[22:21:20] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > Consider the transition systems of two traffic lights for nonintersecting (i.e., parallel) roads. It is assumed that the traffic lights switch completely independent of each other. For         │
           │ example, the traffic lights may be controlled by pedestrians who would like to cross the road. Model a parallel composition of two traffic lights. Model each traffic light as a simple transition │
           │ system with two states, one state modeling a red light, the other one modeling a green light.  In principle, any form of interlocking of the "actions" of the two traffic lights is possible. For  │
           │ instance, in the initial state where both traffic lights are red, there is a non-deterministic choice between which of the lights turns green. Note that this nondeterminism is descriptive, and   │
           │ does not model a scheduling problem between the traffic lights (although it may seem so). Use the variable names red1, green1, red2 and green 2.                                                   │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:21:30] ╭─────────────────────────────────────────── 🧠 Response: ───────────────────────────────────────────╮                                                                                                 utils.py:42
           │ ```python                                                                                          │
           │ class TrafficLightModule(Module):                                                                  │
           │     def locals(self):                                                                              │
           │         # Define two binary state variables for each traffic light                                 │
           │         self.red1 = Boolean()                                                                      │
           │         self.green1 = Boolean()                                                                    │
           │         self.red2 = Boolean()                                                                      │
           │         self.green2 = Boolean()                                                                    │
           │                                                                                                    │
           │     def init(self):                                                                                │
           │         # Initially, both traffic lights are at red                                                │
           │         self.red1 = True                                                                           │
           │         self.green1 = False                                                                        │
           │         self.red2 = True                                                                           │
           │         self.green2 = False                                                                        │
           │                                                                                                    │
           │     def next(self):                                                                                │
           │         # Non-deterministic transitions between red and green for each traffic light               │
           │         if self.red1:                                                                              │
           │             self.green1 = True                                                                     │
           │             self.red1 = False                                                                      │
           │         else:                                                                                      │
           │             self.green1 = False                                                                    │
           │             self.red1 = True                                                                       │
           │                                                                                                    │
           │         if self.red2:                                                                              │
           │             self.green2 = True                                                                     │
           │             self.red2 = False                                                                      │
           │         else:                                                                                      │
           │             self.green2 = False                                                                    │
           │             self.red2 = True                                                                       │
           │                                                                                                    │
           │     def specification(self):                                                                       │
           │         # Specification to ensure mutual exclusivity of red and green states in each traffic light │
           │         spec1 = (self.red1 != self.green1)                                                         │
           │         spec2 = (self.red2 != self.green2)                                                         │
           │         return spec1 and spec2                                                                     │
           │                                                                                                    │
           │     def proof(self):                                                                               │
           │         # Demonstrate the properties using proofs (assumed example control block)                  │
           │         self.induction(1)  # Example induction method call                                         │
           │ ```                                                                                                │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────────────────────── 🤖 Extracted: ───────────────────────────────────────────╮                                                                                                 utils.py:24
           │                                                                                                    │
           │ class TrafficLightModule(Module):                                                                  │
           │     def locals(self):                                                                              │
           │         # Define two binary state variables for each traffic light                                 │
           │         self.red1 = Boolean()                                                                      │
           │         self.green1 = Boolean()                                                                    │
           │         self.red2 = Boolean()                                                                      │
           │         self.green2 = Boolean()                                                                    │
           │                                                                                                    │
           │     def init(self):                                                                                │
           │         # Initially, both traffic lights are at red                                                │
           │         self.red1 = True                                                                           │
           │         self.green1 = False                                                                        │
           │         self.red2 = True                                                                           │
           │         self.green2 = False                                                                        │
           │                                                                                                    │
           │     def next(self):                                                                                │
           │         # Non-deterministic transitions between red and green for each traffic light               │
           │         if self.red1:                                                                              │
           │             self.green1 = True                                                                     │
           │             self.red1 = False                                                                      │
           │         else:                                                                                      │
           │             self.green1 = False                                                                    │
           │             self.red1 = True                                                                       │
           │                                                                                                    │
           │         if self.red2:                                                                              │
           │             self.green2 = True                                                                     │
           │             self.red2 = False                                                                      │
           │         else:                                                                                      │
           │             self.green2 = False                                                                    │
           │             self.red2 = True                                                                       │
           │                                                                                                    │
           │     def specification(self):                                                                       │
           │         # Specification to ensure mutual exclusivity of red and green states in each traffic light │
           │         spec1 = (self.red1 != self.green1)                                                         │
           │         spec2 = (self.red2 != self.green2)                                                         │
           │         return spec1 and spec2                                                                     │
           │                                                                                                    │
           │     def proof(self):                                                                               │
           │         # Demonstrate the properties using proofs (assumed example control block)                  │
           │         self.induction(1)  # Example induction method call                                         │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────╯
[22:21:31] ╭────────── 🤖 Repaired: ───────────╮                                                                                                                                                                  utils.py:24
           │ class TrafficLightModule(Module): │
           │   def locals(self):               │
           │     self.red1 = bool              │
           │     self.green1 = bool            │
           │     self.red2 = bool              │
           │     self.green2 = bool            │
           │                                   │
           │   def init(self):                 │
           │     self.red1 = True              │
           │     self.green1 = False           │
           │     self.red2 = True              │
           │     self.green2 = False           │
           │                                   │
           │   def next(self):                 │
           │     if self.red1:                 │
           │       self.green1 = True          │
           │       self.red1 = False           │
           │     else:                         │
           │       self.green1 = False         │
           │       self.red1 = True            │
           │     if self.red2:                 │
           │       self.green2 = True          │
           │       self.red2 = False           │
           │     else:                         │
           │       self.green2 = False         │
           │       self.red2 = True            │
           │                                   │
           │   def proof(self):                │
           │     self.induction(1)             │
           │                                   │
           │                                   │
           ╰───────────────────────────────────╯
           ╭────── 🤖 Stats: ───────╮                                                                                                                                                                             utils.py:24
           │ Original Lines: 41     │
           │ Final Lines:    30     │
           │ LLM Calls:      1      │
           │ LLM Time:       10.86s │
           │ Repair Time:    0.41s  │
           ╰────────────────────────╯
