Precondition Calculation for Loops Iterating over Data Structures

Precondition calculation is a fundamental program verification technique. Many previous works tried to solve this problem, but ended with limited capability due to loop statements. We conducted a survey on loops manipulating commonly-used data structures occurring in several real-world open-source programs, and found that about 80% of such loops iterate over elements of a data structure, indicating that automatic calculation of preconditions with respect to post-conditions of these loops would cover a great number of real-world programs and greatly ease code verification tasks. In this paper, we specify the execution effect of a program statement using the memories modified by the statement and the new values stored in these memories after executing the statement. Thus, conditional statements and loop statements can be uniformly reduced to a sequence of assignments. Also we present an approach to calculate preconditions with respect to given post-conditions of various program statements including loops that iterate over elements of commonly-used data structures (e.g., acyclic singly-linked lists) based on execution effects of these statements. With execution effects, post-conditions and loop invariants can also be generated. Our approach handles various types of data including numeric, boolean, arrays and user-defined structures. We have implemented the approach and integrated it into the code verification tool, Accumulator. We also evaluated the approach with a variety of programs, and the results show that our approach is able to calculate preconditions for different kinds of post-conditions, including linear ones and universally quantified ones. Preconditions generated with our approach can ease the verification task by reducing the burden of providing loop invariants and preconditions of loop statements manually, which improves the automatic level and efficiency, and makes the verification less error-prone.