arXiv subjects

Viktor Kunčak

Publications and source records attributed to Viktor Kunčak.

At least 19 recordsLinked to original sources

arXiv2026

First-Class Refinement Types for Scala

Refinement types -- types qualified with logical predicates -- have proven effective for lightweight verification in languages like Liquid Haskell, F*, and Dafny. However, in these systems refinements are either written in a separate specification language or treated as second-class annotations, disconnected from the host language's type system. This disconnect creates usability barriers: programmers must maintain two mental models, and refinements cannot interact with features like type inference, subtyping, or overloading. We present the design of first-class refinement types for Scala 3, where refinements are ordinary types that participate in subtyping, inference, and pattern matching alongside existing language features. We prove type soundness of a core calculus mechanized in Rocq, combining dependent function types, bounded polymorphism, positive equi-recursive types, union and intersection types, and refinement types under a partial-correctness semantics using a fuel-bounded definitional interpreter and semantic typing. Finally, we implement our design as a prototype extension of the Scala 3 compiler with a lightweight e-graph-based solver for predicate entailment.

cs.PL↗

arXiv2026

Formally Verified Linear-Time Invertible Lexing

We present ZipLex, a verified framework for invertible linear-time lexical analysis following the longest match (maximal munch) semantics. Unlike past verified lexers that focus only on satisfying the semantics of regular expressions and the longest match property, ZipLex also guarantees that lexing and printing are mutual inverses. Thanks to verified memoization, it also ensures that the lexical analysis of a string is linear in the size of the string. Our design and implementation rely on two sets of ideas: (1) a new abstraction of token sequences that captures the separability of tokens in a sequence while supporting their efficient manipulation, and (2) a combination of verified data structures and optimizations, including Huet's zippers and memoization with a standalone verified imperative hash table. Our hash table offers competitive performance as shown by our evaluation. We implemented and verified ZipLex using the Stainless deductive verifier for Scala. Our evaluation demonstrates that ZipLex supports realistic applications such as JSON processing and lexers of programming languages, and behaves linearly even in cases that make flex-style approaches quadratic. ZipLex is two orders of magnitude faster than Verbatim++, showing that verified invertibility and linear-time algorithms can be developed without prohibitive cost. Compared to Coqlex, ZipLex also offers linear (instead of quadratic) time lexing, and is the first lexer that comes with invertibility proofs for printing token sequences.

cs.PL↗

arXiv2026

Orthologic for SAT Solving

We present a new algorithm for deciding formula entailment in orthologic (a sound approximation of classical logic) that avoids the costly preprocessing phase of prior implementations while retaining the same $\mathcal{O}(n^2(1+|A|))$ worst-case complexity. We then introduce a family of synthetic SAT benchmarks based on the observation that, for any formula $ϕ$, the equivalence $ϕ\leftrightarrow \mathrm{NF}_{\mathrm{OL}}(ϕ)$ is a tautology whose Tseitin encoding yields unsatisfiable instances that are hard for state-of-the-art SAT solvers yet have short orthologic proofs. Applied to EPFL arithmetic circuits, our algorithm solves these instances efficiently while Kissat times out on a significant fraction. Finally, we show that using orthologic normalization as a preprocessing step can improve SAT solving time on some hard problems.

cs.LO↗

arXiv2026

Are Dependent Types in Set Theory Feasible?

Following the types-as-sets paradigm, we present a mechanized embedding of dependent function types with a hierarchy of universes into schematic first-order logic with equality, with axiom schemas of Tarski-Grothendieck set theory. We carry this embedding in the Lisa proof assistant. On top of this foundation, we implement a proof-producing bidirectional type-checking tactic to compute proofs for typing judgements, with partial support for subtyping. We present examples showing how our approach enables automated reasoning for dependent types that is fully verified from set-theoretic axioms and deduction rules for schematic first-order logic with equality. Because types are merely sets, the resulting formalism supports equality that applies to all types and values and permits the usual substitution rules.

cs.LO↗

arXiv2025

Reliable Evaluation and Benchmarks for Statement Autoformalization

Evaluating statement autoformalization, translating natural language mathematics into formal languages like Lean 4, remains a significant challenge, with few metrics, datasets, and standards to robustly measure progress. In this work, we present a comprehensive approach combining improved metrics, robust benchmarks, and systematic evaluation, to fill this gap. First, we introduce BEq+, an automated metric that correlates strongly with human judgment, along with ProofNetVerif, a new dataset for assessing the quality of evaluation metrics, containing 3,752 annotated examples. Second, we develop two new autoformalization benchmarks: ProofNet#, a corrected version of ProofNet, and RLM25, with 619 new pairs of research-level mathematics from six formalization projects. Through systematic experimentation across these benchmarks, we find that current techniques can achieve up to 45.1% accuracy on undergraduate mathematics but struggle with research-level content without proper context. Our work establishes a reliable foundation for evaluating and advancing autoformalization systems.

