[20:49:11] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > Consider the circuit diagram of the sequential circuit with input variable x, output variable y, and register r. The output variable y is given by the negation of x xor r. The register         │
           │ evaluation r changes according to the circuit function next_r = x OR r. Note that once the register evaluation is , r keeps that value. Model the circuit behaviour with a transition system where │
           │ each state corresponds to an evaluation of x and r, and the initial valuation of r is 0. There are two initial states: S1: x=0, r=0 S2: x=1, r=0  Write an LTL property that checks that the       │
           │ output bit y is set infinitely often. You may use auxiliary variables. Use the variable names x, y and r.                                                                                          │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:13] ╭─────────────── 🧠 Response: ────────────────╮                                                                                                                                                        utils.py:42
           │ class SequentialCircuit(Module):            │
           │     def types(self):                        │
           │         self.bit = Boolean()                │
           │                                             │
           │     def locals(self):                       │
           │         self.x = self.bit                   │
           │         self.y = self.bit                   │
           │         self.r = self.bit                   │
           │                                             │
           │     def init(self):                         │
           │         self.r = False                      │
           │                                             │
           │     def next(self):                         │
           │         self.y = not (self.x ^ self.r)      │
           │         self.r = Or(self.x, self.r)         │
           │                                             │
           │     def specification(self):                │
           │         return Eventually(Globally(self.y)) │
           │                                             │
           │ ```                                         │
           ╰─────────────────────────────────────────────╯
           ╭─────────────── 🤖 Extracted: ───────────────╮                                                                                                                                                        utils.py:24
           │                                             │
           │ class SequentialCircuit(Module):            │
           │     def types(self):                        │
           │         self.bit = Boolean()                │
           │                                             │
           │     def locals(self):                       │
           │         self.x = self.bit                   │
           │         self.y = self.bit                   │
           │         self.r = self.bit                   │
           │                                             │
           │     def init(self):                         │
           │         self.r = False                      │
           │                                             │
           │     def next(self):                         │
           │         self.y = not (self.x ^ self.r)      │
           │         self.r = Or(self.x, self.r)         │
           │                                             │
           │     def specification(self):                │
           │         return Eventually(Globally(self.y)) │
           ╰─────────────────────────────────────────────╯
           ╭────────── 🤖 Repaired: ──────────╮                                                                                                                                                                   utils.py:24
           │ class SequentialCircuit(Module): │
           │   def types(self):               │
           │     self.bit = bool              │
           │                                  │
           │   def locals(self):              │
           │     self.x = self.bit            │
           │     self.y = self.bit            │
           │     self.r = self.bit            │
           │                                  │
           │   def init(self):                │
           │     self.r = False               │
           │                                  │
           │   def next(self):                │
           │     self.y = not ??              │
           │     self.r = (self.x or self.r)  │
           │                                  │
           │   def specification(self):       │
           │     return ??                    │
           │                                  │
           │                                  │
           ╰──────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class SequentialCircuit(Module):                                                                                                                                                                   │
           │   def types(self):                                                                                                                                                                                 │
           │     self.bit = bool                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.x = self.bit                                                                                                                                                                              │
           │     self.y = self.bit                                                                                                                                                                              │
           │     self.r = self.bit                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.r = False                                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.y = not ??                                                                                                                                                                                │
           │     self.r = (self.x or self.r)                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ??                                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the circuit diagram of the sequential circuit with input variable x, output variable y, and register r. The output variable y is given by the negation of x xor r. The register         │
           │ evaluation r changes according to the circuit function next_r = x OR r. Note that once the register evaluation is , r keeps that value. Model the circuit behaviour with a transition system where │
           │ each state corresponds to an evaluation of x and r, and the initial valuation of r is 0. There are two initial states: S1: x=0, r=0 S2: x=1, r=0  Write an LTL property that checks that the       │
           │ output bit y is set infinitely often. You may use auxiliary variables. Use the variable names x, y and r.                                                                                          │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:15] ╭───────────── 🧠 Response: ─────────────╮                                                                                                                                                             utils.py:42
           │ class SequentialCircuit(Module):       │
           │     def types(self):                   │
