[20:54:01] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > Consider the following leader election algorithm: For n ∈ N, n processes P1,...,Pn are located in a ring topology where each process is connected by an unidirectional channel to its neighbor   │
           │ in a clockwise manner. To distinguish the processes, each process is assigned a unique identifier id in {1, . . . , n}. The aim is to elect the process with the highest identifier as the leader  │
           │ within the ring. Therefore each process executes the following algorithm: send (id); while (true) do receive (m); if (m = id) then stop; if (m > id) then send (m); od Model the leader election   │
           │ protocol for n processes as a channel system. Use the variable names m, id.                                                                                                                        │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:54:03] ╭──────────────────── 🧠 Response: ─────────────────────╮                                                                                                                                              utils.py:42
           │ from typing import List, Union                        │
           │                                                       │
           │ class LeaderElection(Module):                         │
           │     def types(self):                                  │
           │         self.Message = Union[Integer(), BitVector(8)] │
           │                                                       │
           │     def locals(self):                                 │
           │         self.id = Integer()                           │
           │         self.m = self.Message                         │
           │                                                       │
           │     def inputs(self):                                 │
           │         self.channel_in = self.Message                │
           │                                                       │
           │     def outputs(self):                                │
           │         self.channel_out = self.Message               │
           │                                                       │
           │     def init(self):                                   │
           │         self.channel_out = self.id                    │
           │                                                       │
           │     def next(self):                                   │
           │         if self.m == self.id:                         │
           │             self.stop()                               │
           │         if self.m > self.id:                          │
           │             self.channel_out = self.m                 │
           │ ```                                                   │
           ╰───────────────────────────────────────────────────────╯
           ╭──────────────────── 🤖 Extracted: ────────────────────╮                                                                                                                                              utils.py:24
           │                                                       │
           │ from typing import List, Union                        │
           │                                                       │
           │ class LeaderElection(Module):                         │
           │     def types(self):                                  │
           │         self.Message = Union[Integer(), BitVector(8)] │
           │                                                       │
           │     def locals(self):                                 │
           │         self.id = Integer()                           │
           │         self.m = self.Message                         │
           │                                                       │
           │     def inputs(self):                                 │
           │         self.channel_in = self.Message                │
           │                                                       │
           │     def outputs(self):                                │
           │         self.channel_out = self.Message               │
           │                                                       │
           │     def init(self):                                   │
           │         self.channel_out = self.id                    │
           │                                                       │
           │     def next(self):                                   │
           │         if self.m == self.id:                         │
           │             self.stop()                               │
           │         if self.m > self.id:                          │
           │             self.channel_out = self.m                 │
           ╰───────────────────────────────────────────────────────╯
           ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       ??                            │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class LeaderElection(Module):                                                                                                                                                                      │
           │   def types(self):                                                                                                                                                                                 │
           │     self.Message = int                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.id = int                                                                                                                                                                                  │
           │     self.m = self.Message                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.channel_in = self.Message                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.channel_out = self.Message                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.channel_out = self.id                                                                                                                                                                     │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if (self.m == self.id):                                                                                                                                                                        │
           │       ??                                                                                                                                                                                           │
           │     if (self.m > self.id):                                                                                                                                                                         │
           │       self.channel_out = self.m                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the following leader election algorithm: For n ∈ N, n processes P1,...,Pn are located in a ring topology where each process is connected by an unidirectional channel to its neighbor   │
           │ in a clockwise manner. To distinguish the processes, each process is assigned a unique identifier id in {1, . . . , n}. The aim is to elect the process with the highest identifier as the leader  │
           │ within the ring. Therefore each process executes the following algorithm: send (id); while (true) do receive (m); if (m = id) then stop; if (m > id) then send (m); od Model the leader election   │
           │ protocol for n processes as a channel system. Use the variable names m, id.                                                                                                                        │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:54:05] ╭───────────── 🧠 Response: ──────────────╮                                                                                                                                                            utils.py:42
           │ class LeaderElection(Module):           │
           │     def types(self):                    │
           │         self.Message = int              │
           │                                         │
           │     def locals(self):                   │
           │         self.id = int                   │
           │         self.m = self.Message           │
           │                                         │
           │     def inputs(self):                   │
           │         self.channel_in = self.Message  │
           │                                         │
           │     def outputs(self):                  │
           │         self.channel_out = self.Message │
           │                                         │
           │     def init(self):                     │
           │         self.channel_out = self.id      │
           │                                         │
