50,241 research outputs found
On Automated Lemma Generation for Separation Logic with Inductive Definitions
Separation Logic with inductive definitions is a well-known approach for
deductive verification of programs that manipulate dynamic data structures.
Deciding verification conditions in this context is usually based on
user-provided lemmas relating the inductive definitions. We propose a novel
approach for generating these lemmas automatically which is based on simple
syntactic criteria and deterministic strategies for applying them. Our approach
focuses on iterative programs, although it can be applied to recursive programs
as well, and specifications that describe not only the shape of the data
structures, but also their content or their size. Empirically, we find that our
approach is powerful enough to deal with sophisticated benchmarks, e.g.,
iterative procedures for searching, inserting, or deleting elements in sorted
lists, binary search tress, red-black trees, and AVL trees, in a very efficient
way
Invariant Synthesis for Incomplete Verification Engines
We propose a framework for synthesizing inductive invariants for incomplete
verification engines, which soundly reduce logical problems in undecidable
theories to decidable theories. Our framework is based on the counter-example
guided inductive synthesis principle (CEGIS) and allows verification engines to
communicate non-provability information to guide invariant synthesis. We show
precisely how the verification engine can compute such non-provability
information and how to build effective learning algorithms when invariants are
expressed as Boolean combinations of a fixed set of predicates. Moreover, we
evaluate our framework in two verification settings, one in which verification
engines need to handle quantified formulas and one in which verification
engines have to reason about heap properties expressed in an expressive but
undecidable separation logic. Our experiments show that our invariant synthesis
framework based on non-provability information can both effectively synthesize
inductive invariants and adequately strengthen contracts across a large suite
of programs
Concurrent Data Structures Linked in Time
Arguments about correctness of a concurrent data structure are typically
carried out by using the notion of linearizability and specifying the
linearization points of the data structure's procedures. Such arguments are
often cumbersome as the linearization points' position in time can be dynamic
(depend on the interference, run-time values and events from the past, or even
future), non-local (appear in procedures other than the one considered), and
whose position in the execution trace may only be determined after the
considered procedure has already terminated.
In this paper we propose a new method, based on a separation-style logic, for
reasoning about concurrent objects with such linearization points. We embrace
the dynamic nature of linearization points, and encode it as part of the data
structure's auxiliary state, so that it can be dynamically modified in place by
auxiliary code, as needed when some appropriate run-time event occurs. We name
the idea linking-in-time, because it reduces temporal reasoning to spatial
reasoning. For example, modifying a temporal position of a linearization point
can be modeled similarly to a pointer update in separation logic. Furthermore,
the auxiliary state provides a convenient way to concisely express the
properties essential for reasoning about clients of such concurrent objects. We
illustrate the method by verifying (mechanically in Coq) an intricate optimal
snapshot algorithm due to Jayanti, as well as some clients
- …