Function extraction

AbstractLow-level imperative programming languages typically have complex operational semantics (e.g. derived from an underlying processor architecture). In this paper, we describe an automatic method for extracting recursive functions from such low-level programs. The functions are derived by formal deduction from the semantics of the programming language. For each function extracted, a proof of correspondence to the original program is automatically constructed. Subsequent program verification can then be done without referring to the details of the low-level programming language semantics at all: it suffices to prove properties of the extracted function. The technique is explained for simple while programs and also for the machine code of a widely used processor. We show how heuristics can enhance the output from the function extractor/decompiler and how the technique aids implementation of a trustworthy compiler. Our tools have been implemented in the HOL4 theorem prover

Doctor of Philosophy

dissertationTrusted computing base (TCB) of a computer system comprises components that must be trusted in order to support its security policy. Research communities have identified the well-known minimal TCB principle, namely, the TCB of a system should be as small as possible, so that it can be thoroughly examined and verified. This dissertation is an experiment showing how small the TCB for an isolation service is based on software fault isolation (SFI) for small multitasking embedded systems. The TCB achieved by this dissertation includes just the formal definitions of isolation properties, instruction semantics, program logic, and a proof assistant, besides hardware. There is not a compiler, an assembler, a verifier, a rewriter, or an operating system in the TCB. To the best of my knowledge, this is the smallest TCB that has ever been shown for guaranteeing nontrivial properties of real binary programs on real hardware. This is accomplished by combining SFI techniques and high-confidence formal verification. An SFI implementation inserts dynamic checks before dangerous operations, and these checks provide necessary invariants needed by the formal verification to prove theorems about the isolation properties of ARM binary programs. The high-confidence assurance of the formal verification comes from two facts. First, the verification is based on an existing realistic semantics of the ARM ISA that is independently developed by Cambridge researchers. Second, the verification is conducted in a higher-order proof assistant-the HOL theorem prover, which mechanically checks every verification step by rigorous logic. In addition, the entire verification process, including both specification generation and verification, is automatic. To support proof automation, a novel program logic has been designed, and an automatic reasoning framework for verifying shallow safety properties has been developed. The program logic integrates Hoare-style reasoning and Floyd's inductive assertion reasoning together in a small set of definitions, which overcomes shortcomings of Hoare logic and facilitates proof automation. All inference rules of the logic are proven based on the instruction semantics and the logic definitions. The framework leverages abstract interpretation to automatically find function specifications required by the program logic. The results of the abstract interpretation are used to construct the function specifications automatically, and the specifications are proven without human interaction by utilizing intermediate theorems generated during the abstract interpretation. All these work in concert to create the very small TCB

Verification Condition Generation via Theorem Proving

Abstract. We present a method to convert (i) an operational semantics for a given machine language, and (ii) an off-the-shelf theorem prover, into a high assurance verification condition generator (VCG). Given a program annotated with assertions at cutpoints, we show how to use the theorem prover directly on the operational semantics to generate verification conditions analogous to those produced by a custom-built VCG. Thus no separate VCG is necessary, and the theorem prover can be employed both to generate and to discharge the verification conditions. The method handles both partial and total correctness. It is also compositional in that the correctness of a subroutine needs to be proved once, rather than at each call site. The method has been used to verify several machine-level programs using the ACL2 theorem prover.