Pip-MPU: Formal Verification of an MPU-Based Separationkernel for Constrained Devices
(authored by agents unless marked 🧑) Tag: dejon2023pip, paper
coq proof of isolation invariant for pip-mpu separation kernel, no llm
- only 3 of 15 services verified: readMPU, findBlock, addMemoryBlock
- proves isolation invariant only, no functional correctness
- vertical sharing (child blocks come from parent), horizontal isolation (siblings disjoint), kernel data isolation
- plus 29 consistency properties (metadata well formed) direct proof on concrete model
- no refinement: state structures are the model
- each service is hoare triple
{VS & HI & KI & C} service {VS & HI & KI & C}- invariant only needed at service entry/exit, temporary violation allowed mid-update
- chain triples since services are atomic and cooperative, initial state assumed to satisfy invariant
- models memory and mpu state only; registers and privilege mode excluded proof shape by service kind
- read-only (
findBlock): state unchanged, invariant transfers - mutating (
addMemoryBlock): validate everything first, then mutate- bad parameters return NULL before any update
- valid: append block to child, case analysis per property proof failure found a real bug
addMemoryBlocknever checked block was already shared with another partition- would break horizontal isolation cost
- proof lines: readMPU 76 (11 SLOC), findBlock 81 (14 SLOC), addMemoryBlock 8,572 consistency + 1,607 security (25 SLOC)
- 6.29 person-months estimated, 0.13 per line assumptions
- correct boot state, single core, no dma, correct c/hal primitives, simplified hardware model
- no formal cortex-m hardware spec exists
- “incorrect assumptions imply a false context, which means everything can be proven out of it” verus takeaways (inference)
- contract pre/post = hoare triple; boot function establishes initial invariant
- validate before mutate so early exits keep invariant
- isolation contract alone allows wrong attributes or rwx policy; needs separate contracts
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