Nathan Wasser

We present a novel and well automatable approach to formal verification of programs with underspecified semantics, i.e., a language semantics that leaves open the order of certain evaluations. First, we reduce this problem to non-determinism of distributed systems, automatically extracting a distributed Active Object model from underspecified, sequential C code. This translation process provides a fully formal semantics for the considered C subset. In the extracted model every non-deterministic choice corresponds to one possible evaluation order. This step also automatically translates specifications in the ANSI/ISO C Specification Language (ACSL) into method contracts and object invariants for Active Objects. We then perform verification on the specified Active Objects model. For this we have implemented a theorem prover Crowbar based on the Behavioral Program Logic (BPL), which verifies the extracted model with respect to the translated specification and ensures the original property of the C code for all possible evaluation orders. By using model extraction, we can use standard tools, without designing a new complex program logic to deal with underspecification. The case study used is highly underspecified and cannot be verified with existing tools for C.

Indexed loop scopes have been shown to be a helpful tool in creating sound loop invariant rules in dynamic logic for programming languages with abrupt completion, such as Java. These rules do not require program transformation of the loop body, as other approaches to dealing with abrupt completion do. However, indexed loop scopes were designed specifically to provide a loop invariant rule for while loops and work rather opaquely. Here we propose replacing indexed loop scopes with a more transparent solution, which also lets us extend this idea from while loops to for loops. We further present sound loop unrolling rules for while, do and for loops, which require neither program transformation of the loop body, nor the use of nested modalities. This approach allows for loops to be treated as first-class citizens in proofs -- rather than the usual approach of transforming for loops into while loops -- which makes semi-automated proofs more transparent and easier to follow for the user, whose interactions may be required in order to close the proofs.

Loop scopes have been shown to be a helpful tool in creating sound loop invariant rules which do not require program transformation of the loop body. Here we extend this idea from while-loops to for-loops and also present sound loop unrolling rules for while- and for-loops, which require neither program transformation of the loop body, nor the use of nested modalities. This approach allows for-loops to be treated as first-class citizens -- rather than the usual approach of transforming for-loops into while-loops -- which makes semi-automated proofs easier to follow for the user, who may need to provide help in order to finish the proof.