Publications by Viktor Kuncak | EPFL Graph Search

Mechanized HOL Reasoning in Set Theory

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We present a mechanized embedding of higher-order logic (HOL) and algebraic data types (ADTs) into first-order logic with ZFC axioms. Our approach interprets types as sets, with function (arrow) types coinciding with set-theoretic function spaces. We assum ...

2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in ortho- logic, 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 p ...

2024

Verifying a Realistic Mutable Hash Table: Case Study (Short Paper)

Viktor Kuncak, Samuel Chassot

In this work, we verify, using the Stainless program verifier, the mutable LongMap from the Scala standard library, a hash table using open addressing within a single array. As an executable specification, we write an immutable map based on a list of tuple ...

Springer Science and Business Media Deutschland GmbH2024

Interpolation and Quantifiers in Ortholattices

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

We study quantifiers and interpolation properties in 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 pro ...

Springer International Publishing Ag2024

Succinct ordering and aggregation constraints in algebraic array theories

Viktor Kuncak, Rodrigo Raya

We discuss two extensions to a recently introduced theory of arrays, which are based on considerations coming from the model theory of power structures. First, we discuss how the ordering relation on the index set can be expressed succinctly by referring t ...

Elsevier Science Inc2024

Orthologic with Axioms

Viktor Kuncak, Simon Guilloud

We study the proof theory and algorithms for orthologic, a logical system based on ortholattices, which have shown practical relevance in simplification and normalization of verification conditions. Ortholattices weaken Boolean algebras while having polyno ...

Association for Computing Machinery2024

Formula Normalizations in Verification

Viktor Kuncak, Simon Guilloud, Mario Bucev, Dragana Milovancevic

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2023

On algebraic array theories

Viktor Kuncak, Rodrigo Raya

Automatic verification of programs manipulating arrays relies on specialised decision procedures. A methodology to classify the theories handled by these procedures is introduced. It is based on decomposition theorems in the style of Feferman and Vaught. T ...

Elsevier Science Inc2023

LISA – A Modern Proof System

Viktor Kuncak, Simon Guilloud, Sankalp Gambhir

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 fun ...

Dagstuhl, Germany, Schloss Dagstuhl - Leibniz-Zentrum fur Informatik2023

Proving and Disproving Equivalence of Functional Programming Assignments

Viktor Kuncak, Dragana Milovancevic

We present an automated approach to verify the correctness of programming assignments, such as the ones that arise in a functional programming course. Our approach takes as input student submissions and reference solutions, and uses equivalence checking to ...

2023