           │         self.bit = bool                │
           │                                        │
           │     def locals(self):                  │
           │         self.x = self.bit              │
           │         self.y = self.bit              │
           │         self.r = self.bit              │
           │                                        │
           │     def init(self):                    │
           │         self.r = False                 │
           │                                        │
           │     def next(self):                    │
           │         self.y = not (self.x ^ self.r) │
           │         self.r = (self.x or self.r)    │
           │                                        │
           │     def specification(self):           │
           │         return G(self.y)               │
           │ ```                                    │
           ╰────────────────────────────────────────╯
           ╭──────────── 🤖 Extracted: ─────────────╮                                                                                                                                                             utils.py:24
           │                                        │
           │ class SequentialCircuit(Module):       │
           │     def types(self):                   │
           │         self.bit = bool                │
           │                                        │
           │     def locals(self):                  │
           │         self.x = self.bit              │
           │         self.y = self.bit              │
           │         self.r = self.bit              │
           │                                        │
           │     def init(self):                    │
           │         self.r = False                 │
           │                                        │
           │     def next(self):                    │
           │         self.y = not (self.x ^ self.r) │
           │         self.r = (self.x or self.r)    │
           │                                        │
           │     def specification(self):           │
           │         return G(self.y)               │
           ╰────────────────────────────────────────╯
           ╭────────── 🤖 Repaired: ──────────╮                                                                                                                                                                   utils.py:24
           │ class SequentialCircuit(Module): │
           │   def types(self):               │
           │     self.bit = bool              │
           │                                  │
           │   def locals(self):              │
           │     self.x = self.bit            │
           │     self.y = self.bit            │
           │     self.r = self.bit            │
           │                                  │
           │   def init(self):                │
           │     self.r = False               │
           │                                  │
           │   def next(self):                │
           │     self.y = not ??              │
           │     self.r = (self.x or self.r)  │
           │                                  │
           │   def specification(self):       │
           │     return ??                    │
           │                                  │
           │                                  │
           ╰──────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class SequentialCircuit(Module):                                                                                                                                                                   │
           │   def types(self):                                                                                                                                                                                 │
           │     self.bit = bool                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.x = self.bit                                                                                                                                                                              │
           │     self.y = self.bit                                                                                                                                                                              │
           │     self.r = self.bit                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.r = False                                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.y = not ??                                                                                                                                                                                │
           │     self.r = (self.x or self.r)                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ??                                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the circuit diagram of the sequential circuit with input variable x, output variable y, and register r. The output variable y is given by the negation of x xor r. The register         │
           │ evaluation r changes according to the circuit function next_r = x OR r. Note that once the register evaluation is , r keeps that value. Model the circuit behaviour with a transition system where │
           │ each state corresponds to an evaluation of x and r, and the initial valuation of r is 0. There are two initial states: S1: x=0, r=0 S2: x=1, r=0  Write an LTL property that checks that the       │
           │ output bit y is set infinitely often. You may use auxiliary variables. Use the variable names x, y and r.                                                                                          │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:17] ╭─────────── 🧠 Response: ───────────╮                                                                                                                                                                 utils.py:42
           │ class SequentialCircuit(Module):   │
           │   def types(self):                 │
           │     self.bit = bool                │
           │                                    │
           │   def locals(self):                │
           │     self.x = self.bit              │
           │     self.y = self.bit              │
           │     self.r = self.bit              │
           │                                    │
           │   def init(self):                  │
           │     self.r = False                 │
           │                                    │
           │   def next(self):                  │
           │     self.y = not (self.x ^ self.r) │
           │     self.r = (self.x or self.r)    │
           │                                    │
           │   def specification(self):         │
           │     return G(self.y)               │
           │ ```                                │
           ╰────────────────────────────────────╯
           ╭────────── 🤖 Extracted: ───────────╮                                                                                                                                                                 utils.py:24
           │                                    │
           │ class SequentialCircuit(Module):   │
           │   def types(self):                 │
           │     self.bit = bool                │
           │                                    │
           │   def locals(self):                │
           │     self.x = self.bit              │
           │     self.y = self.bit              │
           │     self.r = self.bit              │
