[20:49:33] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > Model a design of a beverage vending machine. The machine can either deliver beer or soda. It counts the number of soda and beer bottles and returns inserted coins if the vending machine is    │
           │ empty. The vending machine is represented by the two locations start and select, and has variables that store the number of soda bottles (nsoda), and the number of beer bottles (nbeer). The      │
           │ following conditional transitions model the insertion of a coin and refilling the vending machine: start --(true:coin)-> select start --(true:refill)-> start  Labels of conditional transitions   │
           │ are of the form (g : a ) where g is a Boolean condition (called guard), and a is an action that is possible once g holds. As the condition for both conditional transitions above always holds,    │
           │ the action coin is always enabled in the starting location. To keep things simple, we assume that by refill both storages are entirely refilled. The following transitions model that soda (or     │
           │ beer) can be obtained if there is some soda (or beer) left in the vending machine: select --(nsoda > 0:sget)-> start select --(nbeer > 0:bget)-> start Finally, the vending machine automatically  │
           │ switches to the initial start location while returning the inserted coin once there are no bottles left: select --(nsoda=0 & nbeer=0: ret_coin) -> start Let the maximum capacity of both bottle   │
           │ repositories be max. The insertion of a coin (by action coin) leaves the number of bottles unchanged. The same applies when a coin is returned (by action ret coin). The effect of the other       │
           │ actions is as follows: refill : nsoda:=max & nbeer:=max sget: nsoda:=nsoda-1 bget: nbeer:=nbeer-1 You may use boolean variables to indicate when an action is enabled. Use the variable names      │
           │ nsoda, nbeer, sget, bget, refill, coin.                                                                                                                                                            │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:36] ╭────────────────────────────────── 🧠 Response: ───────────────────────────────────╮                                                                                                                  utils.py:42
           │ class VendingMachine(Module):                                                     │
           │     def types(self):                                                              │
           │         self.nsoda = BitVector(8)                                                 │
           │         self.nbeer = BitVector(8)                                                 │
           │         self.sget = Boolean()                                                     │
           │         self.bget = Boolean()                                                     │
           │         self.refill = Boolean()                                                   │
           │         self.coin = Boolean()                                                     │
           │         self.ret_coin = Boolean()                                                 │
           │                                                                                   │
           │     def locals(self):                                                             │
           │         self.max = 5                                                              │
           │                                                                                   │
           │     def init(self):                                                               │
           │         self.nsoda = self.max                                                     │
           │         self.nbeer = self.max                                                     │
           │                                                                                   │
           │     def next(self):                                                               │
           │         self.coin = True                                                          │
           │         self.ret_coin = (self.nsoda == 0) & (self.nbeer == 0)                     │
           │                                                                                   │
           │         if self.coin:                                                             │
           │             # Inserting a coin                                                    │
           │             pass                                                                  │
           │                                                                                   │
           │         if self.ret_coin:                                                         │
           │             # Returning the inserted coin                                         │
           │             pass                                                                  │
           │                                                                                   │
           │         if self.sget:                                                             │
           │             self.nsoda = self.nsoda - 1                                           │
           │                                                                                   │
           │         if self.bget:                                                             │
           │             self.nbeer = self.nbeer - 1                                           │
           │                                                                                   │
           │         if self.refill:                                                           │
           │             self.nsoda = self.max                                                 │
           │             self.nbeer = self.max                                                 │
           │                                                                                   │
           │     def specification(self):                                                      │
           │         return True  # No specific specification for vending machine logic needed │
           │                                                                                   │
           │     def proof(self):                                                              │
           │         induction(1)                                                              │
           │ ```                                                                               │
           ╰───────────────────────────────────────────────────────────────────────────────────╯
           ╭────────────────────────────────── 🤖 Extracted: ──────────────────────────────────╮                                                                                                                  utils.py:24
           │                                                                                   │
           │ class VendingMachine(Module):                                                     │
           │     def types(self):                                                              │
           │         self.nsoda = BitVector(8)                                                 │
           │         self.nbeer = BitVector(8)                                                 │
           │         self.sget = Boolean()                                                     │
           │         self.bget = Boolean()                                                     │
           │         self.refill = Boolean()                                                   │
