29,443 research outputs found
Introduction to Categories and Categorical Logic
The aim of these notes is to provide a succinct, accessible introduction to
some of the basic ideas of category theory and categorical logic. The notes are
based on a lecture course given at Oxford over the past few years. They contain
numerous exercises, and hopefully will prove useful for self-study by those
seeking a first introduction to the subject, with fairly minimal prerequisites.
The coverage is by no means comprehensive, but should provide a good basis for
further study; a guide to further reading is included. The main prerequisite is
a basic familiarity with the elements of discrete mathematics: sets, relations
and functions. An Appendix contains a summary of what we will need, and it may
be useful to review this first. In addition, some prior exposure to abstract
algebra - vector spaces and linear maps, or groups and group homomorphisms -
would be helpful.Comment: 96 page
Conditions, constraints and contracts: on the use of annotations for policy modeling.
Organisational policies express constraints on generation and processing of resources. However, application domains rely on transformation processes, which are in principle orthogonal to policy specifications and domain rules and policies may evolve in a non-synchronised way. In previous papers, we have proposed annotations as a flexible way to model aspects of some policy, and showed how they could be used to impose constraints on domain configurations, how to derive application conditions on transformations, and how to annotate complex patterns. We extend the approach by: allowing domain model elements to be annotated with collections of elements, which can be collectively applied to individual resources or collections thereof; proposing an original construction to solve the problem of annotations remaining orphan , when annotated resources are consumed; introducing a notion of contract, by which a policy imposes additional pre-conditions and post-conditions on rules for deriving new resources. We discuss a concrete case study of linguistic resources, annotated with information on the licenses under which they can be used. The annotation framework allows forms of reasoning such as identifying conflicts among licenses, enforcing the presence of licenses, or ruling out some modifications of a licence configuration
Modeling and Reasoning over Distributed Systems using Aspect-Oriented Graph Grammars
Aspect-orientation is a relatively new paradigm that introduces abstractions
to modularize the implementation of system-wide policies. It is based on a
composition operation, called aspect weaving, that implicitly modifies a base
system by performing related changes within the system modules. Aspect-oriented
graph grammars (AOGG) extend the classic graph grammar formalism by defining
aspects as sets of rule-based modifications over a base graph grammar. Despite
the advantages of aspect-oriented concepts regarding modularity, the implicit
nature of the aspect weaving operation may also introduce issues when reasoning
about the system behavior. Since in AOGGs aspect weaving is characterized by
means of rule-based rewriting, we can overcome these problems by using known
analysis techniques from the graph transformation literature to study aspect
composition. In this paper, we present a case study of a distributed
client-server system with global policies, modeled as an aspect-oriented graph
grammar, and discuss how to use the AGG tool to identify potential conflicts in
aspect weaving
Relational Foundations For Functorial Data Migration
We study the data transformation capabilities associated with schemas that
are presented by directed multi-graphs and path equations. Unlike most
approaches which treat graph-based schemas as abbreviations for relational
schemas, we treat graph-based schemas as categories. A schema is a
finitely-presented category, and the collection of all -instances forms a
category, -inst. A functor between schemas and , which can be
generated from a visual mapping between graphs, induces three adjoint data
migration functors, -inst-inst, -inst -inst, and -inst -inst. We present an algebraic query
language FQL based on these functors, prove that FQL is closed under
composition, prove that FQL can be implemented with the
select-project-product-union relational algebra (SPCU) extended with a
key-generation operation, and prove that SPCU can be implemented with FQL
Quantum Programming Made Easy
We present IQu, namely a quantum programming language that extends Reynold's
Idealized Algol, the paradigmatic core of Algol-like languages. IQu combines
imperative programming with high-order features, mediated by a simple type
theory. IQu mildly merges its quantum features with the classical programming
style that we can experiment through Idealized Algol, the aim being to ease a
transition towards the quantum programming world. The proposed extension is
done along two main directions. First, IQu makes the access to quantum
co-processors by means of quantum stores. Second, IQu includes some support for
the direct manipulation of quantum circuits, in accordance with recent trends
in the development of quantum programming languages. Finally, we show that IQu
is quite effective in expressing well-known quantum algorithms.Comment: In Proceedings Linearity-TLLA 2018, arXiv:1904.0615
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