counterexample-debugger

# Counterexample-Guided Proof Debugger Analyze counterexamples from Nitpick or QuickChick to explain proof failures and suggest corrections to specifications or proofs. ## Workflow ### 1. Receive Counterexample Information Identify what information is provided: - **Counterexample output**: From Nitpick or QuickChick - **Failed theorem**: The statement that couldn't be proven - **Proof attempt**: Any partial proof or tactics tried - **Context**: Definitions and lemmas involved ### 2. Choose Target System Determine which proof assistant is being used: - **Isabelle/HOL with Nitpick**: Finite model finder - **Coq with QuickChick**: Property-based testing - **Both**: Provide analysis for both systems ### 3. Analyze the Counterexample Examine the counterexample systematically: **Verify the counterexample**: - Manually compute the result for the given values - Confirm it actually violates the theorem - Check if it's a genuine counterexample or tool limitation **Identify the violation**: - Which part of the theorem fails? - What values cause the failure? - Is it an edge case or fundamental issue? **Determine the root cause**: - Missing precondition? - Incorrect specification? - Wrong quantifier order? - Implementation bug? - Off-by-one error? - Type constraint issue? ### 4. Explain the Failure Provide clear explanation: **What went wrong**: - Describe why the counterexample violates the theorem - Show the computation step-by-step - Highlight the specific point of failur...