On inter-procedural analysis of programs with lists and data

Abstract

We address the problem of automatic synthesis of assertions on sequential programs with singly-linked lists containing data over infinite domains such as integers or reals. Our approach is based on an accurate abstract inter-procedural analysis. Program configurations are represented by graphs where nodes represent list segments without sharing. The data in these list segments are characterized by constraints in abstract domains. We consider a domain where constraints are in a universally quantified fragment of the first-order logic over sequences, as well as a domain constraining the multisets of data in sequences. Our analysis computes the effect of each procedure in a local manner, by considering only the reachable part of the heap from its actual parameters. In order to avoid losses of information, we introduce a mechanism based on unfolding/folding operations allowing to strengthen the analysis in the domain of first-order formulas by the analysis in the multisets domain. The same mechanism is used for strengthening the sound (but incomplete) entailment operator of the domain of first-order formulas. We have implemented our techniques in a prototype tool and we have shown that our approach is powerful enough for automatic (1) generation of non-trivial procedure summaries, (2) pre/post-condition reasoning, and (3) procedure equivalence checking.