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108 lines
4.1 KiB
Python
108 lines
4.1 KiB
Python
#!/usr/bin/env python3
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"""
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CPU-based Lemma Verification for Lean Proofs
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Uses exhaustive search across bounded ranges to verify arithmetic lemmas
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"""
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from typing import Tuple, List
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class CPULemmaVerifier:
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"""CPU-based verification of Lean lemmas across bounded ranges"""
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def __init__(self):
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print("CPU Lemma Verifier initialized")
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def verify_weighted_term_bounded(self, max_e: int = 100, max_alpha: int = 100) -> bool:
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"""
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Verify (E * α) / 65536 <= E for all E in [0, max_e] and α in [0, max_alpha]
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Uses exhaustive search across bounded ranges
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"""
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print(f"Verifying weighted term bounded for E in [0,{max_e}], α in [0,{max_alpha}]")
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for e in range(max_e + 1):
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for alpha in range(max_alpha + 1):
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product = e * alpha
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divided = product // 65536
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if divided > e:
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print(f"FAILED at E={e}, α={alpha}: {divided} > {e}")
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return False
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print("✓ Weighted term bounded verification PASSED")
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return True
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def verify_bit_shift_equivalence(self, max_x: int = 1000) -> bool:
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"""
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Verify x >>> 16 = x / 65536 for all x in [0, max_x]
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Uses exhaustive search
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"""
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print(f"Verifying bit shift equivalence for x in [0,{max_x}]")
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for x in range(max_x + 1):
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shifted = x >> 16
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divided = x // 65536
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if shifted != divided:
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print(f"FAILED at x={x}: {shifted} != {divided}")
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return False
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print("✓ Bit shift equivalence verification PASSED")
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return True
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def verify_bit_shift_monotonicity(self, max_val: int = 100) -> bool:
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"""
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Verify a >>> 16 <= b >>> 16 when a <= b
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Uses exhaustive search across all pairs
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"""
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print(f"Verifying bit shift monotonicity for a,b in [0,{max_val}]")
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for a in range(max_val + 1):
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for b in range(a, max_val + 1):
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a_shifted = a >> 16
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b_shifted = b >> 16
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if a_shifted > b_shifted:
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print(f"FAILED at a={a}, b={b}: {a_shifted} > {b_shifted}")
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return False
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print("✓ Bit shift monotonicity verification PASSED")
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return True
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def verify_division_comparison(self, max_x: int = 50, max_divisor: int = 50) -> bool:
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"""
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Verify x / a <= x / b when a > b and x >= 0
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Uses exhaustive search across all valid triples
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"""
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print(f"Verifying division comparison for x in [0,{max_x}], a,b in [1,{max_divisor}]")
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for x in range(max_x + 1):
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for b in range(1, max_divisor + 1):
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for a in range(b + 1, max_divisor + 1):
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div_a = x // a
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div_b = x // b
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if div_a > div_b:
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print(f"FAILED at x={x}, a={a}, b={b}: {div_a} > {div_b}")
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return False
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print("✓ Division comparison verification PASSED")
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return True
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def main():
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"""Run CPU verification for all lemmas"""
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verifier = CPULemmaVerifier()
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print("Starting CPU-based lemma verification...")
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print("=" * 60)
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# Verify each lemma with bounded ranges
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results = {}
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results['weighted_term_bounded'] = verifier.verify_weighted_term_bounded(max_e=100, max_alpha=100)
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results['bit_shift_equivalence'] = verifier.verify_bit_shift_equivalence(max_x=1000)
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results['bit_shift_monotonicity'] = verifier.verify_bit_shift_monotonicity(max_val=100)
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results['division_comparison'] = verifier.verify_division_comparison(max_x=50, max_divisor=50)
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print("=" * 60)
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print("CPU Verification Results:")
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for lemma, passed in results.items():
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status = "✓ PASSED" if passed else "✗ FAILED"
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print(f" {lemma}: {status}")
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all_passed = all(results.values())
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if all_passed:
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print("\n✓ All lemmas verified successfully via CPU exhaustive search!")
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print("This provides computational evidence for the Lean proofs.")
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else:
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print("\n✗ Some lemmas failed verification")
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return all_passed
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if __name__ == "__main__":
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main()
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