[20:48:55] ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │ Write Python code that extends the `Module` class below to complete the following task.                                                                                                            │
           │                                                                                                                                                                                                    │
           │ > Build a model of a concurrent program, in which three processes, Inc, Dec, and Reset, cooperate. They operate on the shared integer variable x with arbitrary initial value that can be accessed │
           │ (i.e., read), and modified (i.e., written) by each of the individual processes. The processes are: proc Inc = while true do if x<200 then x:=x+1 fi od proc Dec = while true do if x>0 then x:=    │
           │ x−1 fi od proc Reset = while true do if x=200 then x:=0 fi od Process Inc increments x if its value is smaller than 200, Dec decrements x if its value is at least 1, and Reset resets x once it   │
           │ has reached the value 200. They all do so repetitively. Write an invariant that checks if the value of x is always between (and including) 0 and 200. Use the variable name x.                     │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:48:57] ╭────────────────── 🧠 Response: ──────────────────╮                                                                                                                                                   utils.py:42
           │ from uclid import Module, Integer                │
           │                                                  │
           │ class ConcurrentProcess(Module):                 │
           │                                                  │
           │     def types(self):                             │
           │         self.x = Integer()                       │
           │                                                  │
           │     def shared_vars(self):                       │
           │         self.x = Integer()                       │
           │                                                  │
           │     def init(self):                              │
           │         self.x = 0                               │
           │                                                  │
           │     def next(self):                              │
           │                                                  │
           │         def Inc():                               │
           │             return self.x < 200                  │
           │                                                  │
           │         def Dec():                               │
           │             return self.x > 0                    │
           │                                                  │
           │         def Reset():                             │
           │             return self.x == 200                 │
           │                                                  │
           │         def Invariant():                         │
           │             return self.x >= 0 and self.x <= 200 │
           │                                                  │
           │         self.x = If(Inc(), self.x + 1,           │
           │                     If(Dec(), self.x - 1,        │
           │                     If(Reset(), 0, self.x)))     │
           │                                                  │
           │         assert(Invariant())                      │
           │ ```                                              │
           ╰──────────────────────────────────────────────────╯
           ╭───────────────── 🤖 Extracted: ──────────────────╮                                                                                                                                                   utils.py:24
           │                                                  │
           │ from uclid import Module, Integer                │
           │                                                  │
           │ class ConcurrentProcess(Module):                 │
           │                                                  │
           │     def types(self):                             │
           │         self.x = Integer()                       │
           │                                                  │
           │     def shared_vars(self):                       │
           │         self.x = Integer()                       │
           │                                                  │
           │     def init(self):                              │
           │         self.x = 0                               │
           │                                                  │
           │     def next(self):                              │
           │                                                  │
           │         def Inc():                               │
           │             return self.x < 200                  │
           │                                                  │
           │         def Dec():                               │
           │             return self.x > 0                    │
           │                                                  │
           │         def Reset():                             │
           │             return self.x == 200                 │
           │                                                  │
           │         def Invariant():                         │
           │             return self.x >= 0 and self.x <= 200 │
           │                                                  │
           │         self.x = If(Inc(), self.x + 1,           │
           │                     If(Dec(), self.x - 1,        │
           │                     If(Reset(), 0, self.x)))     │
           │                                                  │
           │         assert(Invariant())                      │
           ╰──────────────────────────────────────────────────╯
[20:48:58] ╭───────────────────────────────────── 🤖 Repaired: ─────────────────────────────────────╮                                                                                                             utils.py:24
           │ class ConcurrentProcess(Module):                                                       │
           │   def locals(self):                                                                    │
           │     self.x = int                                                                       │
           │                                                                                        │
           │   def init(self):                                                                      │
           │     self.x = 0                                                                         │
           │                                                                                        │
           │   def next(self):                                                                      │
           │     self.x = ((self.x + 1) if ?? else ((self.x - 1) if ?? else (0 if ?? else self.x))) │
           │     assert ??                                                                          │
           │                                                                                        │
           │                                                                                        │
           ╰────────────────────────────────────────────────────────────────────────────────────────╯
           ╭──────────────────────────────────────────────────────────────────────────────────────────── 🤖 Prompt: ────────────────────────────────────────────────────────────────────────────────────────────╮ utils.py:24
           │                                                                                                                                                                                                    │
           │ Fix the following Python code by replacing every occurrence of `??` with the correct code.                                                                                                         │
           │ ```python                                                                                                                                                                                          │
           │ class ConcurrentProcess(Module):                                                                                                                                                                   │
           │   def locals(self):                                                                                                                                                                                │
           │     self.x = int                                                                                                                                                                                   │
           │                                                                                                                                                                                                    │
           │   def init(self):                                                                                                                                                                                  │
