Laboratory for Automated Reasoning and Analysis

Laboratory

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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 ...

Formally verifying the correctness of software is necessary to merit the trust people put in software systems. Currently, formal verification requires human effort to prove that a piece of code matches its specification and code changes to improve verifiab ...

Data races have long been a notorious problem in concurrent programming. They are subtle to detect, and lead to non-deterministic behaviours. There has been a lot of interest in type systems that statically guarantee data race freedom. Significant progress ...

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 ...

Type systems are a device for verifying properties of programs without running them. Many programming languages used in the industry have always had a type system, while others were initially created without a type system and later adopted one, when the ad ...

Type inference in the presence of first-class or "impredicative" second-order polymorphism a la System F has been an active research area for several decades, with original works dating back to the end of the 80s. Yet, until now many basic problems remain ...

We consider the problem of comparing several samples of stochastic processes with respect to their second-order structure, and describing the main modes of variation in this second order structure, if present. These tasks can be seen as an Analysis of Vari ...

Type systems usually characterize the shape of values but not their free variables. However, many desirable safety properties could be guaranteed if one knew the free variables captured by values. We describe CC

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 ...

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 ...

An integer linear program is a problem of the form max{c^T x : Ax=b, x >= 0, x integer}, where A is in Z^(n x m), b in Z^m, and c in Z^n. Solving an integer linear program is NP-hard in general, but there are several assumptions for which it becomes fixed ...

The Dependent Object Type (DOT) calculus was designed to put Scala on a sound basis, but while DOT relies on structural subtyping, Scala is a fundamentally class-based language. This impedance mismatch means that a proof of DOT soundness by itself is ...

While software applications, programming languages, and hardware have changed, operating systems have not. Widely-used commodity operating systems are still modeled after the ones designed in the seventies. The accumulated burden of backward compatibility ...

Graph Neural Networks (GNNs) have emerged as a powerful tool for learning on graphs, demonstrating exceptional performance in various domains. However, as GNNs become increasingly popular, new challenges arise. One of the most pressing is the need to ensur ...

Formal verification of real-world software systems remains challenging for a number of reasons, including lack of automation, friction in specifying properties, and limited support for the diverse programming paradigms used in industry. In this thesis we m ...

Type-level programming is becoming more and more popular in the realm of functional programming. However, the combination of type-level programming and subtyping remains largely unexplored in practical programming languages. This paper presents match types ...

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 ...

Formally verifying the correctness of software network functions (NFs) is necessary for network reliability, yet existing techniques require full source code and mandate the use of specific data structures. We describe an automated technique to verify NF b ...

Many programming languages in the OO tradition now support pattern matching in some form. Historical examples include Scala and Ceylon, with the more recent additions of Java, Kotlin, TypeScript, and Flow. But pattern matching on generic class hierarchies ...

We show that the satisfiability problem for the quantifier-free theory of product structures with the equicardinality relation is inNP. As an application, we extend the combinatory array logic fragmentto handle cardinality constraints. The resulting fragme ...

Laboratory for Automated Reasoning and Analysis

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Orthologic with Axioms

Automated Formal Verification of Software Network Functions

Degrees of Separation: A Flexible Type System for Safe Concurrency

Interpolation and Quantifiers in Ortholattices

Formal Foundations of Capture Tracking

When Subtyping Constraints Liberate A Novel Type Inference Approach for First-Class Polymorphism

Transportation-based functional ANOVA and PCA for covariance operators

Capturing Types

LISA – A Modern Proof System

On algebraic array theories

Results on Sparse Integer Programming and Geometric Independent Sets

Type-Preserving Compilation of Class-Based Languages

Dynamic Linkers Are the Narrow Waist of Operating Systems

Privacy-Preserving Machine Learning on Graphs

Scaling Language Features for Program Verification

Type-Level Programming with Match Types

Formula Normalizations in Verification

Automated Verification of Network Function Binaries

A case for DOT: Theoretical Foundations for Objects with Pattern Matching and GADT-Style Reasoning

NP Satisfiability for Arrays as Powers