):                                                                                                                                                                                │
           │         if self.door_open:                                                                                                                                                                         │
           │             self.light_on = True                                                                                                                                                                   │
           │             self.time = 30                                                                                                                                                                         │
           │         else:                                                                                                                                                                                      │
           │             if self.time > 0:                                                                                                                                                                      │
           │                 self.time -= 1                                                                                                                                                                     │
           │                 self.light_on = True                                                                                                                                                               │
           │             else:                                                                                                                                                                                  │
           │                 self.light_on = False                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │     def specification(self):                                                                                                                                                                       │
           │         return ((self.door_open or self.time > 0) == self.light_on)                                                                                                                                │
           │ ```                                                                                                                                                                                                │
           │ This code models a dome light in an automobile that turns on when any door is opened and remains on for 30 seconds after all doors are closed. The `DomeLightModule` inherits from the abstract    │
           │ class `Module` and defines the appropriate behavior through its methods.                                                                                                                           │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────────────── 🤖 Extracted: ──────────────────────────────────╮                                                                                                                  utils.py:24
           │                                                                                   │
           │ class Module:                                                                     │
           │     """An abstract class to represent a UCLID5 module."""                         │
           │                                                                                   │
           │     def types(self):                                                              │
           │         """(Optional) Defines the type declarations."""                           │
           │         pass                                                                      │
           │                                                                                   │
           │     def locals(self):                                                             │
           │         """(Optional) Defines the local variables and their types."""             │
           │         pass                                                                      │
           │                                                                                   │
           │     def inputs(self):                                                             │
           │         """(Optional) Defines the input variables and their types."""             │
           │         pass                                                                      │
           │                                                                                   │
           │     def outputs(self):                                                            │
           │         """(Optional) Defines the output variables and their types."""            │
           │         pass                                                                      │
           │                                                                                   │
           │     def shared_vars(self):                                                        │
           │         """(Optional) Defines the shared variables and their types."""            │
           │         pass                                                                      │
           │                                                                                   │
           │     def instances(self):                                                          │
           │         """(Optional) Defines the instances of other modules."""                  │
           │         pass                                                                      │
           │                                                                                   │
           │     def init(self):                                                               │
           │         """(Optional) Defines how variables are initialized."""                   │
           │         pass                                                                      │
           │                                                                                   │
           │     def next(self):                                                               │
           │         """(Optional) Defines the transition relation."""                         │
           │         pass                                                                      │
           │                                                                                   │
           │     def specification(self):                                                      │
           │         """(Optional) Defines the specification in terms of invariant properties. │
           │                                                                                   │
           │         Returns:                                                                  │
           │             bool: True if the specification is satisfied, False otherwise.        │
           │         """                                                                       │
           │         pass                                                                      │
           │                                                                                   │
           │     def proof(self):                                                              │
           │         """(Optional) Defines the control block."""                               │
           │         pass                                                                      │
           │                                                                                   │
           │ class DomeLightModule(Module):                                                    │
           │     def locals(self):                                                             │
           │         self.light_on = bool                                                      │
           │         self.time = int                                                           │
           │                                                                                   │
           │     def inputs(self):                                                             │
           │         self.door_open = bool                                                     │
           │                                                                                   │
           │     def outputs(self):                                                            │
           │         self.dome_light_status = bool                                             │
           │                                                                                   │
           │     def init(self):                                                               │
           │         self.light_on = False                                                     │
           │         self.time = 0                                                             │
           │                                                                                   │
           │     def next(self):                                                               │
           │         if self.door_open:                                                        │
           │             self.light_on = True                                                  │
           │             self.time = 30                                                        │
           │         else:                                                                     │
           │             if self.time > 0:                                                     │
           │                 self.time -= 1                                                    │
           │                 self.light_on = True                                              │
           │             else:                                                                 │
           │                 self.light_on = False                                             │
           │                                                                                   │
           │     def specification(self):                                                      │
           │         return ((self.door_open or self.time > 0) == self.light_on)               │
           ╰───────────────────────────────────────────────────────────────────────────────────╯
[22:44:05] ╭────────────────────────── 🤖 Repaired: ───────────────────────────╮                                                                                                                                  utils.py:24
           │ class Module(Module):                                             │
           │   def next(self):                                                 │
           │     ??                                                            │