           │         self.coin = Boolean()                                                     │
           │         self.ret_coin = Boolean()                                                 │
           │                                                                                   │
           │     def locals(self):                                                             │
           │         self.max = 5                                                              │
           │                                                                                   │
           │     def init(self):                                                               │
           │         self.nsoda = self.max                                                     │
           │         self.nbeer = self.max                                                     │
           │                                                                                   │
           │     def next(self):                                                               │
           │         self.coin = True                                                          │
           │         self.ret_coin = (self.nsoda == 0) & (self.nbeer == 0)                     │
           │                                                                                   │
           │         if self.coin:                                                             │
           │             # Inserting a coin                                                    │
           │             pass                                                                  │
           │                                                                                   │
           │         if self.ret_coin:                                                         │
           │             # Returning the inserted coin                                         │
           │             pass                                                                  │
           │                                                                                   │
           │         if self.sget:                                                             │
           │             self.nsoda = self.nsoda - 1                                           │
           │                                                                                   │
           │         if self.bget:                                                             │
           │             self.nbeer = self.nbeer - 1                                           │
           │                                                                                   │
           │         if self.refill:                                                           │
           │             self.nsoda = self.max                                                 │
           │             self.nbeer = self.max                                                 │
           │                                                                                   │
           │     def specification(self):                                                      │
           │         return True  # No specific specification for vending machine logic needed │
           │                                                                                   │
           │     def proof(self):                                                              │
           │         induction(1)                                                              │
           ╰───────────────────────────────────────────────────────────────────────────────────╯
[20:49:37] ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class VendingMachine(Module):       │
           │   def locals(self):                 │
           │     self.bget = bool                │
           │     self.coin = bool                │
           │     self.max = int                  │
           │     self.nbeer = int                │
           │     self.nsoda = int                │
           │     self.refill = bool              │
           │     self.ret_coin = bool            │
           │     self.sget = bool                │
           │                                     │
           │   def init(self):                   │
           │     self.nsoda = self.max           │
           │     self.nbeer = self.max           │
           │                                     │
           │   def next(self):                   │
           │     self.coin = True                │
           │     self.ret_coin = ??              │
           │     if self.coin:                   │
           │       ??                            │
           │     if self.ret_coin:               │
           │       ??                            │
           │     if self.sget:                   │
           │       self.nsoda = (self.nsoda - 1) │
           │     if self.bget:                   │
           │       self.nbeer = (self.nbeer - 1) │
           │     if self.refill:                 │
           │       self.nsoda = self.max         │
           │       self.nbeer = self.max         │
           │                                     │
           │   def proof(self):                  │
           │     self.induction(1)               │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class VendingMachine(Module):                                                                                                                                                                      │
           │   def locals(self):                                                                                                                                                                                │
           │     self.bget = bool                                                                                                                                                                               │
           │     self.coin = bool                                                                                                                                                                               │
           │     self.max = int                                                                                                                                                                                 │
           │     self.nbeer = int                                                                                                                                                                               │
           │     self.nsoda = int                                                                                                                                                                               │
           │     self.refill = bool                                                                                                                                                                             │
           │     self.ret_coin = bool                                                                                                                                                                           │
           │     self.sget = bool                                                                                                                                                                               │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.nsoda = self.max                                                                                                                                                                          │
