Type-based data structure verification

Abstract

We present a refinement type-based approach for the static verification of complex data structure invariants. Our approach is based on the observation that complex data structures are typically fashioned from two elements: recursion (e.g., lists and trees), and maps (e.g., arrays and hash tables). We introduce two novel type-based mechanisms targeted towards these elements: recursive refinements and polymorphic refinements. These mechanisms automate the challenging work of generalizing and instantiating rich universal invariants by piggybacking simple refinement predicates on top of types, and carefully dividing the labor of analysis between the type system and an SMT solver [6]. Further, the mechanisms permit the use of the abstract interpretation framework of liquid type inference [22] to automatically synthesize complex invariants from simple logical qualifiers, thereby almost completely automating the verification. We have implemented our approach in DSOLVE, which uses liquid types to verify OCAML programs. We present experiments that show that our type-based approach reduces the manual annotation required to verify complex properties like sortedness, balancedness, binary-search-ordering, and acyclicity by more than an order of magnitude.

Abstract Refinement Types

“…We have evaluated HSOLVE over the following list of benchmarks which, in total, represent the different kinds of reasoning described in § 2. While we can prove, and previously have proved [16], many so-called "functional correctness" properties of these data structures using refinement types, in this work we focus on the key invariants which are captured by abstract refinements.…”

“…Refinement types have been applied to the verification of a variety of program properties [26,7,2,10]. In the most closely related work to our own, Kawaguchi et al [16] introduce recursive and polymorphic refinements for data structure properties. The present work unifies and generalizes these two somewhat ad-hoc notions into a single, strictly and significantly more expressive mechanism of abstract refinements.…”

“…Several groups have shown how refinement types can be used to verify properties ranging from partial correctness concerns like array bounds checking [26,22] and data structure invariants [16] to the correctness of security protocols [2], web applications [14] and implementations of cryptographic protocols [10].…”

A Fully Verified Container Library

“…Vazou et al [VSJ14] apply these techniques to verify termination, memory safety, and selected functional properties of over 10,000 lines of Haskell code from realistic libraries. Kawaguchi et al [KRJ09] apply similar techniques to verify ML implementations of lists, vectors, maps, and trees. As they target quantifier-free constraints, Liquid Haskell's techniques are completely automatic: whenever they are applicable, type inference algorithms supply all the intermediate type annotations (including invariants).…”

Automatically refining partial specifications for heap-manipulating programs

“…Meanwhile, we can utilise such works as our pure solver, for example the disjunction inference [10]. Semi-automatic approaches [37,38] are also used to infer numerical constraints for given type templates in functional programs, where data structures are mostly immutable.…”