           │                                                                   │
           │ class DomeLightModule(Module):                                    │
           │   def locals(self):                                               │
           │     self.light_on = bool                                          │
           │     self.time = int                                               │
           │                                                                   │
           │   def inputs(self):                                               │
           │     self.door_open = bool                                         │
           │                                                                   │
           │   def outputs(self):                                              │
           │     self.dome_light_status = bool                                 │
           │                                                                   │
           │   def init(self):                                                 │
           │     self.light_on = False                                         │
           │     self.time = 0                                                 │
           │                                                                   │
           │   def next(self):                                                 │
           │     if self.door_open:                                            │
           │       self.light_on = True                                        │
           │       self.time = 30                                              │
           │     else:                                                         │
           │       if (self.time > 0):                                         │
           │         self.time = (self.time - 1)                               │
           │         self.light_on = True                                      │
           │       else:                                                       │
           │         self.light_on = False                                     │
           │                                                                   │
           │   def specification(self):                                        │
           │     return ((self.door_open or (self.time > 0)) == self.light_on) │
           │                                                                   │
           │                                                                   │
           ╰───────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class Module(Module):                                                                                                                                                                              │
           │   def next(self):                                                                                                                                                                                  │
           │     ??                                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │ class DomeLightModule(Module):                                                                                                                                                                     │
           │   def locals(self):                                                                                                                                                                                │
           │     self.light_on = bool                                                                                                                                                                           │
           │     self.time = int                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.door_open = bool                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.dome_light_status = bool                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.light_on = False                                                                                                                                                                          │
           │     self.time = 0                                                                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if self.door_open:                                                                                                                                                                             │
           │       self.light_on = True                                                                                                                                                                         │
           │       self.time = 30                                                                                                                                                                               │
           │     else:                                                                                                                                                                                          │
           │       if (self.time > 0):                                                                                                                                                                          │
           │         self.time = (self.time - 1)                                                                                                                                                                │
           │         self.light_on = True                                                                                                                                                                       │
           │       else:                                                                                                                                                                                        │
           │         self.light_on = False                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ((self.door_open or (self.time > 0)) == self.light_on)                                                                                                                                  │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Model the following feature for an automobile: A dome light that is turned on as soon as any door is opened. It stays on for 30 seconds after all doors are shut. Use the variable names         │
           │ light_on, door_open, time.                                                                                                                                                                         │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:44:14] ╭──────────────────────────── 🧠 Response: ─────────────────────────────╮                                                                                                                              utils.py:42
           │ ```python                                                             │
           │ class Module:                                                         │
           │     """An abstract class to represent a UCLID5 module."""             │
           │                                                                       │
           │     def types(self):                                                  │
           │         pass                                                          │
           │                                                                       │
           │     def locals(self):                                                 │
           │         pass                                                          │
           │                                                                       │
           │     def inputs(self):                                                 │
           │         pass                                                          │
           │                                                                       │
           │     def outputs(self):                                                │
           │         pass                                                          │
           │                                                                       │
           │     def shared_vars(self):                                            │
           │         pass                                                          │
           │                                                                       │
           │     def instances(self):                                              │
           │         pass                                                          │
           │                                                                       │
           │     def init(self):                                                   │
           │         pass                                                          │
           │                                                                       │
           │     def next(self):                                                   │
           │         pass                                                          │
           │                                                                       │
           │     def specification(self):                                          │
           │         pass                                                          │
           │                                                                       │
           │     def proof(self):                                                  │
           │         pass                                                          │
           │                                                                       │
           │ class DomeLightModule(Module):                                        │
           │     def locals(self):                                                 │
           │         self.light_on = bool                                          │
           │         self.time = int                                               │
           │                                                                       │
           │     def inputs(self):                                                 │
           │         self.door_open = bool                                         │
           │                                                                       │
           │     def outputs(self):                                                │
           │         self.dome_light_status = bool                                 │
           │                                                                       │
           │     def init(self):                                                   │
           │         self.light_on = False                                         │
           │         self.time = 0                                                 │
           │                                                                       │