           │     def next(self):                     │
           │         if (self.m == self.id):         │
           │             stop()                      │
           │         if (self.m > self.id):          │
           │             self.channel_out = self.m   │
           │ ```                                     │
           ╰─────────────────────────────────────────╯
           ╭───────────── 🤖 Extracted: ─────────────╮                                                                                                                                                            utils.py:24
           │                                         │
           │ class LeaderElection(Module):           │
           │     def types(self):                    │
           │         self.Message = int              │
           │                                         │
           │     def locals(self):                   │
           │         self.id = int                   │
           │         self.m = self.Message           │
           │                                         │
           │     def inputs(self):                   │
           │         self.channel_in = self.Message  │
           │                                         │
           │     def outputs(self):                  │
           │         self.channel_out = self.Message │
           │                                         │
           │     def init(self):                     │
           │         self.channel_out = self.id      │
           │                                         │
           │     def next(self):                     │
           │         if (self.m == self.id):         │
           │             stop()                      │
           │         if (self.m > self.id):          │
           │             self.channel_out = self.m   │
           ╰─────────────────────────────────────────╯
[20:54:06] ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       ??                            │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class LeaderElection(Module):                                                                                                                                                                      │
           │   def types(self):                                                                                                                                                                                 │
           │     self.Message = int                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.id = int                                                                                                                                                                                  │
           │     self.m = self.Message                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.channel_in = self.Message                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.channel_out = self.Message                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.channel_out = self.id                                                                                                                                                                     │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if (self.m == self.id):                                                                                                                                                                        │
           │       ??                                                                                                                                                                                           │
           │     if (self.m > self.id):                                                                                                                                                                         │
           │       self.channel_out = self.m                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the following leader election algorithm: For n ∈ N, n processes P1,...,Pn are located in a ring topology where each process is connected by an unidirectional channel to its neighbor   │
           │ in a clockwise manner. To distinguish the processes, each process is assigned a unique identifier id in {1, . . . , n}. The aim is to elect the process with the highest identifier as the leader  │
           │ within the ring. Therefore each process executes the following algorithm: send (id); while (true) do receive (m); if (m = id) then stop; if (m > id) then send (m); od Model the leader election   │
           │ protocol for n processes as a channel system. Use the variable names m, id.                                                                                                                        │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:54:08] ╭─────────── 🧠 Response: ────────────╮                                                                                                                                                                utils.py:42
           │ ```python                           │
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │         halt()                      │
           │     if (self.m > self.id):          │
           │         self.channel_out = self.m   │
           │ ```                                 │
           ╰─────────────────────────────────────╯
           ╭─────────── 🤖 Extracted: ───────────╮                                                                                                                                                                utils.py:24
           │                                     │
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │         halt()                      │
           │     if (self.m > self.id):          │
           │         self.channel_out = self.m   │
           ╰─────────────────────────────────────╯
           ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       ??                            │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class LeaderElection(Module):                                                                                                                                                                      │
           │   def types(self):                                                                                                                                                                                 │
           │     self.Message = int                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.id = int                                                                                                                                                                                  │
           │     self.m = self.Message                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.channel_in = self.Message                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.channel_out = self.Message                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.channel_out = self.id                                                                                                                                                                     │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if (self.m == self.id):                                                                                                                                                                        │
           │       ??                                                                                                                                                                                           │
           │     if (self.m > self.id):                                                                                                                                                                         │
           │       self.channel_out = self.m                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the following leader election algorithm: For n ∈ N, n processes P1,...,Pn are located in a ring topology where each process is connected by an unidirectional channel to its neighbor   │
           │ in a clockwise manner. To distinguish the processes, each process is assigned a unique identifier id in {1, . . . , n}. The aim is to elect the process with the highest identifier as the leader  │
           │ within the ring. Therefore each process executes the following algorithm: send (id); while (true) do receive (m); if (m = id) then stop; if (m > id) then send (m); od Model the leader election   │
           │ protocol for n processes as a channel system. Use the variable names m, id.                                                                                                                        │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:54:10] ╭───────────── 🧠 Response: ──────────────╮                                                                                                                                                            utils.py:42
