Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1610.05156

Reachability Analysis of Innermost Rewriting

Thomas Genet·Yann Salmon
View original source ↗Read source document ↗Export metadata ↓

Abstract

We consider the problem of inferring a grammar describing the output of a functional program given a grammar describing its input. Solutions to this problem are helpful for detecting bugs or proving safety properties of functional programs, and several rewriting tools exist for solving this problem. However, known grammar inference techniques are not able to take evaluation strategies of the program into account. This yields very imprecise results when the evaluation strategy matters. In this work, we adapt the Tree Automata Completion algorithm to approximate accurately the set of terms reachable by rewriting under the innermost strategy. We formally prove that the proposed technique is sound and precise w.r.t. innermost rewriting. We show that those results can be extended to the leftmost and rightmost innermost case. The algorithms for the general innermost case have been implemented in the Timbuk reachability tool. Experiments show that it noticeably improves the accuracy of static analysis for functional programs using the call-by-value evaluation strategy.

Explore related subjects

cs.LO

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Thomas Genet, Yann Salmon. 2017-03-21. Reachability Analysis of Innermost Rewriting. https://doi.org/10.23638/lmcs-13(1%3A12)2017

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Verifying Numerical Methods with Isabelle/HOL

Modern machine learning pipelines and ODE solvers are built on numerical algorithms. Reliable numerical methods are thus a prerequisite for trustworthy machine learning and cyber-physical systems. We evaluate a framework designed for verifying imperative programs and the Isabelle proof assistant as tools for proving the total correctness of four numerical algorithms: the bisection method, the fixed-point method, the perceptron, and the gradient descent algorithm. Our verifications required subtle extensions and generalisations to Isabelle's version of Taylor's theorem and higher-order derivatives. Finally, we reflect on the framework's automation, friendly syntax, and on further requirements to turn it into a verification tool for numerical methods.

cs.LO↗
arXiv2026

Trace-Tree Magmas: Proof-Producing Infinite Countermodels and 28 New Order-Five Austin Classifications

Finite model finders cannot witness an Austin law: an identity whose finite models are all trivial but which has a nontrivial infinite model. We introduce rank-decreasing sparse trace-tree magmas, finitely presented total operations on a countably infinite constructor-tree carrier. The default product pairs its arguments; finitely many positive Horn clauses define exceptions. Our main procedure derives clauses from symbolic evaluation traces. For every model found, it proves functionality of the exceptional relation by descent on constructor size, proves the identity by exhaustive symbolic case analysis, and emits a self-contained Lean 4 certificate. A least simultaneous fixed point gives an implementation-independent semantics, so bounded search may miss models but cannot invalidate certified results. On ETP's 96 order-five Austin candidates, we discover and Lean-verify infinite countermodels for 28 identities with no prior public classification in our audit. They form 14 duality classes and establish 28 new Austin classifications. Four ALPS-known cases bring the total to 32 certified candidates. On Canonical-4187, the deduplicated union of Order5-130 and the 4,141-row ALPS pool, a fresh trace run produces 636 certificates, all accepted by Judge v3. At equal resource limits, Vampire 5.0.1, E 3.5.1, and complete Twee 2.6.1 jointly prove implications in 94 canonical classes. Only Twee returns trusted counter-satisfiable outcomes, for 18 classes; independent finite-side certificates force 16 to be infinite. None of these ATPs emits an explicit model or Lean certificate, and none decides the 28 new classifications. To the best of our audit, this is the first automated system to synthesize this trace-tree model family, generate well-founded inversion proofs, and emit self-contained Lean 4 certificates.

cs.LO↗
arXiv2026

Don't Blame the Model, Verify the Data: An Evaluation of SMT-based Dataset Verification (Extended Version)

The EU AI Act mandates that datasets for high-risk machine learning (ML) systems meet strict quality criteria such as soundness and bias mitigation. While Satisfiability Modulo Theory (SMT) solving offers a formal approach to verifying these properties, its scalability in realistic ML settings remains unexplored. To bridge this gap, this work presents the first large-scale empirical study of SMT-based dataset verification on two real-world ML datasets. We systematically evaluate how solver performance is shaped by three key dimensions: the type of data-quality property, the specification style, and the dataset encoding strategy. Our findings demonstrate that SMT-based verification is feasible for practical scenarios, but each dimension shapes it: the property type sets the tractability limit, the specification style drives scalability (exceeding $2{,}000{\times}$ for aggregate properties), and the encoding strategy has a systematic effect, with extracted feature columns performing best.

cs.LO↗