Predicate Abstraction for Linked Data Structures

TL;DR

This paper introduces Alias Refinement Types (ART), a novel method combining shape and logical reasoning to verify linked data structures more efficiently, reducing annotation effort significantly.

Contribution

The paper proposes ART, a new type-based approach that integrates alias and refinement types for precise heap reasoning and verification of data structures.

Findings

ART reduces annotation requirements by 79% compared to existing techniques.

ART is sound, translating types into separation logic assertions.

Empirical evaluation shows ART's effectiveness on data-structure benchmarks.

Abstract

We present Alias Refinement Types (ART), a new approach to the verification of correctness properties of linked data structures. While there are many techniques for checking that a heap-manipulating program adheres to its specification, they often require that the programmer annotate the behavior of each procedure, for example, in the form of loop invariants and pre- and post-conditions. Predicate abstraction would be an attractive abstract domain for performing invariant inference, existing techniques are not able to reason about the heap with enough precision to verify functional properties of data structure manipulating programs. In this paper, we propose a technique that lifts predicate abstraction to the heap by factoring the analysis of data structures into two orthogonal components: (1) Alias Types, which reason about the physical shape of heap structures, and (2) Refinement Types, which use simple predicates from an SMT decidable theory to capture the logical or semantic properties of the structures. We prove ART sound by translating types into separation logic assertions, thus translating typing derivations in ART into separation logic proofs. We evaluate ART by implementing a tool that performs type inference for an imperative language, and empirically show, using a suite of data-structure benchmarks, that ART requires only 21% of the annotations needed by other state-of-the-art verification techniques.