Verifying properties of well-founded linked lists

Author:

Lahiri Shuvendu K.1,Qadeer Shaz1

Affiliation:

1. Microsoft Research

Abstract

We describe a novel method for verifying programs that manipulate linked lists, based on two new predicates that characterize reachability of heap cells. These predicates allow reasoning about both acyclic and cyclic lists uniformly with equal ease. The crucial insight behind our approach is that a circular list invariably contains a distinguished head cell that provides a handle on the list. This observation suggests a programming methodology that requires the heap of the program at each step to be well-founded , i.e., for any field f in the program, every sequence u .f, u .f.f, ... contains at least one head cell. We believe that our methodology captures the most common idiom of programming with linked data structures. We enforce our methodology by automatically instrumenting the program with updates to two auxiliary variables representing these predicates and adding assertions in terms of these auxiliary variables.To prove program properties and the instrumented assertions, we provide a first-order axiomatization of our two predicates. We also introduce a novel induction principle made possible by the well-foundedness of the heap. We use our induction principle to derive from two basic axioms a small set of additional first-order axioms that are useful for proving the correctness of several programs.We have implemented our method in a tool and used it to verify the correctness of a variety of nontrivial programs manipulating both acyclic and cyclic singly-linked lists and doubly-linked lists. We also demonstrate the use of indexed predicate abstraction to automatically synthesize loop invariants for these examples.

Publisher

Association for Computing Machinery (ACM)

Subject

Computer Graphics and Computer-Aided Design,Software

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1. Verifying OpenJDK’s LinkedList using KeY (extended paper);International Journal on Software Tools for Technology Transfer;2022-10

2. BOUNDED QUANTIFIER INSTANTIATION FOR CHECKING INDUCTIVE INVARIANTS;LOG METH COMPUT SCI;2019

3. Bounded Quantifier Instantiation for Checking Inductive Invariants;Tools and Algorithms for the Construction and Analysis of Systems;2017

4. Semantics-based program verifiers for all languages;Proceedings of the 2016 ACM SIGPLAN International Conference on Object-Oriented Programming, Systems, Languages, and Applications;2016-10-19

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