{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# PHASE 7: Proof Tool Integration\n", "\n", "**Implements SEC-006: Replace proof tool stubs with real execution**\n", "\n", "## Objective\n", "\n", "Integrate actual proof verifiers (Agda, Ada/SPARK, Lean 4, Z3) instead of stub predicates.\n", "\n", "| Tool | Language | Purpose | Status |\n", "|------|----------|---------|--------|\n", "| **Agda** | Proof Assistant | Type checking, invariant proofs | PHASE 7.1 |\n", "| **Ada/SPARK** | Formal Methods | Loop & invariant verification | PHASE 7.2 |\n", "| **Lean 4** | Proof Language | Curry-Howard isomorphism | PHASE 7.3 |\n", "| **Z3** | SMT Solver | Symbolic execution | PHASE 7.4 |\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PHASE 7.1: Agda Integration\n", "\n", "### Task: Invoke Agda for type checking\n", "\n", "**File:** `crates/proof-validator/src/adapters/agda_adapter.rs`\n", "\n", "```rust\n", "pub struct AgdaAdapter {\n", " agda_bin: PathBuf,\n", " library_path: Vec,\n", "}\n", "\n", "impl AgdaAdapter {\n", " pub async fn verify_type(&self, source: &str, expected_type: &str) -> Result {\n", " // 1. Write source to temp file\n", " // 2. Invoke: agda --check source.agda\n", " // 3. Parse output (OK / ERROR)\n", " // 4. Return ProofStatus::Proved or ProofStatus::Disproved\n", " }\n", "}\n", "```\n", "\n", "**Evidence:**\n", "- Creates temp Agda files\n", "- Spawns agda process\n", "- Parses exit code + stderr\n", "- Returns deterministic result" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PHASE 7.2: Ada/SPARK Integration\n", "\n", "### Task: SPARK verifier for loop invariants\n", "\n", "**File:** `crates/proof-validator/src/adapters/spark_adapter.rs`\n", "\n", "```rust\n", "pub struct SparkAdapter {\n", " spark_bin: PathBuf,\n", " timeout_secs: u64,\n", "}\n", "\n", "impl SparkAdapter {\n", " pub async fn verify_loop_invariant(&self, ada_source: &str, invariant: &str) -> Result {\n", " // 1. Extract loop from source\n", " // 2. Annotate with --# loop_invariant pragma\n", " // 3. Run: gnatprove -P project.gpr\n", " // 4. Check proof results\n", " // 5. Return Proved / Disproved / Timeout\n", " }\n", "}\n", "```\n", "\n", "**Evidence:**\n", "- Parses Ada loop syntax\n", "- Instruments with SPARK pragmas\n", "- Invokes gnatprove\n", "- Deterministic timeout handling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PHASE 7.3: Lean 4 Integration\n", "\n", "### Task: Curry-Howard type checking\n", "\n", "**File:** `crates/proof-validator/src/adapters/lean4_adapter.rs`\n", "\n", "```rust\n", "pub struct Lean4Adapter {\n", " lean_bin: PathBuf,\n", " stdlib_path: PathBuf,\n", "}\n", "\n", "impl Lean4Adapter {\n", " pub async fn verify_curry_howard(&self, lean_proof: &str, theorem: &str) -> Result {\n", " // 1. Write proof to .lean file\n", " // 2. Run: lean --check proof.lean\n", " // 3. Parse Lean diagnostics\n", " // 4. Match theorem signature\n", " // 5. Return Proved or error message\n", " }\n", "}\n", "```\n", "\n", "**Evidence:**\n", "- Validates proof term structure\n", "- Type-checks against theorem statement\n", "- Extracts proof witness\n", "- Returns serializable proof object" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## PHASE 7.4: Z3 SMT Solver Integration\n", "\n", "### Task: Symbolic execution for invariant extraction\n", "\n", "**File:** `crates/proof-validator/src/adapters/z3_adapter.rs`\n", "\n", "```rust\n", "pub struct Z3Adapter {\n", " z3_ctx: z3::Context,\n", "}\n", "\n", "impl Z3Adapter {\n", " pub fn verify_invariant(&self, formula: &str, invariant: &str) -> Result {\n", " // 1. Parse formula to Z3 expression\n", " // 2. Assert (NOT invariant)\n", " // 3. Check satisfiability\n", " // 4. If UNSAT: invariant proven\n", " // 5. If SAT: return counterexample\n", " }\n", "}\n", "```\n", "\n", "**Evidence:**\n", "- Uses z3-rs bindings\n", "- SMT-LIB syntax support\n", "- Counterexample extraction\n", "- Proof object construction" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Implementation Checklist\n", "\n", "### PHASE 7.1: Agda\n", "- [ ] Create `agda_adapter.rs`\n", "- [ ] Implement `verify_type()` method\n", "- [ ] Add temp file creation\n", "- [ ] Parse agda exit codes\n", "- [ ] Unit tests (3 test