| % Proof Obligation Rules (PHASE 7-10) | |
| % Maps proof obligations to verifiers (Agda, Ada/SPARK, Lean 4, Z3) | |
| :- module(proof_obligations, [ | |
| proof_obligation/3, | |
| proof_verified/3, | |
| proof_tool_assignment/2, | |
| all_obligations_discharged/0 | |
| ]). | |
| % PROOF OBLIGATIONS | |
| :- dynamic(proof_obligation/3). | |
| % proof_obligation(ObligationID, Type, Context). | |
| % 1. INVARIANT PRESERVATION (via Z3 SMT solver) | |
| % Verify: ∀ state. invariant(state) ∧ transition(state, state') → invariant(state') | |
| proof_obligation('inv-001', 'invariant_preservation', 'receipt_chain'). | |
| proof_obligation('inv-002', 'invariant_preservation', 'memory_state'). | |
| proof_obligation('inv-003', 'invariant_preservation', 'authorization_gates'). | |
| % 2. SEMANTIC PRESERVATION (via Lean 4) | |
| % Verify: ∀ source. semantics(compile(source)) = semantics(source) | |
| proof_obligation('sem-001', 'semantic_preservation', 'subleq_codegen'). | |
| proof_obligation('sem-002', 'semantic_preservation', 'unicode_roundtrip'). | |
| proof_obligation('sem-003', 'semantic_preservation', 'polyglot_compilation'). | |
| % 3. LOOP INVARIANT MAINTENANCE (via Ada/SPARK) | |
| % Verify: ∀ i. loop_invariant(i) ∧ loop_condition(i) → loop_invariant(i+1) | |
| proof_obligation('loop-001', 'loop_invariant', 'receipt_append'). | |
| proof_obligation('loop-002', 'loop_invariant', 'cell_iteration'). | |
| proof_obligation('loop-003', 'loop_invariant', 'nonce_verification'). | |
| % 4. RECEIPT CHAIN INTEGRITY (via Agda) | |
| % Verify: ∀ r1, r2. r1.sequence < r2.sequence ∧ r2.prev_hash = r1.hash → chain_valid(r1, r2) | |
| proof_obligation('chain-001', 'receipt_chain_integrity', 'v2_chain'). | |
| proof_obligation('chain-002', 'receipt_chain_integrity', 'replay_detection'). | |
| proof_obligation('chain-003', 'receipt_chain_integrity', 'merkle_tree'). | |
| % TOOL ASSIGNMENT (which verifier for each obligation) | |
| :- dynamic(proof_tool_assignment/2). | |
| % For v1 (stubs): all return true | |
| proof_tool_assignment('invariant_preservation', 'z3'). | |
| proof_tool_assignment('semantic_preservation', 'lean4'). | |
| proof_tool_assignment('loop_invariant', 'spark'). | |
| proof_tool_assignment('receipt_chain_integrity', 'agda'). | |
| % PROOF STATUS | |
| :- dynamic(proof_verified/3). | |
| % proof_verified(ObligationID, Tool, Status). | |
| % Status: proved | disproved | manual | error | timeout | |
| % Current stub status (v1 - pre-PHASE-7) | |
| proof_verified('inv-001', 'stub', 'assumed'). | |
| proof_verified('inv-002', 'stub', 'assumed'). | |
| proof_verified('inv-003', 'stub', 'assumed'). | |
| proof_verified('sem-001', 'stub', 'assumed'). | |
| proof_verified('sem-002', 'stub', 'assumed'). | |
| proof_verified('sem-003', 'stub', 'assumed'). | |
| proof_verified('loop-001', 'stub', 'assumed'). | |
| proof_verified('loop-002', 'stub', 'assumed'). | |
| proof_verified('loop-003', 'stub', 'assumed'). | |
| proof_verified('chain-001', 'stub', 'assumed'). | |
| proof_verified('chain-002', 'stub', 'assumed'). | |
| proof_verified('chain-003', 'stub', 'assumed'). | |
| % DISPATCH LOGIC (pre-PHASE-7: stubs / post-PHASE-7: real verifiers) | |
| % After PHASE 7, this becomes: | |
| % | |
| % proof_verified(ObligationID, Tool, proved) :- | |
| % proof_obligation(ObligationID, Type, _), | |
| % proof_tool_assignment(Type, Tool), | |
| % % Call actual verifier (e.g., agda_adapter:verify(...)) | |
| % agda_adapter:verify_obligation(ObligationID, Tool). | |
| % VERIFICATION PREDICATE (comprehensive check) | |
| verify_proof_obligation(ObligationID) :- | |
| proof_obligation(ObligationID, Type, Context), | |
| proof_tool_assignment(Type, Tool), | |
| proof_verified(ObligationID, Tool, Status), | |
| % Current: all stubs assumed | |
| (Status = assumed ; Status = proved). | |
| % RELEASE GATE: All proof obligations discharged | |
| all_obligations_discharged :- | |
| % 1. All obligations must exist | |
| findall(ID, proof_obligation(ID, _, _), ObligationIDs), | |
| length(ObligationIDs, Count), | |
| Count > 0, | |
| % 2. All must be verified (either proved or assumed) | |
| forall( | |
| proof_obligation(OID, Type, _), | |
| ( proof_tool_assignment(Type, Tool), | |
| proof_verified(OID, Tool, Status), | |
| (Status = proved ; Status = assumed) | |
| ) | |
| ), | |
| % 3. No timeouts or errors | |
| \+ proof_verified(_, _, error), | |
| \+ proof_verified(_, _, timeout). | |
| % DEBUG: Check obligation status | |
| check_obligation_status :- | |
| format('PROOF OBLIGATIONS STATUS~n', []), | |
| format('========================~n', []), | |
| forall( | |
| proof_obligation(ID, Type, Context), | |
| ( proof_tool_assignment(Type, Tool), | |
| proof_verified(ID, Tool, Status), | |
| format('~w: ~w (~w) [~w]~n', [ID, Type, Tool, Status]) | |
| ) | |
| ), | |
| format('~n', []), | |
| ( all_obligations_discharged | |
| -> format('✓ ALL OBLIGATIONS DISCHARGED~n', []) | |
| ; format('✗ UNMET OBLIGATIONS EXIST~n', []) | |
| ). | |
| % STATISTICS | |
| obligation_stats(Total, Proved, Assumed, Errors) :- | |
| findall(ID, proof_obligation(ID, _, _), AllIDs), | |
| length(AllIDs, Total), | |
| findall(ID, proof_verified(ID, _, proved), ProvedList), | |
| length(ProvedList, Proved), | |
| findall(ID, proof_verified(ID, _, assumed), AssumedList), | |
| length(AssumedList, Assumed), | |
| findall(ID, proof_verified(ID, _, error), ErrorList), | |
| length(ErrorList, Errors). | |