Nico Lehmann | Searcharxiv

arXiv2026

Foundational Constraint Solving for Expressive Refinement Typing

SMT-based program verifiers are hamstrung by two problems: expressiveness, because predictable verification restricts to the boundaries of SMT decidability, and trust, because the solver is a large, unverified artifact whose soundness bugs may quietly compromise every tool built on it. We present FLEX, a foundational Constrained Horn Clause (CHC) solver implemented in LEAN, that reduces the trusted base to the kernel alone, and allows using LEAN's entire proof ecosystem to verify low-level systems code, via three contributions. First, FLEX encodes CHCs as plain LEAN propositions where the Horn variables are existentially bound predicates, and shows how to implement CHC solvers as tactics (meta-programs) that compute kernel checkable proofs of the CHC propositions. Second, we show how to implement two verified CHC generators in LEAN: a Floyd-Hoare style generator for an imperative language, and a refinement-type-based generator for a functional calculus, which can be composed with the solving tactics to yield the first end-to-end foundational CHC-based verifiers. Finally, we show how FLEX allows us to leapfrog the expressiveness limitations of SMT by unleashing LEAN's entire ecosystem of proof machinery to prove arbitrary functional correctness properties of various low-level Rust libraries using the FLUX refinement type checker, and demonstrate the viability of FLEX as a trustworthy CHC backend, by showing it automatically discharges 95.7% of the CHCs from FLUX's benchmark suite.

cs.PL↗

arXiv2022

Flux: Liquid Types for Rust

We introduce Flux, which shows how logical refinements can work hand in glove with Rust's ownership mechanisms to yield ergonomic type-based verification of low-level pointer manipulating programs. First, we design a novel refined type system for Rust that indexes mutable locations, with pure (immutable) values that can appear in refinements, and then exploits Rust's ownership mechanisms to abstract sub-structural reasoning about locations within Rust's polymorphic type constructors, while supporting strong updates. We formalize the crucial dependency upon Rust's strong aliasing guarantees by exploiting the stacked borrows aliasing model to prove that ``well-borrowed evaluations of well-typed programs do not get stuck''. Second, we implement our type system in Flux, a plug-in to the Rust compiler that exploits the factoring of complex invariants into types and refinements to efficiently synthesize loop annotations -- including complex quantified invariants describing the contents of containers -- via liquid inference. Third, we evaluate Flux with a benchmark suite of vector manipulating programs and parts of a previously verified secure sandboxing library to demonstrate the advantages of refinement types over program logics as implemented in the state-of-the-art Prusti verifier. While Prusti's more expressive program logic can, in general, verify deep functional correctness specifications, for the lightweight but ubiquitous and important verification use-cases covered by our benchmarks, liquid typing makes verification ergonomic by slashing specification lines by a factor of two, verification time by an order of magnitude, and annotation overhead from up to 24% of code size (average 9%) to nothing at all.

cs.PL↗