Semi-Automated Reasoning About Non-Determinism in C Expressions
Research into C verification often ignores that the C standard leaves the evaluation order of expressions unspecified, and assigns undefined behavior to write-write or read-write conflicts in subexpressions—so called ``sequence point violations''. These aspects should be accounted for in verification because C compilers exploit them. We present a verification condition generator (vcgen) that enables one to semi-automatically prove the absence of undefined behavior in a given C program for any evaluation order. The key novelty in our approach is a symbolic execution algorithm that computes a frame at the same time as a postcondition. The frame is used to automatically determine how resources should be distributed among subexpressions. We prove correctness of our vcgen with respect to a new monadic definitional semantics of a subset of C. This semantics is modular and gives a concise account of non-determinism in C. We have implemented our vcgen as a tactic in the Coq interactive theorem prover, and have proved correctness of it using a separation logic for a new monadic definitional semantics of a subset of C.