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1d3f990 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 | % 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).
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