cases)\n", "- [ ] Integration test with sample proof\n", "\n", "### PHASE 7.2: Ada/SPARK\n", "- [ ] Create `spark_adapter.rs`\n", "- [ ] Implement `verify_loop_invariant()`\n", "- [ ] Pragma injection\n", "- [ ] gnatprove subprocess handling\n", "- [ ] Timeout + cleanup\n", "- [ ] Unit tests (2 test cases)\n", "\n", "### PHASE 7.3: Lean 4\n", "- [ ] Create `lean4_adapter.rs`\n", "- [ ] Implement `verify_curry_howard()`\n", "- [ ] .lean file writing\n", "- [ ] Lean diagnostics parsing\n", "- [ ] Proof term extraction\n", "- [ ] Unit tests (3 test cases)\n", "\n", "### PHASE 7.4: Z3\n", "- [ ] Create `z3_adapter.rs`\n", "- [ ] Implement `verify_invariant()`\n", "- [ ] SMT-LIB formula construction\n", "- [ ] Satisfiability checking\n", "- [ ] Counterexample extraction\n", "- [ ] Unit tests (4 test cases)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Proof Obligations\n", "\n", "### InvariantPreservation\n", "```\n", "∀ state: State.\n", " invariant(state) ∧ transition(state, state') →\n", " invariant(state')\n", "```\n", "\n", "**Verified by:** Z3 SMT solver (symbolic execution)\n", "\n", "### SemanticPreservation\n", "```\n", "∀ source: String.\n", " semantics(compile(source)) = semantics(source)\n", "```\n", "\n", "**Verified by:** Lean 4 (Curry-Howard proof)\n", "\n", "### LoopInvariantMaintenance\n", "```\n", "∀ i: Nat.\n", " loop_invariant(i) ∧ loop_condition(i) →\n", " loop_invariant(i+1)\n", "```\n", "\n", "**Verified by:** Ada/SPARK (gnatprove)\n", "\n", "### ReceiptChainIntegrity\n", "```\n", "∀ r1, r2: Receipt.\n", " r1.sequence < r2.sequence ∧\n", " r2.previous_hash = r1.hash →\n", " chain_valid(r1, r2)\n", "```\n", "\n", "**Verified by:** Agda (type checking)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Release Gate Integration\n", "\n", "### Prolog Gate (logic/rules/release_ready.pl)\n", "\n", "```prolog\n", "% Before Phase 7: stubs always return true\n", "proof_verified(_, stub, true) :- !.\n", "\n", "% After Phase 7: real verifiers required\n", "proof_verified(Obligation, agda, true) :-\n", " agda_adapter:verify_type(Obligation, _).\n", "\n", "proof_verified(Obligation, spark, true) :-\n", " spark_adapter:verify_loop_invariant(Obligation, _).\n", "\n", "proof_verified(Obligation, lean4, true) :-\n", " lean4_adapter:verify_curry_howard(Obligation, _).\n", "\n", "proof_verified(Obligation, z3, true) :-\n", " z3_adapter:verify_invariant(Obligation, _).\n", "```\n", "\n", "### Release Readiness Check\n", "\n", "```prolog\n", "release_ready(proof_obligations_discharged) :-\n", " forall(\n", " proof_obligation(Obligation, Tool, _),\n", " proof_verified(Obligation, Tool, true)\n", " ).\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Execution Flow\n", "\n", "### Cell Execution → Proof Validation → Receipt\n", "\n", "```\n", "1. Notebook cell executes (user code)\n", " ↓\n", "2. Invariant extractor infers proof obligations\n", " ↓\n", "3. Dispatch to appropriate verifier:\n", " - Agda for type safety\n", " - Ada/SPARK for loop invariants\n", " - Lean 4 for semantic preservation\n", " - Z3 for symbolic execution\n", " ↓\n", "4. Verifier returns ProofStatus (Proved/Disproved/Manual/Error)\n", " ↓\n", "5. If all proofs Proved:\n", " - Create WORM-sealed receipt\n", " - Link to receipt chain\n", " - Mark cell as VERIFIED\n", " ↓\n", "6. If any proof fails:\n", " - Rollback cell\n", " - Return error to notebook\n", " - Operator must fix and retry\n", "```" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Success Criteria\n", "\n", "✅ **PHASE 7 Complete When:**\n", "\n", "1. All 4 adapters implemented (Agda, SPARK, Lean 4, Z3)\n", "2. Each adapter has 2-4 unit tests (12+ total)\n", "3. Each adapter can be invoked from release gate\n", "4. Prolog predicates updated to call real verifiers\n", "5. End-to-end test: execute cell → verify proof → seal receipt\n", "6. No stubs remaining (all ProofStatus calls reach actual tools)\n", "7. Timeout + error handling for each tool\n", "8. 37+ existing tests still passing\n", "9. All commits pushed to GitHub\n", "10. Notebook artifact committed (`.ipynb` file)\n", "\n", "**Status: READY FOR IMPLEMENTATION**" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.0" } }, "nbformat": 4, "nbformat_minor": 2 }