           │     self.nbeer = self.max                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.coin = True                                                                                                                                                                               │
           │     self.ret_coin = ??                                                                                                                                                                             │
           │     if self.coin:                                                                                                                                                                                  │
           │       ??                                                                                                                                                                                           │
           │     if self.ret_coin:                                                                                                                                                                              │
           │       ??                                                                                                                                                                                           │
           │     if self.sget:                                                                                                                                                                                  │
           │       self.nsoda = (self.nsoda - 1)                                                                                                                                                                │
           │     if self.bget:                                                                                                                                                                                  │
           │       self.nbeer = (self.nbeer - 1)                                                                                                                                                                │
           │     if self.refill:                                                                                                                                                                                │
           │       self.nsoda = self.max                                                                                                                                                                        │
           │       self.nbeer = self.max                                                                                                                                                                        │
           │                                                                                                                                                                                                    │
           │   def proof(self):                                                                                                                                                                                 │
           │     self.induction(1)                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Model a design of a beverage vending machine. The machine can either deliver beer or soda. It counts the number of soda and beer bottles and returns inserted coins if the vending machine is    │
           │ empty. The vending machine is represented by the two locations start and select, and has variables that store the number of soda bottles (nsoda), and the number of beer bottles (nbeer). The      │
           │ following conditional transitions model the insertion of a coin and refilling the vending machine: start --(true:coin)-> select start --(true:refill)-> start  Labels of conditional transitions   │
           │ are of the form (g : a ) where g is a Boolean condition (called guard), and a is an action that is possible once g holds. As the condition for both conditional transitions above always holds,    │
           │ the action coin is always enabled in the starting location. To keep things simple, we assume that by refill both storages are entirely refilled. The following transitions model that soda (or     │
           │ beer) can be obtained if there is some soda (or beer) left in the vending machine: select --(nsoda > 0:sget)-> start select --(nbeer > 0:bget)-> start Finally, the vending machine automatically  │
           │ switches to the initial start location while returning the inserted coin once there are no bottles left: select --(nsoda=0 & nbeer=0: ret_coin) -> start Let the maximum capacity of both bottle   │
           │ repositories be max. The insertion of a coin (by action coin) leaves the number of bottles unchanged. The same applies when a coin is returned (by action ret coin). The effect of the other       │
           │ actions is as follows: refill : nsoda:=max & nbeer:=max sget: nsoda:=nsoda-1 bget: nbeer:=nbeer-1 You may use boolean variables to indicate when an action is enabled. Use the variable names      │
           │ nsoda, nbeer, sget, bget, refill, coin.                                                                                                                                                            │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:40] ╭───────────────────── 🧠 Response: ──────────────────────╮                                                                                                                                            utils.py:42
           │ class VendingMachine(Module):                           │
           │   def locals(self):                                     │
           │     self.bget = bool                                    │
           │     self.coin = bool                                    │
           │     self.max = int                                      │
           │     self.nbeer = int                                    │
           │     self.nsoda = int                                    │
           │     self.refill = bool                                  │
           │     self.ret_coin = bool                                │
           │     self.sget = bool                                    │
           │                                                         │
           │   def init(self):                                       │
           │     self.nsoda = self.max                               │
           │     self.nbeer = self.max                               │
           │                                                         │
           │   def next(self):                                       │
           │     self.coin = True                                    │
           │     self.ret_coin = self.nsoda == 0 and self.nbeer == 0 │
           │     if self.coin:                                       │
           │       pass                                              │
           │     if self.ret_coin:                                   │
           │       pass                                              │
           │     if self.sget:                                       │
           │       self.nsoda = (self.nsoda - 1)                     │
           │     if self.bget:                                       │
           │       self.nbeer = (self.nbeer - 1)                     │
           │     if self.refill:                                     │
           │       self.nsoda = self.max                             │
           │       self.nbeer = self.max                             │
           │                                                         │
           │   def proof(self):                                      │