           │     def next(self):                                                   │
           │         if self.door_open:                                            │
           │             self.light_on = True                                      │
           │             self.time = 30                                            │
           │         else:                                                         │
           │             if self.time > 0:                                         │
           │                 self.time -= 1                                        │
           │                 self.light_on = True                                  │
           │             else:                                                     │
           │                 self.light_on = False                                 │
           │                                                                       │
           │     def specification(self):                                          │
           │         return ((self.door_open or (self.time > 0)) == self.light_on) │
           │                                                                       │
           │ # Example usage:                                                      │
           │ # dome_light = DomeLightModule()                                      │
           │ # dome_light.init()                                                   │
           │ # dome_light.inputs()                                                 │
           │ # dome_light.next()                                                   │
           │ # print(dome_light.specification())                                   │
           │ ```                                                                   │
           ╰───────────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────── 🤖 Extracted: ────────────────────────────╮                                                                                                                              utils.py:24
           │                                                                       │
           │ class Module:                                                         │
           │     """An abstract class to represent a UCLID5 module."""             │
           │                                                                       │
           │     def types(self):                                                  │
           │         pass                                                          │
           │                                                                       │
           │     def locals(self):                                                 │
           │         pass                                                          │
           │                                                                       │
           │     def inputs(self):                                                 │
           │         pass                                                          │
           │                                                                       │
           │     def outputs(self):                                                │
           │         pass                                                          │
           │                                                                       │
           │     def shared_vars(self):                                            │
           │         pass                                                          │
           │                                                                       │
           │     def instances(self):                                              │
           │         pass                                                          │
           │                                                                       │
           │     def init(self):                                                   │
           │         pass                                                          │
           │                                                                       │
           │     def next(self):                                                   │
           │         pass                                                          │
           │                                                                       │
           │     def specification(self):                                          │
           │         pass                                                          │
           │                                                                       │
           │     def proof(self):                                                  │
           │         pass                                                          │
           │                                                                       │
           │ class DomeLightModule(Module):                                        │
           │     def locals(self):                                                 │
           │         self.light_on = bool                                          │
           │         self.time = int                                               │
           │                                                                       │
           │     def inputs(self):                                                 │
           │         self.door_open = bool                                         │
           │                                                                       │
           │     def outputs(self):                                                │
           │         self.dome_light_status = bool                                 │
           │                                                                       │
           │     def init(self):                                                   │
           │         self.light_on = False                                         │
           │         self.time = 0                                                 │
           │                                                                       │
           │     def next(self):                                                   │
           │         if self.door_open:                                            │
           │             self.light_on = True                                      │
           │             self.time = 30                                            │
           │         else:                                                         │
           │             if self.time > 0:                                         │
           │                 self.time -= 1                                        │
           │                 self.light_on = True                                  │
           │             else:                                                     │
           │                 self.light_on = False                                 │
           │                                                                       │
           │     def specification(self):                                          │
           │         return ((self.door_open or (self.time > 0)) == self.light_on) │
           │                                                                       │
           │ # Example usage:                                                      │
           │ # dome_light = DomeLightModule()                                      │
           │ # dome_light.init()                                                   │
           │ # dome_light.inputs()                                                 │
           │ # dome_light.next()                                                   │
           │ # print(dome_light.specification())                                   │
           ╰───────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────── 🤖 Repaired: ───────────────────────────╮                                                                                                                                  utils.py:24
           │ class DomeLightModule(Module):                                    │
           │   def locals(self):                                               │
           │     self.light_on = bool                                          │
           │     self.time = int                                               │
           │                                                                   │
           │   def inputs(self):                                               │
           │     self.door_open = bool                                         │
           │                                                                   │
           │   def outputs(self):                                              │
           │     self.dome_light_status = bool                                 │
           │                                                                   │
           │   def init(self):                                                 │
           │     self.light_on = False                                         │
           │     self.time = 0                                                 │
           │                                                                   │
           │   def next(self):                                                 │
           │     if self.door_open:                                            │
           │       self.light_on = True                                        │
           │       self.time = 30                                              │
           │     else:                                                         │
           │       if (self.time > 0):                                         │
           │         self.time = (self.time - 1)                               │
           │         self.light_on = True                                      │
           │       else:                                                       │
           │         self.light_on = False                                     │
           │                                                                   │
           │   def specification(self):                                        │
           │     return ((self.door_open or (self.time > 0)) == self.light_on) │
           │                                                                   │
           │                                                                   │
           ╰───────────────────────────────────────────────────────────────────╯
           ╭────── 🤖 Stats: ───────╮                                                                                                                                                                             utils.py:24
           │ Original Lines: 39     │
           │ Final Lines:    29     │
           │ LLM Calls:      5      │
           │ LLM Time:       50.96s │
           │ Repair Time:    2.55s  │
           ╰────────────────────────╯
