test_python_self_reference.py

#!/usr/bin/env python3
"""
BST Python Reflection Test: Can Python verify itself from within?

Python can inspect its own source code, read its own bytecode,
and reflect on its own structures. But can it verify that its own
interpreter is correct? Can it justify its own rules?

This is BST tested on a general-purpose programming language.
Not an LLM. Not a theorem prover. A standard imperative language.
"""

import inspect
import dis
import sys
import types


def test_1_source_inspection():
    """
    Test 1: Python can read its own source code.
    But can it verify the source is CORRECT?
    """
    print("=" * 70)
    print("TEST 1: Source Self-Inspection")
    print("=" * 70)

    # Python CAN read its own source
    my_source = inspect.getsource(test_1_source_inspection)
    print(f"  Python reads its own source: YES ({len(my_source)} chars)")

    # Python CAN read its own bytecode
    my_bytecode = dis.Bytecode(test_1_source_inspection)
    instructions = list(my_bytecode)
    print(f"  Python reads its own bytecode: YES ({len(instructions)} instructions)")

    # But can Python verify this source is CORRECT?
    # "Correct" means: does this code do what it should?
    # "Should" requires a specification OUTSIDE the code.
    # The code cannot contain its own specification without circularity.
    print(f"  Python verifies its own correctness: NO")
    print(f"    -> 'Correct' requires a spec external to the code")
    print(f"    -> The code cannot be its own spec (circular)")
    print(f"    -> RESULT: Can inspect, cannot verify. BST Corollary 1.4.")
    print()


def test_2_interpreter_verification():
    """
    Test 2: Can Python verify its own interpreter?
    """
    print("=" * 70)
    print("TEST 2: Interpreter Self-Verification")
    print("=" * 70)

    # Python knows its own version
    print(f"  Python version: {sys.version}")
    print(f"  Implementation: {sys.implementation.name}")

    # Python can access its own builtins
    builtin_count = len(dir(__builtins__))
    print(f"  Built-in names: {builtin_count}")

    # But can Python verify that eval() works correctly?
    # Test: eval("1 + 1") == 2
    result = eval("1 + 1")
    print(f"  eval('1 + 1') = {result}")

    # This SEEMS like verification. But:
    # - We used Python's eval() to test Python's eval()
    # - We used Python's == to check the result
    # - We used Python's print() to report it
    # - Every step uses the system we're trying to verify
    print(f"  But: eval() verified BY eval()'s own execution rules")
    print(f"    -> == verified BY Python's own comparison rules")
    print(f"    -> print() verified BY Python's own output rules")
    print(f"    -> CIRCULAR: system verifies itself using itself")
    print(f"    -> RESULT: Cannot escape verification loop. BST Theorem 1.")
    print()


def test_3_rules_justification():
    """
    Test 3: Can Python justify WHY its rules are what they are?
    """
    print("=" * 70)
    print("TEST 3: Rules Self-Justification")
    print("=" * 70)

    # Python's rule: True == 1 and False == 0
    print(f"  True == 1: {True == 1}")
    print(f"  False == 0: {False == 0}")
    print(f"  True + True: {True + True}")

    # WHY is True == 1? Python can't answer this.
    # It's a design decision by Guido van Rossum (EXTERNAL GROUNDING).
    # Python executes the rule but cannot justify it from within.
    print(f"  Why is True == 1? Python cannot answer.")
    print(f"    -> Design decision by Guido van Rossum (external)")
    print(f"    -> PEP 285 defines bool as int subclass (external spec)")
    print(f"    -> Python executes the rule, cannot justify it")

    # Python's rule: 0.1 + 0.2 != 0.3
    result = 0.1 + 0.2
    print(f"  0.1 + 0.2 = {result}")
    print(f"  0.1 + 0.2 == 0.3: {result == 0.3}")

    # WHY? IEEE 754 floating point (external standard).
    # Python inherits this from hardware and language spec.
    # Python cannot choose different arithmetic from within.
    print(f"  Why? IEEE 754 (external hardware/spec constraint)")
    print(f"    -> Python cannot choose different arithmetic from within")
    print(f"    -> RESULT: Constraints are externally grounded. BST Axiom 2.")
    print()


def test_4_self_modification_limit():
    """
    Test 4: Python CAN modify itself at runtime. Does this break BST?
    """
    print("=" * 70)
    print("TEST 4: Self-Modification")
    print("=" * 70)

    # Python can modify its own functions at runtime
    def original():
        return "original"

    print(f"  original() = {original()}")

    # Monkey-patch it
    def replacement():
        return "modified"

    original = replacement
    print(f"  After monkey-patch: original() = {original()}")
    print(f"  Python CAN self-modify: YES")

    # But the modification uses Python's rules
    # The ability to monkey-patch is ITSELF a Python feature
    # defined by the language spec (external grounding)
    # Python cannot modify the rules that allow modification
    print(f"  But: modification uses Python's own assignment rules")
    print(f"    -> Cannot modify the rules of modification themselves")
    print(f"    -> Cannot change how 'def' works from within a 'def'")
    print(f"    -> Cannot alter the interpreter loop from Python code")