           │ class LeaderElection(Module):           │
           │     def types(self):                    │
           │         self.Message = int              │
           │                                         │
           │     def locals(self):                   │
           │         self.id = int                   │
           │         self.m = self.Message           │
           │                                         │
           │     def inputs(self):                   │
           │         self.channel_in = self.Message  │
           │                                         │
           │     def outputs(self):                  │
           │         self.channel_out = self.Message │
           │                                         │
           │     def init(self):                     │
           │         self.channel_out = self.id      │
           │                                         │
           │     def next(self):                     │
           │         if (self.m == self.id):         │
           │             stop()                      │
           │         if (self.m > self.id):          │
           │             self.channel_out = self.m   │
           │ ```                                     │
           ╰─────────────────────────────────────────╯
           ╭───────────── 🤖 Extracted: ─────────────╮                                                                                                                                                            utils.py:24
           │                                         │
           │ class LeaderElection(Module):           │
           │     def types(self):                    │
           │         self.Message = int              │
           │                                         │
           │     def locals(self):                   │
           │         self.id = int                   │
           │         self.m = self.Message           │
           │                                         │
           │     def inputs(self):                   │
           │         self.channel_in = self.Message  │
           │                                         │
           │     def outputs(self):                  │
           │         self.channel_out = self.Message │
           │                                         │
           │     def init(self):                     │
           │         self.channel_out = self.id      │
           │                                         │
           │     def next(self):                     │
           │         if (self.m == self.id):         │
           │             stop()                      │
           │         if (self.m > self.id):          │
           │             self.channel_out = self.m   │
           ╰─────────────────────────────────────────╯
           ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       ??                            │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class LeaderElection(Module):                                                                                                                                                                      │
           │   def types(self):                                                                                                                                                                                 │
           │     self.Message = int                                                                                                                                                                             │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.id = int                                                                                                                                                                                  │
           │     self.m = self.Message                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def inputs(self):                                                                                                                                                                                │
           │     self.channel_in = self.Message                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def outputs(self):                                                                                                                                                                               │
           │     self.channel_out = self.Message                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.channel_out = self.id                                                                                                                                                                     │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     if (self.m == self.id):                                                                                                                                                                        │
           │       ??                                                                                                                                                                                           │
           │     if (self.m > self.id):                                                                                                                                                                         │
           │       self.channel_out = self.m                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the following leader election algorithm: For n ∈ N, n processes P1,...,Pn are located in a ring topology where each process is connected by an unidirectional channel to its neighbor   │
           │ in a clockwise manner. To distinguish the processes, each process is assigned a unique identifier id in {1, . . . , n}. The aim is to elect the process with the highest identifier as the leader  │
           │ within the ring. Therefore each process executes the following algorithm: send (id); while (true) do receive (m); if (m = id) then stop; if (m > id) then send (m); od Model the leader election   │
           │ protocol for n processes as a channel system. Use the variable names m, id.                                                                                                                        │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:54:12] ╭─────────── 🧠 Response: ────────────╮                                                                                                                                                                utils.py:42
           │ ```python                           │
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       stop()                        │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           │ ```                                 │
           ╰─────────────────────────────────────╯
           ╭─────────── 🤖 Extracted: ───────────╮                                                                                                                                                                utils.py:24
           │                                     │
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       stop()                        │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           ╰─────────────────────────────────────╯
           ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class LeaderElection(Module):       │
           │   def types(self):                  │
           │     self.Message = int              │
           │                                     │
           │   def locals(self):                 │
           │     self.id = int                   │
           │     self.m = self.Message           │
           │                                     │
           │   def inputs(self):                 │
           │     self.channel_in = self.Message  │
           │                                     │
           │   def outputs(self):                │
           │     self.channel_out = self.Message │
           │                                     │
           │   def init(self):                   │
           │     self.channel_out = self.id      │
           │                                     │
           │   def next(self):                   │
           │     if (self.m == self.id):         │
           │       ??                            │
           │     if (self.m > self.id):          │
           │       self.channel_out = self.m     │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭────── 🤖 Stats: ───────╮                                                                                                                                                                             utils.py:24
           │ Original Lines: 25     │
           │ Final Lines:    23     │
           │ LLM Calls:      5      │
           │ LLM Time:       10.19s │
           │ Repair Time:    1.43s  │
           ╰────────────────────────╯