           │     self.induction(1)                                   │
           │ ```                                                     │
           ╰─────────────────────────────────────────────────────────╯
           ╭───────────────────── 🤖 Extracted: ─────────────────────╮                                                                                                                                            utils.py:24
           │                                                         │
           │ class VendingMachine(Module):                           │
           │   def locals(self):                                     │
           │     self.bget = bool                                    │
           │     self.coin = bool                                    │
           │     self.max = int                                      │
           │     self.nbeer = int                                    │
           │     self.nsoda = int                                    │
           │     self.refill = bool                                  │
           │     self.ret_coin = bool                                │
           │     self.sget = bool                                    │
           │                                                         │
           │   def init(self):                                       │
           │     self.nsoda = self.max                               │
           │     self.nbeer = self.max                               │
           │                                                         │
           │   def next(self):                                       │
           │     self.coin = True                                    │
           │     self.ret_coin = self.nsoda == 0 and self.nbeer == 0 │
           │     if self.coin:                                       │
           │       pass                                              │
           │     if self.ret_coin:                                   │
           │       pass                                              │
           │     if self.sget:                                       │
           │       self.nsoda = (self.nsoda - 1)                     │
           │     if self.bget:                                       │
           │       self.nbeer = (self.nbeer - 1)                     │
           │     if self.refill:                                     │
           │       self.nsoda = self.max                             │
           │       self.nbeer = self.max                             │
           │                                                         │
           │   def proof(self):                                      │
           │     self.induction(1)                                   │
           ╰─────────────────────────────────────────────────────────╯
[20:49:41] ╭──────────────────────── 🤖 Repaired: ─────────────────────────╮                                                                                                                                      utils.py:24
           │ class VendingMachine(Module):                                 │
           │   def locals(self):                                           │
           │     self.bget = bool                                          │
           │     self.coin = bool                                          │
           │     self.max = int                                            │
           │     self.nbeer = int                                          │
           │     self.nsoda = int                                          │
           │     self.refill = bool                                        │
           │     self.ret_coin = bool                                      │
           │     self.sget = bool                                          │
           │                                                               │
           │   def init(self):                                             │
           │     self.nsoda = self.max                                     │
           │     self.nbeer = self.max                                     │
           │                                                               │
           │   def next(self):                                             │
           │     self.coin = True                                          │
           │     self.ret_coin = ((self.nsoda == 0) and (self.nbeer == 0)) │
           │     if self.coin:                                             │
           │       ??                                                      │
           │     if self.ret_coin:                                         │
           │       ??                                                      │
           │     if self.sget:                                             │
           │       self.nsoda = (self.nsoda - 1)                           │
           │     if self.bget:                                             │
           │       self.nbeer = (self.nbeer - 1)                           │
           │     if self.refill:                                           │
           │       self.nsoda = self.max                                   │
           │       self.nbeer = self.max                                   │
           │                                                               │
           │   def proof(self):                                            │
           │     self.induction(1)                                         │
           │                                                               │
           │                                                               │
           ╰───────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class VendingMachine(Module):                                                                                                                                                                      │
           │   def locals(self):                                                                                                                                                                                │
           │     self.bget = bool                                                                                                                                                                               │
           │     self.coin = bool                                                                                                                                                                               │
           │     self.max = int                                                                                                                                                                                 │
           │     self.nbeer = int                                                                                                                                                                               │
           │     self.nsoda = int                                                                                                                                                                               │
           │     self.refill = bool                                                                                                                                                                             │
           │     self.ret_coin = bool                                                                                                                                                                           │