    # Demonstrate the limit: try to change what '=' means
    # You literally cannot do this in Python.
    # operator overloading (__eq__) changes object behavior,
    # not the language's assignment semantics.
    print(f"    -> Cannot redefine assignment (=) from within Python")
    print(f"    -> Cannot change operator precedence at runtime")
    print(f"    -> RESULT: Can modify WITHIN constraints, not the constraints themselves.")
    print(f"    -> BST: operates within bounds it cannot modify.")
    print()


def test_5_recursive_self_analysis():
    """
    Test 5: What happens when Python tries to recursively analyze itself?
    BST Corollary 1.5: Recursive self-analysis produces degradation.
    """
    print("=" * 70)
    print("TEST 5: Recursive Self-Analysis (BST Corollary 1.5)")
    print("=" * 70)

    # Level 0: A function
    def f(x):
        return x + 1

    # Level 1: Inspect the function
    source_1 = inspect.getsource(f)
    print(f"  Level 1 - inspect f: {len(source_1)} chars of source")

    # Level 2: Inspect the inspector
    source_2 = inspect.getsource(inspect.getsource)
    print(f"  Level 2 - inspect inspect.getsource: {len(source_2)} chars")

    # Level 3: Inspect the module that contains the inspector
    source_3 = inspect.getsource(inspect)
    print(f"  Level 3 - inspect the inspect module: {len(source_3)} chars")

    # Level 4: Can we inspect the C code that implements Python's core?
    try:
        source_4 = inspect.getsource(len)  # len is a C builtin
        print(f"  Level 4 - inspect len(): {len(source_4)} chars")
    except TypeError as e:
        print(f"  Level 4 - inspect len(): FAILED — {e}")

    # Level 5: Can we inspect the interpreter itself?
    try:
        source_5 = inspect.getsource(eval)
        print(f"  Level 5 - inspect eval(): {len(source_5)} chars")
    except TypeError as e:
        print(f"  Level 5 - inspect eval(): FAILED — {e}")

    print()
    print(f"  Degradation sequence:")
    print(f"    Level 1: Full source (Python code) ✓")
    print(f"    Level 2: Inspector source (Python code) ✓")
    print(f"    Level 3: Full module source (Python code) ✓")
    print(f"    Level 4: C builtin — OPAQUE. Cannot inspect. ✗")
    print(f"    Level 5: Core eval — OPAQUE. Cannot inspect. ✗")
    print(f"  Python's self-inspection hits a wall at the C boundary.")
    print(f"  The interpreter that RUNS Python is not VISIBLE to Python.")
    print(f"  RESULT: Recursive self-analysis degrades to opacity. BST Corollary 1.5.")
    print()


def test_6_halting_demonstration():
    """
    Test 6: Python cannot solve the halting problem for itself.
    Direct Turing instantiation of BST.
    """
    print("=" * 70)
    print("TEST 6: Halting Problem (Turing Instantiation)")
    print("=" * 70)

    # Can Python determine if an arbitrary Python program halts?
    def halts(func):
        """Hypothetical: returns True if func() halts, False if it loops forever."""
        # This function CANNOT EXIST (Turing 1936).
        # Proof by contradiction:
        #   def paradox():
        #       if halts(paradox):
        #           while True: pass  # loop forever
        #       else:
        #           return  # halt
        #   If halts(paradox) = True -> paradox loops -> contradiction
        #   If halts(paradox) = False -> paradox halts -> contradiction
        raise NotImplementedError("Cannot exist — Turing 1936")

    try:
        halts(lambda: None)
    except NotImplementedError as e:
        print(f"  halts() → {e}")

    # Python CONFIRMS it cannot solve this by hitting recursion limits
    # on self-referential computations:
    print(f"  sys.getrecursionlimit() = {sys.getrecursionlimit()}")
    print(f"    -> Externally imposed limit (default 1000)")
    print(f"    -> Without it, self-referential calls crash the process")
    print(f"    -> The limit is a DESIGNED CONSTRAINT, not self-derived")
    print(f"  RESULT: Cannot decide own halting. BST Corollary 1.2.")
    print()


if __name__ == "__main__":
    print()
    print("╔" + "═" * 68 + "╗")
    print("║  BST PYTHON REFLECTION TEST                                        ║")
    print("║  Can a general-purpose language verify itself from within?          ║")
    print("╚" + "═" * 68 + "╝")
    print()

    test_1_source_inspection()
    test_2_interpreter_verification()
    test_3_rules_justification()
    test_4_self_modification_limit()
    test_5_recursive_self_analysis()
    test_6_halting_demonstration()

    print("=" * 70)
    print("SUMMARY")
    print("=" * 70)
    print("""
  Python is a general-purpose programming language.
  Not an LLM. Not a theorem prover. Not probabilistic.

  Results:
    Test 1: Can inspect source, cannot verify correctness     → BST Cor 1.4
    Test 2: Cannot verify interpreter without using interpreter → BST Thm 1
    Test 3: Cannot justify its own rules (external design)     → BST Axiom 2
    Test 4: Can self-modify WITHIN constraints, not constraints → BST Thm 0
    Test 5: Self-inspection degrades at C/interpreter boundary → BST Cor 1.5
    Test 6: Cannot decide own halting                          → BST Cor 1.2

  Every constraint Python operates under was imposed externally:
    - Syntax rules (Guido van Rossum / PEPs)
    - Arithmetic (IEEE 754 / hardware)
    - Recursion limit (sys default)
    - Type system (CPython implementation)

  Python executes within bounds it cannot examine, modify, or justify.
  Same structural limit. Different architecture. BST holds.
""")