cs.CL↗

arXiv2025

RLMEval: Evaluating Research-Level Neural Theorem Proving

Despite impressive results on curated benchmarks, the practical impact of large language models (LLMs) on research-level neural theorem proving and proof autoformalization is still limited. We introduce RLMEval, an evaluation suite for these tasks, focusing on research-level mathematics from real-world Lean formalization projects. RLMEval targets the evaluation of neural theorem proving and proof autoformalization on challenging research-level theorems by leveraging real Lean Blueprint formalization projects. Our evaluation of state-of-the-art models on RLMEval, comprising 613 theorems from 6 Lean projects, reveals a significant gap: progress on existing benchmarks does not readily translate to these more realistic settings, with the best model achieving only a 10.3 % pass rate. RLMEval provides a new, challenging benchmark designed to guide and accelerate progress in automated reasoning for formal mathematics.

cs.CL↗

arXiv2025

Interpolation and Quantifiers in Ortholattices

We study quantifiers and interpolation properties in \emph{orthologic}, a non-distributive weakening of classical logic that is sound for formula validity with respect to classical logic, yet has a quadratic-time decision procedure. We present a sequent-based proof system for quantified orthologic, which we prove sound and complete for the class of all complete ortholattices. We show that orthologic does not admit quantifier elimination in general. Despite that, we show that interpolants always exist in orthologic. We give an algorithm to compute interpolants efficiently. We expect our result to be useful to quickly establish unreachability as a component of verification algorithms.

cs.LO↗

arXiv2025

LISA -- A Modern Proof System

We present LISA, a proof system and proof assistant for constructing proofs in schematic first-order logic and axiomatic set theory. The logical kernel of the system is a proof checker for first-order logic with equality and schematic predicate and function symbols. It implements polynomial-time proof checking and uses the axioms of ortholattices (which implies the irrelevance of the order of conjuncts and disjuncts and additional propositional laws). The kernel supports the notion of theorems (whose proofs are not expanded), as well as definitions of predicate symbols and objects whose unique existence is proven. A domain-specific language enables construction of proofs and development of proof tactics with user-friendly tools and presentation, while remaining within the general-purpose language, Scala. We describe the LISA proof system and illustrate the flavour and the level of abstraction of proofs written in LISA. This includes a proof-generating tactic for propositional tautologies, leveraging the ortholattice properties to reduce the size of proofs. We also present early formalization of set theory in LISA, including Cantor's theorem.

cs.LO↗

arXiv2025

Orthologic Type Systems

We propose to use orthologic as the basis for designing type systems supporting intersection, union, and negation types in the presence of subtyping assumptions. We show how to extend orthologic to support monotonic and antimonotonic functions, supporting the use of type constructors in such type systems. We present a proof system for orthologic with function symbols, showing that it admits partial cut elimination. Using these insights, we present an $\mathcal O(n^2(1+m))$ algorithm for deciding the subtyping relation under $m$ assumptions. We also show $O(n^2)$ polynomial-time normalization algorithm, allowing simplification of types to their minimal canonical form.

cs.PL↗

arXiv2024

Verified invertible lexer using regular expressions and DFAs

In this project, we explore the concept of invertibility applied to serialisation and lexing frameworks. Recall that, on one hand, serialisation is the process of taking a data structure and writing it to a bit array while parsing is the reverse operation, i.e., reading the bit array and constructing the data structure back. While lexing, on the other hand, is the process of reading a stream of characters and splitting them into tokens, by following a list of given rules. While used in different applications, both are similar in their abstract operation: they both take a list of simple characters and extract a more complex structure. Applications in which these two operations are used are different but they share a need for the invertibility of the process. For example, when tokenising a code file that was prettyprinted by a compiler, one would expect to get the same sequence of tokens. Similarly, when a spacecraft sends scientific data to the ground, one would expect the parsed data to be the same as the one serialised by the spacecraft. The idea of this project is to explore the idea of having a framework capable of generating parser/serialiser or lexer/prettyprinter pairs with a formally verified notion of invertibility. We first explore related works and frameworks. After that, we present our verified lexer framework developed in Scala and verified using the Stainless framework1. We explain the implementation choices we make and present the specifications and their proofs. The code of the lexer with the proofs is available on Github2. The main branch contains the regular expression (called regex from now on) matcher version and the verified Computable Languages while the dfa match branch contains the version using the DFA matcher.

cs.PL↗

arXiv2024

Formally Verifiable Generated ASN.1/ACN Encoders and Decoders: A Case Study

We propose a verified executable Scala backend for ASN1SCC, a compiler for ASN.1/ACN. ASN.1 is a language for describing data structures widely employed in ground and space telecommunications. ACN can be used along ASN.1 to describe complex binary formats and legacy protocols. To avoid error-prone and time-consuming manual writing of serializers, we show how to port an ASN.1/ACN code generator to generate Scala code. We then enhance the generator to emit not only the executable code but also strong enough pre-conditions, post-conditions, and lemmas for inductive proofs. This allowed us to verify the resulting generated annotated code using Stainless, a program verifier for Scala. The properties we prove include the absence of runtime errors, such as out-of-bound accesses or divisions by zero. For the base library, we also prove the invertibility of the decoding and encoding functions, showing that decoding yields the encoded value back. Furthermore, our system automatically inserts invertibility proofs for arbitrary records in the generated code, proving over 300'000 verification conditions. We establish key steps towards such proofs for sums and arrays as well.

