Constrained Type Families

We present an approach to support partiality in type-level computation without compromising expressiveness or type safety. Existing frameworks for type-level computation either require totality or implicitly assume it. For example, type families in Haskell provide a powerful, modular means of defining type-level computation. However, their current design implicitly assumes that type families are total, introducing nonsensical types and significantly complicating the metatheory of type families and their extensions. We propose an alternative design, using qualified types to pair type-level computations with predicates that capture their domains. Our approach naturally captures the intuitive partiality of type families, simplifying their metatheory. As evidence, we present the first complete proof of consistency for a language with closed type families.Comment: Originally presented at ICFP 2017; extended editio

Bogoliubov Renormalization Group and Symmetry of Solution in Mathematical Physics

Evolution of the concept known in the theoretical physics as the Renormalization Group (RG) is presented. The corresponding symmetry, that has been first introduced in QFT in mid-fifties, is a continuous symmetry of a solution with respect to transformation involving parameters (e.g., of boundary condition) specifying some particular solution. After short detour into Wilson's discrete semi-group, we follow the expansion of QFT RG and argue that the underlying transformation, being considered as a reparameterisation one, is closely related to the self-similarity property. It can be treated as its generalization, the Functional Self-similarity (FS). Then, we review the essential progress during the last decade of the FS concept in application to boundary value problem formulated in terms of differential equations. A summary of a regular approach recently devised for discovering the RG = FS symmetries with the help of the modern Lie group analysis and some of its applications are given. As a main physical illustration, we give application of new approach to solution for a problem of self-focusing laser beam in a non-linear medium.Comment: Contribution to the proceedings of conference "RG 2000" (Taxco, Mexico, Jan. 1999). To be published in Physics Report

Ontology Based Data Access in Statoil

Ontology Based Data Access (OBDA) is a prominent approach to query databases which uses an ontology to expose data in a conceptually clear manner by abstracting away from the technical schema-level details of the underlying data. The ontology is ‘connected’ to the data via mappings that allow to automatically translate queries posed over the ontology into data-level queries that can be executed by the underlying database management system. Despite a lot of attention from the research community, there are still few instances of real world industrial use of OBDA systems. In this work we present data access challenges in the data-intensive petroleum company Statoil and our experience in addressing these challenges with OBDA technology. In particular, we have developed a deployment module to create ontologies and mappings from relational databases in a semi-automatic fashion; a query processing module to perform and optimise the process of translating ontological queries into data queries and their execution over either a single DB of federated DBs; and a query formulation module to support query construction for engineers with a limited IT background. Our modules have been integrated in one OBDA system, deployed at Statoil, integrated with Statoil’s infrastructure, and evaluated with Statoil’s engineers and data

Automated Deduction – CADE 28

This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions

A domain-extensible compiler with controllable automation of optimisations

In high performance domains like image processing, physics simulation or machine learning, program performance is critical. Programmers called performance engineers are responsible for the challenging task of optimising programs. Two major challenges prevent modern compilers targeting heterogeneous architectures from reliably automating optimisation. First, domain specific compilers such as Halide for image processing and TVM for machine learning are difficult to extend with the new optimisations required by new algorithms and hardware. Second, automatic optimisation is often unable to achieve the required performance, and performance engineers often fall back to painstaking manual optimisation. This thesis shows the potential of the Shine compiler to achieve domain-extensibility, controllable automation, and generate high performance code. Domain-extensibility facilitates adapting compilers to new algorithms and hardware. Controllable automation enables performance engineers to gradually take control of the optimisation process. The first research contribution is to add 3 code generation features to Shine, namely: synchronisation barrier insertion, kernel execution, and storage folding. Adding these features requires making novel design choices in terms of compiler extensibility and controllability. The rest of this thesis builds on these features to generate code with competitive runtime compared to established domain-specific compilers. The second research contribution is to demonstrate how extensibility and controllability are exploited to optimise a standard image processing pipeline for corner detection. Shine achieves 6 well-known image processing optimisations, 2 of them not being supported by Halide. Our results on 4 ARM multi-core CPUs show that the code generated by Shine for corner detection runs up to 1.4× faster than the Halide code. However, we observe that controlling rewriting is tedious, motivating the need for more automation. The final research contribution is to introduce sketch-guided equality saturation, a semiautomated technique that allows performance engineers to guide program rewriting by specifying rewrite goals as sketches: program patterns that leave details unspecified. We evaluate this approach by applying 7 realistic optimisations of matrix multiplication. Without guidance, the compiler fails to apply the 5 most complex optimisations even given an hour and 60GB of RAM. With the guidance of at most 3 sketch guides, each 10 times smaller than the complete program, the compiler applies the optimisations in seconds using less than 1GB

Proceedings of the 21st Conference on Formal Methods in Computer-Aided Design – FMCAD 2021

The Conference on Formal Methods in Computer-Aided Design (FMCAD) is an annual conference on the theory and applications of formal methods in hardware and system verification. FMCAD provides a leading forum to researchers in academia and industry for presenting and discussing groundbreaking methods, technologies, theoretical results, and tools for reasoning formally about computing systems. FMCAD covers formal aspects of computer-aided system design including verification, specification, synthesis, and testing