Data flow refinement type inference

Abstract

Refinement types enable lightweight verification of functional programs. Algorithms for statically inferring refinement types typically work by reduction to solving systems of constrained Horn clauses extracted from typing derivations. An example is Liquid type inference, which solves the extracted constraints using predicate abstraction. However, the reduction to constraint solving in itself already signifies an abstraction of the program semantics that affects the precision of the overall static analysis. To better understand this issue, we study the type inference problem in its entirety through the lens of abstract interpretation. We propose a new refinement type system that is parametric with the choice of the abstract domain of type refinements as well as the degree to which it tracks context-sensitive control flow information. We then derive an accompanying parametric inference algorithm as an abstract interpretation of a novel data flow semantics of functional programs. We further show that the type system is sound and complete with respect to the constructed abstract semantics. Our theoretical development reveals the key abstraction steps inherent in refinement type inference algorithms. The trade-off between precision and efficiency of these abstraction steps is controlled by the parameters of the type system. Existing refinement type systems and their respective inference algorithms, such as Liquid types, are captured by concrete parameter instantiations. We have implemented our framework in a prototype tool and evaluated it for a range of new parameter instantiations (e.g., using octagons and polyhedra for expressing type refinements). The tool compares favorably against other existing tools. Our evaluation indicates that our approach can be used to systematically construct new refinement type inference algorithms that are both robust and precise.

Automatic HFL(Z) Validity Checking for Program Verification

“…Various techniques have been proposed and implemented for automated verification of various properties of higher-order programs, including safety properties [26,28,14,27,23,25,34], termination [19], non-termination [18], fair termination [21], and fair non-termination [32]. In contrast to those studies, which developed separate techniques and tools for proving different properties, our HFL(Z) checker serves as a common backend for all of those properties.…”

“…By combining the proposed method with the above-mentioned reduction [16,33], we can obtain a fully automated verification method for arbitrary regular temporal properties of higher-order programs. The properties that can be verified in a uniform manner using our method include safety [26,28,14,27,23,25,34], termination [19], non-termination [18], fair termination [21], and fair non-termination [32], for which separate methods and tools have been developed so far.…”