Finally, a Polymorphic Linear Algebra Language

Publications associées (30)

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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

A full characterization of invariant embeddability of unimodular planar graphs

Laszlo Marton Toth

When can a unimodular random planar graph be drawn in the Euclidean or the hyperbolic plane in a way that the distribution of the random drawing is isometry-invariant? This question was answered for one-ended unimodular graphs in Benjamini and Timar, using ...

WILEY2023

Nonperturbative aspects of scattering amplitudes

Miguel Alexandre Ribeiro Correia

In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...

EPFL2023

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

Yichen Xu, Lionel Emile Vincent Parreaux, Aleksander Slawomir Boruch-Gruszecki

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 ...

Assoc Computing Machinery2022

Type-Level Programming with Match Types

Martin Odersky, Olivier Eric Paul Blanvillain

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 ...

ASSOC COMPUTING MACHINERY2022

Scaling Language Features for Program Verification

Georg Stefan Schmid

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 ...

EPFL2022

Abstractions for Type-Level Programming

Olivier Eric Paul Blanvillain

Over the past decade, the Scala community has shown great interest in using type-level programming to obtain additional type safety. Unfortunately, the lack of support from the Scala compiler has been a barrier to the adoption of that technique, notably du ...

EPFL2022

Statistical limits of dictionary learning: Random matrix theory and the spectral replica method

Nicolas Macris, Jean François Emmanuel Barbier

We consider increasingly complex models of matrix denoising and dictionary learning in the Bayes-optimal setting, in the challenging regime where the matrices to infer have a rank growing linearly with the system size. This is in contrast with most existin ...

AMER PHYSICAL SOC2022

DIVIDE-AND-CONQUER METHODS FOR FUNCTIONS OF MATRICES WITH BANDED OR HIERARCHICAL LOW-RANK STRUCTURE\ast

Daniel Kressner, Stefano Massei, Alice Cortinovis

This work is concerned with approximating matrix functions for banded matrices, hierarchically semiseparable matrices, and related structures. We develop a new divide-and-conquer method based on (rational) Krylov subspace methods for performing low-rank up ...

SIAM PUBLICATIONS2022

TimeEvolver: A program for time evolution with improved error bound

Sebastian Zell

We present TimeEvolver, a program for computing time evolution in a generic quantum system. It relies on well-known Krylov subspace techniques to tackle the problem of multiplying the exponential of a large sparse matrix iH, where His the Hamiltonian, with ...

ELSEVIER2022

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