SimplifyCFG pass: block merging proofs #18
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Proof structure for the SimplifyCFG pass following phi_elimination pattern: - cfgTransformScript.sml: transformation definitions (merge_blocks, thread_jump) - cfgWellFormedScript.sml: well-formedness conditions - cfgBlockScript.sml: block-level correctness theorems - cfgFunctionScript.sml: function-level correctness theorems Main theorems (sketched with cheat): - merge_blocks_execution: merged block equiv to sequential execution - simplify_cfg_merge_correct: block merge preserves semantics - simplify_cfg_thread_correct: jump threading preserves semantics - simplify_cfg_steps_correct: sequence of steps preserves semantics 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <[email protected]>
Add helper lemmas for CFG simplification proofs: - eval_operand_replace_label: label replacement doesn't affect eval_operand - replace_label_inst_opcode/output: label replacement preserves opcode/output - exec_binop/unop/modop_replace_label: exec functions ignore label changes Prove replace_label_inst_preserves_step showing that for non-JMP/JNZ/PHI instructions, label replacement doesn't change step_inst semantics. Also fix proofs in cfgWellFormedScript.sml and cfgTransformScript.sml: - all_distinct_map_filter, remove_block_unique_labels - map_preserves_unique_labels - lookup_block_remove, lookup_block_map 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <[email protected]>
- Add data_equiv definition (state equiv ignoring control flow fields) - Add state_equiv_merge and result_equiv_merge for block merging - Prove data_equiv helper lemmas: refl, sym, trans - Prove eval_operand_data_equiv, update_var_data_equiv - Prove mload/mstore/sload/sstore/tload/tstore_data_equiv - Prove halt_state/revert_state/next_inst_data_equiv - Prove exec_binop/unop/modop_data_equiv - Prove step_inst_data_equiv for non-PHI/non-branch instructions - Add step_in_block_data_equiv_no_phi (cheated, structure verified) - Fix inst_output -> inst_outputs in replace_label_inst_outputs 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <[email protected]>
- Add jump_to_data_equiv: JMP preserves data_equiv - Add next_inst_data_equiv_full: next_inst preserves data_equiv and control flow - Add step_inst_preserves_ctrl: non-JMP/JNZ instructions preserve vs_current_bb/vs_inst_idx - Add step_inst_jmp_data_equiv: JMP preserves data_equiv with control flow - Add step_inst_jnz_data_equiv: JNZ preserves data_equiv with control flow - Add non_jmp_jnz_terminator_not_ok: non-JMP/JNZ terminators never return OK - Complete proof of step_in_block_data_equiv_no_phi 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <[email protected]>
This theorem shows that running the same no_phi block from two data-equivalent states produces result_equiv_merge results. Key proof technique: - Complete induction on remaining instructions - Uses step_in_block_data_equiv_no_phi for each step - Handles OK/OK case with subcases for halted and terminator 🤖 Generated with [Claude Code](https://claude.com/claude-code) Co-Authored-By: Claude Opus 4.5 <[email protected]>
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Summary
run_block_data_equiv_no_phitheorem proving that running the same no-phi block from data-equivalent states produces equivalent resultsmerge_blocks_executionstep_in_block_data_equiv_no_phi,data_equivinfrastructureTest plan
VFMDIR=/home/ubuntu/verifereum Holmake --qofpasses🤖 Generated with Claude Code