Related papers: Functorial Data Migration
Multi-model databases are designed to store, manage, and query data in various models, such as relational, hierarchical, and graph data, simultaneously. In this paper, we provide a theoretical basis for querying categorical databases. We…
The relational data model requires a theory of relations in which tuples are not only many-sorted, but can also have indexes that are not necessarily numerical. In this paper we develop such a theory and define operations on relations that…
In \cite{Spi}, we developed a category of databases in which the schema of a database is represented as a simplicial set. Each simplex corresponds to a table in the database. There, our main concern was to find a categorical formulation of…
Variables are a crucial element in logic and are also addressed in institution theory, an effort to axiomatize logic. In institution theory, we typically use extensions (signature morphisms) obtained from variables instead of introducing…
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…
This article is first in a series of papers where we reprove the statements in constructing the Enhanced Operation Map and the abstract six-functor formalism developed by Liu-Zheng. In this paper, we prove a theorem regarding constructing…
In this paper, we introduce a novel approach to deductive databases meant to take into account the needs of current applications in the area of data integration. To this end, we extend the formalism of standard deductive databases to the…
Contemporary database systems, while effective, suffer severe issues related to complexity and usability, especially among individuals who lack technical expertise but are unfamiliar with query languages like Structured Query Language…
This paper addresses the question of automatic data extraction from the Wiktionary, which is a multilingual and multifunctional dictionary. Wiktionary is a collaborative project working on the same principles as the Wikipedia. The…
This extended abstract gives a brief outline of the connections between the descriptions and variable concepts. Thus, the notion of a concept is extended to include both the syntax and semantics features. The evaluation map in use is…
In this paper, we use a categorical and functorial set up to model the syntax and inference of logics with algebraic signature, extending previous works on algebraisation of logics. The main feature of this work is that structurality, or…
Previous work has demonstrated that categories are useful and expressive models for databases. In the present paper we build on that model, showing that certain queries and constraints correspond to lifting problems, as found in modern…
This vision paper lays the preliminary foundations for Data Narrative Management Systems (DNMS), systems that enable the storage, sharing, and manipulation of data narratives. We motivate the need for such formal foundations and introduce a…
We introduce a notion of complexity of diagrams (and in particular of objects and morphisms) in an arbitrary category, as well as a notion of complexity of functors between categories equipped with complexity functions. We discuss several…
This tutorial gives an advanced introduction to string diagrams and graph languages for higher-order computation. The subject matter develops in a principled way, starting from the two dimensional syntax of key categorical concepts such as…
Foundation Models (FMs) are models trained on large corpora of data that, at very large scale, can generalize to new tasks without any task-specific finetuning. As these models continue to grow in size, innovations continue to push the…
An attempt at unifying logic and functional programming is reported. As a starting point, we take the view that "logic programs" are not about logic but constitute inductive definitions of sets and relations. A skeletal language design…
User defined recursive types are a fundamental feature of modern functional programming languages like Haskell, Clean, and the ML family of languages. Properties of programs defined by recursion on the structure of recursive types are…
Database migration is a key task in software modernization, increasingly involving transformations across heterogeneous data models such as relational and NoSQL systems. Existing approaches are typically designed for specific source-target…
This paper presents a new technique for migrating data between different schemas. Our method expresses the schema mapping as a Datalog program and automatically synthesizes a Datalog program from simple input-output examples to perform data…