Assertion Checking Unified

We revisit the connection between equality assertion checking in programs and unification. Using a general formalization of this connection, we establish interesting connections between the complexity of assertion checking in programs and unification theory of the underlying program expressions. In particular, we show that assertion checking is:

• PTIME for programs with nondeterministic conditionals that use expressions from a strict unitary theory,
• coNP-hard for programs with nondeterministic conditionals that use expressions from a bitary theory, and
• decidable for programs with disequality guards that use expressions from a convex finitary theory.

These results generalize several recently published results and also establish several new results. In essence, they provide new techniques for backward analysis of programs based on novel integration of theorem proving technology in program analysis.