           │     self.sget = bool                                                                                                                                                                               │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.nsoda = self.max                                                                                                                                                                          │
           │     self.nbeer = self.max                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.coin = True                                                                                                                                                                               │
           │     self.ret_coin = ((self.nsoda == 0) and (self.nbeer == 0))                                                                                                                                      │
           │     if self.coin:                                                                                                                                                                                  │
           │       ??                                                                                                                                                                                           │
           │     if self.ret_coin:                                                                                                                                                                              │
           │       ??                                                                                                                                                                                           │
           │     if self.sget:                                                                                                                                                                                  │
           │       self.nsoda = (self.nsoda - 1)                                                                                                                                                                │
           │     if self.bget:                                                                                                                                                                                  │
           │       self.nbeer = (self.nbeer - 1)                                                                                                                                                                │
           │     if self.refill:                                                                                                                                                                                │
           │       self.nsoda = self.max                                                                                                                                                                        │
           │       self.nbeer = self.max                                                                                                                                                                        │
           │                                                                                                                                                                                                    │
           │   def proof(self):                                                                                                                                                                                 │
           │     self.induction(1)                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Model a design of a beverage vending machine. The machine can either deliver beer or soda. It counts the number of soda and beer bottles and returns inserted coins if the vending machine is    │
           │ empty. The vending machine is represented by the two locations start and select, and has variables that store the number of soda bottles (nsoda), and the number of beer bottles (nbeer). The      │
           │ following conditional transitions model the insertion of a coin and refilling the vending machine: start --(true:coin)-> select start --(true:refill)-> start  Labels of conditional transitions   │
           │ are of the form (g : a ) where g is a Boolean condition (called guard), and a is an action that is possible once g holds. As the condition for both conditional transitions above always holds,    │
           │ the action coin is always enabled in the starting location. To keep things simple, we assume that by refill both storages are entirely refilled. The following transitions model that soda (or     │
           │ beer) can be obtained if there is some soda (or beer) left in the vending machine: select --(nsoda > 0:sget)-> start select --(nbeer > 0:bget)-> start Finally, the vending machine automatically  │
           │ switches to the initial start location while returning the inserted coin once there are no bottles left: select --(nsoda=0 & nbeer=0: ret_coin) -> start Let the maximum capacity of both bottle   │
           │ repositories be max. The insertion of a coin (by action coin) leaves the number of bottles unchanged. The same applies when a coin is returned (by action ret coin). The effect of the other       │
           │ actions is as follows: refill : nsoda:=max & nbeer:=max sget: nsoda:=nsoda-1 bget: nbeer:=nbeer-1 You may use boolean variables to indicate when an action is enabled. Use the variable names      │
           │ nsoda, nbeer, sget, bget, refill, coin.                                                                                                                                                            │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:45] ╭──────────────────────── 🧠 Response: ─────────────────────────╮                                                                                                                                      utils.py:42
           │ class VendingMachine(Module):                                 │
           │   def locals(self):                                           │
           │     self.bget = bool                                          │
           │     self.coin = bool                                          │
           │     self.max = int                                            │
           │     self.nbeer = int                                          │
           │     self.nsoda = int                                          │
           │     self.refill = bool                                        │
           │     self.ret_coin = bool                                      │
           │     self.sget = bool                                          │
           │                                                               │
           │   def init(self):                                             │
           │     self.nsoda = self.max                                     │
           │     self.nbeer = self.max                                     │
           │                                                               │
           │   def next(self):                                             │
           │     self.coin = True                                          │
           │     self.ret_coin = ((self.nsoda == 0) and (self.nbeer == 0)) │
           │     if self.coin:                                             │
           │       self.sget = ((self.nsoda > 0) and (self.nbeer == 0))    │
           │       self.bget = ((self.nsoda == 0) and (self.nbeer > 0))    │
           │     if self.ret_coin:                                         │
           │       self.ret_coin = True                                    │
           │       self.coin = False                                       │
           │       self.nsoda = (self.nsoda + 1)                           │