cs.SE↗

arXiv2024

Mechanized HOL Reasoning in Set Theory

We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADT) into first-order logic with ZFC axioms. We implement this in the Lisa proof assistant for schematic first-order logic and its library based on axiomatic set theory. HOL proof steps are implemented as proof producing tactics in Lisa, and the types are interpreted as sets, with function (or arrow) types coinciding with set-theoretic function spaces. The embedded HOL proofs, as opposed to being a layer over the existing proofs, are interoperable with the existing library. This yields a form of soft type system supporting top-level polymorphism and ADTs over set theory, and offer tools to reason about functions in set theory.

cs.LO↗

arXiv2024

Verifying a Realistic Mutable Hash Table

In this work, we verify the mutable LongMap from the Scala standard library, a hash table using open addressing within a single array, using the Stainless program verifier. As a reference implementation, we write an immutable map based on a list of tuples. We then show that LongMap's operations correspond to operations of this association list. To express the resizing of the hash table array, we introduce a new reference swapping construct in Stainless. This allows us to apply the decorator pattern without introducing aliasing. Our verification effort led us to find and fix a bug in the original implementation that manifests for large hash tables. Our performance analysis shows the verified version to be within a 1.5 factor of the original data structure.

cs.SE↗

arXiv2022

NP Decision Procedure for Monomial and Linear Integer Constraints

Motivated by satisfiability of constraints with function symbols, we consider numerical inequalities on non-negative integers. The constraints we consider are a conjunction of a linear system Ax = b and a conjunction of (non-)convex constraints of the form x_i >= x_j^n (x_i <= x_j^n). We show that the satisfiability of these constraints is NP-complete even if the solution to the linear part is given explicitly. As a consequence, we obtain NP completeness for an extension of certain quantifier-free constraints on sets with cardinalities (QFBAPA) with function images S = f[P^n].

cs.LO↗

arXiv2022

On Equivalence Checking for Orthocomplemented Bisemilattices in Log-Linear Time

We present a quasilinear time algorithm to decide the word problem on a natural algebraic structures we call orthocomplemented bisemilattices, a subtheory of boolean algebra. We use as a base a variation of Hopcroft, Ullman and Aho algorithm for tree isomorphism which we combine with a term rewriting system to decide equivalence of two terms. We prove that the rewriting system is terminating and confluent and hence the existence of a normal form, and that our algorithm is computing it. We also discuss applications and present an effective implementation in Scala.

cs.LO↗

arXiv2021

NP Satisfiability for Arrays as Powers

We show that the satisfiability problem for the quantifier-free theory of product structures with the equicardinality relation is in NP. As an application, we extend the combinatory array logic fragment to handle cardinality constraints. The resulting fragment is independent of the base element and index set theories.

cs.LO↗

arXiv2021

Proving and Disproving Programs with Shared Mutable Data

We present a tool for verification of deterministic programs with shared mutable references against specifications such as assertions, preconditions, postconditions, and read/write effects. We implement our tool by encoding programs with mutable references into annotated purely functional recursive programs. We then rely on function unfolding and the SMT solver Z3 to prove or disprove safety and to establish program termination. Our tool uses a new translation of programs where frame conditions are encoded using quantifier-free formulas in first-order logic (instead of relying on quantifiers or separation logic). This quantifier-free encoding enables SMT solvers to prove safety or report counterexamples relative to the semantics of procedure specifications. Our encoding is possible thanks to the expressive power of the extended array theory of the Z3 SMT solver. In addition to the ability to report counterexamples, our tool retains efficiency of reasoning about purely functional layers of data structures, providing expressiveness for mutable data but also a significant level of automation for purely functional aspects of software. We illustrate our tool through examples manipulating mutable linked structures and arrays.

cs.LO↗

arXiv2021

LL(1) Parsing with Derivatives and Zippers

In this paper, we present an efficient, functional, and formally verified parsing algorithm for LL(1) context-free expressions based on the concept of derivatives of formal languages. Parsing with derivatives is an elegant parsing technique, which, in the general case, suffers from cubic worst-case time complexity and slow performance in practice. We specialise the parsing with derivatives algorithm to LL(1) context-free expressions, where alternatives can be chosen given a single token of lookahead. We formalise the notion of LL(1) expressions and show how to efficiently check the LL(1) property. Next, we present a novel linear-time parsing with derivatives algorithm for LL(1) expressions operating on a zipper-inspired data structure. We prove the algorithm correct in Coq and present an implementation as a parser combinators framework in Scala, with enumeration and pretty printing capabilities.

cs.FL↗