           │                                    │
           │   def init(self):                  │
           │     self.r = False                 │
           │                                    │
           │   def next(self):                  │
           │     self.y = not (self.x ^ self.r) │
           │     self.r = (self.x or self.r)    │
           │                                    │
           │   def specification(self):         │
           │     return G(self.y)               │
           ╰────────────────────────────────────╯
           ╭────────── 🤖 Repaired: ──────────╮                                                                                                                                                                   utils.py:24
           │ class SequentialCircuit(Module): │
           │   def types(self):               │
           │     self.bit = bool              │
           │                                  │
           │   def locals(self):              │
           │     self.x = self.bit            │
           │     self.y = self.bit            │
           │     self.r = self.bit            │
           │                                  │
           │   def init(self):                │
           │     self.r = False               │
           │                                  │
           │   def next(self):                │
           │     self.y = not ??              │
           │     self.r = (self.x or self.r)  │
           │                                  │
           │   def specification(self):       │
           │     return ??                    │
           │                                  │
           │                                  │
           ╰──────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class SequentialCircuit(Module):                                                                                                                                                                   │
           │   def types(self):                                                                                                                                                                                 │
           │     self.bit = bool                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.x = self.bit                                                                                                                                                                              │
           │     self.y = self.bit                                                                                                                                                                              │
           │     self.r = self.bit                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.r = False                                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.y = not ??                                                                                                                                                                                │
           │     self.r = (self.x or self.r)                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ??                                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the circuit diagram of the sequential circuit with input variable x, output variable y, and register r. The output variable y is given by the negation of x xor r. The register         │
           │ evaluation r changes according to the circuit function next_r = x OR r. Note that once the register evaluation is , r keeps that value. Model the circuit behaviour with a transition system where │
           │ each state corresponds to an evaluation of x and r, and the initial valuation of r is 0. There are two initial states: S1: x=0, r=0 S2: x=1, r=0  Write an LTL property that checks that the       │
           │ output bit y is set infinitely often. You may use auxiliary variables. Use the variable names x, y and r.                                                                                          │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:19] ╭─────────── 🧠 Response: ────────────╮                                                                                                                                                                utils.py:42
           │ class SequentialCircuit(Module):    │
           │   def types(self):                  │
           │     self.bit = bool                 │
           │                                     │
           │   def locals(self):                 │
           │     self.x = self.bit               │
           │     self.y = self.bit               │
           │     self.r = self.bit               │
           │                                     │
           │   def init(self):                   │
           │     self.r = False                  │
           │                                     │
           │   def next(self):                   │
           │     self.y = not (self.x != self.r) │
           │     self.r = (self.x or self.r)     │
           │                                     │
           │   def specification(self):          │
           │     return globally(self.y)         │
           │                                     │
           │ ```                                 │
           ╰─────────────────────────────────────╯
           ╭─────────── 🤖 Extracted: ───────────╮                                                                                                                                                                utils.py:24
           │                                     │
           │ class SequentialCircuit(Module):    │
           │   def types(self):                  │
           │     self.bit = bool                 │
           │                                     │
           │   def locals(self):                 │
           │     self.x = self.bit               │
           │     self.y = self.bit               │
           │     self.r = self.bit               │
           │                                     │
           │   def init(self):                   │
           │     self.r = False                  │
           │                                     │
           │   def next(self):                   │
           │     self.y = not (self.x != self.r) │
           │     self.r = (self.x or self.r)     │
           │                                     │
           │   def specification(self):          │
           │     return globally(self.y)         │
           ╰─────────────────────────────────────╯
           ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class SequentialCircuit(Module):    │
           │   def types(self):                  │
           │     self.bit = bool                 │
           │                                     │
           │   def locals(self):                 │
           │     self.x = self.bit               │
           │     self.y = self.bit               │
           │     self.r = self.bit               │
           │                                     │
           │   def init(self):                   │
           │     self.r = False                  │
           │                                     │
           │   def next(self):                   │
           │     self.y = not (self.x != self.r) │
           │     self.r = (self.x or self.r)     │
           │                                     │
           │   def specification(self):          │
           │     return ??                       │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class SequentialCircuit(Module):                                                                                                                                                                   │