           │     self.x = 0                                                                                                                                                                                     │
           │                                                                                                                                                                                                    │
           │   def next(self):                                                                                                                                                                                  │
           │     self.x = ((self.x + 1) if ?? else ((self.x - 1) if ?? else (0 if ?? else self.x)))                                                                                                             │
           │     assert ??                                                                                                                                                                                      │
           │                                                                                                                                                                                                    │
           │                                                                                                                                                                                                    │
           │ ```                                                                                                                                                                                                │
           │ Make sure that your code extends the `Module` class below and that it completes the following task.                                                                                                │
           │                                                                                                                                                                                                    │
           │ > Build a model of a concurrent program, in which three processes, Inc, Dec, and Reset, cooperate. They operate on the shared integer variable x with arbitrary initial value that can be accessed │
           │ (i.e., read), and modified (i.e., written) by each of the individual processes. The processes are: proc Inc = while true do if x<200 then x:=x+1 fi od proc Dec = while true do if x>0 then x:=    │
           │ x−1 fi od proc Reset = while true do if x=200 then x:=0 fi od Process Inc increments x if its value is smaller than 200, Dec decrements x if its value is at least 1, and Reset resets x once it   │
           │ has reached the value 200. They all do so repetitively. Write an invariant that checks if the value of x is always between (and including) 0 and 200. Use the variable name x.                     │
           │                                                                                                                                                                                                    │
           │ 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                                                                                                                                                                                          │
           │                                                                                                                                                                                                    │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:48:59] ╭──────────────────────────────────────────────────── 🧠 Response: ────────────────────────────────────────────────────╮                                                                               utils.py:42
           │ class ConcurrentProcess(Module):                                                                                     │
           │   def locals(self):                                                                                                  │
           │     self.x = Integer()                                                                                               │
           │                                                                                                                      │
           │   def init(self):                                                                                                    │
           │     self.x = 0                                                                                                       │
           │                                                                                                                      │
           │   def next(self):                                                                                                    │
           │     self.x = ((self.x + 1) if self.x < 200 else ((self.x - 1) if self.x >= 1 else (0 if self.x == 200 else self.x))) │
           │     assert 0 <= self.x <= 200                                                                                        │
           │ ```                                                                                                                  │
           ╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭─────────────────────────────────────────────────── 🤖 Extracted: ────────────────────────────────────────────────────╮                                                                               utils.py:24
           │                                                                                                                      │
           │ class ConcurrentProcess(Module):                                                                                     │
           │   def locals(self):                                                                                                  │
           │     self.x = Integer()                                                                                               │
           │                                                                                                                      │
           │   def init(self):                                                                                                    │
           │     self.x = 0                                                                                                       │
           │                                                                                                                      │
           │   def next(self):                                                                                                    │
           │     self.x = ((self.x + 1) if self.x < 200 else ((self.x - 1) if self.x >= 1 else (0 if self.x == 200 else self.x))) │
           │     assert 0 <= self.x <= 200                                                                                        │
           ╰──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
[20:49:00] ╭─────────────────────────────────────────────────────── 🤖 Repaired: ───────────────────────────────────────────────────────╮                                                                         utils.py:24
           │ class ConcurrentProcess(Module):                                                                                           │
           │   def locals(self):                                                                                                        │
           │     self.x = int                                                                                                           │
           │                                                                                                                            │
           │   def init(self):                                                                                                          │
           │     self.x = 0                                                                                                             │
           │                                                                                                                            │
           │   def next(self):                                                                                                          │
           │     self.x = ((self.x + 1) if (self.x < 200) else ((self.x - 1) if (self.x >= 1) else (0 if (self.x == 200) else self.x))) │
           │     assert ((0 <= self.x) and (self.x <= 200))                                                                             │
           │                                                                                                                            │
           │                                                                                                                            │
           ╰────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────╯
           ╭────── 🤖 Stats: ──────╮                                                                                                                                                                              utils.py:24
           │ Original Lines: 33    │
           │ Final Lines:    11    │
           │ LLM Calls:      2     │
           │ LLM Time:       4.18s │
           │ Repair Time:    0.61s │
           ╰───────────────────────╯