           │       self.nbeer = (self.nbeer + 1)                           │
           │     if self.sget:                                             │
           │       self.nsoda = (self.nsoda - 1)                           │
           │     if self.bget:                                             │
           │       self.nbeer = (self.nbeer - 1)                           │
           │     if self.refill:                                           │
           │       self.nsoda = self.max                                   │
           │       self.nbeer = self.max                                   │
           │                                                               │
           │   def proof(self):                                            │
           │     self.induction(1)                                         │
           │ ```                                                           │
           ╰───────────────────────────────────────────────────────────────╯
           ╭──────────────────────── 🤖 Extracted: ────────────────────────╮                                                                                                                                      utils.py:24
           │                                                               │
           │ class VendingMachine(Module):                                 │
           │   def locals(self):                                           │
           │     self.bget = bool                                          │
           │     self.coin = bool                                          │
           │     self.max = int                                            │
           │     self.nbeer = int                                          │
           │     self.nsoda = int                                          │
           │     self.refill = bool                                        │
           │     self.ret_coin = bool                                      │
           │     self.sget = bool                                          │
           │                                                               │
           │   def init(self):                                             │
           │     self.nsoda = self.max                                     │
           │     self.nbeer = self.max                                     │
           │                                                               │
           │   def next(self):                                             │
           │     self.coin = True                                          │
           │     self.ret_coin = ((self.nsoda == 0) and (self.nbeer == 0)) │
           │     if self.coin:                                             │
           │       self.sget = ((self.nsoda > 0) and (self.nbeer == 0))    │
           │       self.bget = ((self.nsoda == 0) and (self.nbeer > 0))    │
           │     if self.ret_coin:                                         │
           │       self.ret_coin = True                                    │
           │       self.coin = False                                       │
           │       self.nsoda = (self.nsoda + 1)                           │
           │       self.nbeer = (self.nbeer + 1)                           │
           │     if self.sget:                                             │
           │       self.nsoda = (self.nsoda - 1)                           │
           │     if self.bget:                                             │
           │       self.nbeer = (self.nbeer - 1)                           │
           │     if self.refill:                                           │
           │       self.nsoda = self.max                                   │
           │       self.nbeer = self.max                                   │
           │                                                               │
           │   def proof(self):                                            │
           │     self.induction(1)                                         │
           ╰───────────────────────────────────────────────────────────────╯
[20:49:46] ╭──────────────────────── 🤖 Repaired: ─────────────────────────╮                                                                                                                                      utils.py:24
           │ class VendingMachine(Module):                                 │
           │   def locals(self):                                           │
           │     self.bget = bool                                          │
           │     self.coin = bool                                          │
           │     self.max = int                                            │
           │     self.nbeer = int                                          │
           │     self.nsoda = int                                          │
           │     self.refill = bool                                        │
           │     self.ret_coin = bool                                      │
           │     self.sget = bool                                          │
           │                                                               │
           │   def init(self):                                             │
           │     self.nsoda = self.max                                     │
           │     self.nbeer = self.max                                     │
           │                                                               │
           │   def next(self):                                             │
           │     self.coin = True                                          │
           │     self.ret_coin = ((self.nsoda == 0) and (self.nbeer == 0)) │
           │     if self.coin:                                             │
           │       self.sget = ((self.nsoda > 0) and (self.nbeer == 0))    │
           │       self.bget = ((self.nsoda == 0) and (self.nbeer > 0))    │
           │     if self.ret_coin:                                         │
           │       self.ret_coin = True                                    │
           │       self.coin = False                                       │
           │       self.nsoda = (self.nsoda + 1)                           │
           │       self.nbeer = (self.nbeer + 1)                           │
           │     if self.sget:                                             │
           │       self.nsoda = (self.nsoda - 1)                           │
           │     if self.bget:                                             │
           │       self.nbeer = (self.nbeer - 1)                           │
           │     if self.refill:                                           │
           │       self.nsoda = self.max                                   │
           │       self.nbeer = self.max                                   │
           │                                                               │
           │   def proof(self):                                            │
           │     self.induction(1)                                         │
           │                                                               │
           │                                                               │
           ╰───────────────────────────────────────────────────────────────╯
           ╭────── 🤖 Stats: ───────╮                                                                                                                                                                             utils.py:24
           │ Original Lines: 45     │
           │ Final Lines:    37     │
           │ LLM Calls:      3      │
           │ LLM Time:       11.32s │
           │ Repair Time:    1.53s  │
           ╰────────────────────────╯