           │   def types(self):                                                                                                                                                                                 │
           │     self.bit = bool                                                                                                                                                                                │
           │                                                                                                                                                                                                    │
           │   def locals(self):                                                                                                                                                                                │
           │     self.x = self.bit                                                                                                                                                                              │
           │     self.y = self.bit                                                                                                                                                                              │
           │     self.r = self.bit                                                                                                                                                                              │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.r = False                                                                                                                                                                                 │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.y = not (self.x != self.r)                                                                                                                                                                │
           │     self.r = (self.x or self.r)                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │   def specification(self):                                                                                                                                                                         │
           │     return ??                                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Consider the circuit diagram of the sequential circuit with input variable x, output variable y, and register r. The output variable y is given by the negation of x xor r. The register         │
           │ evaluation r changes according to the circuit function next_r = x OR r. Note that once the register evaluation is , r keeps that value. Model the circuit behaviour with a transition system where │
           │ each state corresponds to an evaluation of x and r, and the initial valuation of r is 0. There are two initial states: S1: x=0, r=0 S2: x=1, r=0  Write an LTL property that checks that the       │
           │ output bit y is set infinitely often. You may use auxiliary variables. Use the variable names x, y and r.                                                                                          │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:21] ╭───────────── 🧠 Response: ──────────────╮                                                                                                                                                            utils.py:42
           │ class SequentialCircuit(Module):        │
           │     def types(self):                    │
           │         self.bit = bool                 │
           │                                         │
           │     def locals(self):                   │
           │         self.x = self.bit               │
           │         self.y = self.bit               │
           │         self.r = self.bit               │
           │                                         │
           │     def init(self):                     │
           │         self.r = False                  │
           │                                         │
           │     def next(self):                     │
           │         self.y = not (self.x != self.r) │
           │         self.r = (self.x or self.r)     │
           │                                         │
           │     def specification(self):            │
           │         return self.G(self.y)           │
           │ ```                                     │
           ╰─────────────────────────────────────────╯
           ╭───────────── 🤖 Extracted: ─────────────╮                                                                                                                                                            utils.py:24
           │                                         │
           │ class SequentialCircuit(Module):        │
           │     def types(self):                    │
           │         self.bit = bool                 │
           │                                         │
           │     def locals(self):                   │
           │         self.x = self.bit               │
           │         self.y = self.bit               │
           │         self.r = self.bit               │
           │                                         │
           │     def init(self):                     │
           │         self.r = False                  │
           │                                         │
           │     def next(self):                     │
           │         self.y = not (self.x != self.r) │
           │         self.r = (self.x or self.r)     │
           │                                         │
           │     def specification(self):            │
           │         return self.G(self.y)           │
           ╰─────────────────────────────────────────╯
           ╭─────────── 🤖 Repaired: ────────────╮                                                                                                                                                                utils.py:24
           │ class SequentialCircuit(Module):    │
           │   def types(self):                  │
           │     self.bit = bool                 │
           │                                     │
           │   def locals(self):                 │
           │     self.x = self.bit               │
           │     self.y = self.bit               │
           │     self.r = self.bit               │
           │                                     │
           │   def init(self):                   │
           │     self.r = False                  │
           │                                     │
           │   def next(self):                   │
           │     self.y = not (self.x != self.r) │
           │     self.r = (self.x or self.r)     │
           │                                     │
           │   def specification(self):          │
           │     return ??                       │
           │                                     │
           │                                     │
           ╰─────────────────────────────────────╯
           ╭────── 🤖 Stats: ──────╮                                                                                                                                                                              utils.py:24
           │ Original Lines: 19    │
           │ Final Lines:    19    │
           │ LLM Calls:      5     │
           │ LLM Time:       9.02s │
           │ Repair Time:    1.24s │
           ╰───────────────────────╯
