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Dominique Duval

Publications and source records attributed to Dominique Duval.

At least 19 recordsLinked to original sources
arXiv2026

Sketch-Oriented Databases

This paper introduces sketch-oriented databases, a categorical framework that encodes database paradigms as finite-limit sketches and individual databases and schemas as set-valued models. It illustrates the formalism through graph-oriented paradigms such as quivers, RDF triplestores and property graphs. It also shows how common graph features such as labels, attributes, typing, and paths, are uniformly captured by sketch constructions. Because paths play an important role in queries, we propose inference rules formalized via localizers to compute useful paths lazily; such localizers are also useful for tasks like database type conformance. Finally, the paper introduces stuttering sketches, whose aim is to facilitate modular composition and scalable model growth: stuttering sketches are finite-limit sketches in which relations are specified by a single limit instead of two nested limits, and the paper proves that finite unions of models of a stuttering sketch are pointwise colimits.

cs.LO↗
arXiv2022

A Rule-based Operational Semantics of Graph Query Languages

We consider a core language of graph queries. These queries are seen as formulas to be solved with respect to graph-oriented databases. For this purpose, we first define a graph query algebra where some operations over graphs and sets of graph homomorphisms are specified. Then, the notion of pattern is introduced to represent a kind of recursively defined formula over graphs. The syntax and formal semantics of patterns are provided. Afterwards, we propose a new sound and complete calculus to solve patterns. This calculus, which is based on a rewriting system, develops only one derivation per pattern to be solved. Our calculus is generic in the sense that it can be adapted to different kinds of graph databases provided that the notions of graph and graph homomorphism (match) are well defined.

cs.LO↗
arXiv2021

Querying RDF Databases with Sub-CONSTRUCTs

Graph query languages feature mainly two kinds of queries when applied to a graph database: those inspired by relational databases which return tables such as SELECT queries and those which return graphs such as CONSTRUCT queries in SPARQL. The latter are object of study in the present paper. For this purpose, a core graph query language GrAL is defined with focus on CONSTRUCT queries. Queries in GrAL form the final step of a recursive process involving so-called GrAL patterns. By evaluating a query over a graph one gets a graph, while by evaluating a pattern over a graph one gets a set of matches which involves both a graph and a table. CONSTRUCT queries are based on CONSTRUCT patterns, and sub-CONSTRUCT patterns come for free from the recursive definition of patterns. The semantics of GrAL is based on RDF graphs with a slight modification which consists in accepting isolated nodes. Such an extension of RDF graphs eases the definition of the evaluation semantics, which is mainly captured by a unique operation called Merge. Besides, we define aggregations as part of GrAL expressions, which leads to an original local processing of aggregations.

cs.DB↗
arXiv2020

An Algebraic Graph Transformation Approach for RDF and SPARQL

We consider the recommendations of the World Wide Web Consortium (W3C) about RDF framework and its associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We define RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

cs.DB↗
arXiv2020

All You Need Is CONSTRUCT

In SPARQL, the query forms SELECT and CONSTRUCT have been the subject of several studies, both theoretical and practical. However, the composition of such queries and their interweaving when forming involved nested queries has not yet received much interest in the literature. We mainly tackle the problem of composing such queries. For this purpose, we introduce a language close to SPARQL where queries can be nested at will, involving either CONSTRUCT or SELECT query forms and provide a formal semantics for it. This semantics is based on a uniform interpretation of queries. This uniformity is due to an extension of the notion of RDF graphs to include isolated items such as variables. As a key feature of this work, we show how classical SELECT queries can be easily encoded as a particular case of CONSTRUCT queries.

cs.DB↗
arXiv2020

On foundational aspects of RDF and SPARQL

We consider the recommendations of the World Wide Web Consortium (W3C) about the Resource Description Framework (RDF) and the associated query language SPARQL. We propose a new formal framework based on category theory which provides clear and concise formal definitions of the main basic features of RDF and SPARQL. We propose to define the notions of RDF graphs as well as SPARQL basic graph patterns as objects of some nested categories. This allows one to clarify, in particular, the role of blank nodes. Furthermore, we consider basic SPARQL CONSTRUCT and SELECT queries and formalize their operational semantics following a novel algebraic graph transformation approach called POIM.

cs.DB↗
arXiv2015

Hilbert-Post completeness for the state and the exception effects

In this paper, we present a novel framework for studying the syntactic completeness of computational effects and we apply it to the exception effect. When applied to the states effect, our framework can be seen as a generalization of Pretnar's work on this subject. We first introduce a relative notion of Hilbert-Post completeness, well-suited to the composition of effects. Then we prove that the exception effect is relatively Hilbert-Post complete, as well as the "core" language which may be used for implementing it; these proofs have been formalized and checked with the proof assistant Coq.

cs.LO↗
arXiv2015

AGREE -- Algebraic Graph Rewriting with Controlled Embedding (Long Version)

The several algebraic approaches to graph transformation proposed in the literature all ensure that if an item is preserved by a rule, so are its connections with the context graph where it is embedded. But there are applications in which it is desirable, for example when cloning an item, to specify different embeddings for the original and for the copy. Therefore we propose a conservative extension of these approaches where a rule can specify how the embedding of a preserved item should be changed, typically by removing certain connections.

cs.LO↗
arXiv2014

Program certification with computational effects

Dynamic evaluation is a paradigm in computer algebra which was introduced for computing with algebraic numbers. In linear algebra, for instance, dynamic evaluation can be used to apply programs which have been written for matrices with coefficients modulo some prime number to matrices with coefficients modulo some composite number. A way to implement dynamic evaluation in modern computing languages is to use the exceptions mechanism provided by the language. In this paper, we pesent a proof system for exceptions which involves both raising and handling, by extending Moggi's approach based on monads. Moreover, the core part of this proof system is dual to a proof system for the state effect in imperative languages, which relies on the categorical notion of comonad. Both proof systems are implemented in the Coq proof assistant, and they are combined in order to deal with both effects at the same time.

cs.LO↗
arXiv2014

Certified proofs in programs involving exceptions

Exception handling is provided by most modern programming languages. It allows to deal with anomalous or exceptional events which require special processing. In computer algebra, exception handling is an efficient way to implement the dynamic evaluation paradigm: for instance, in linear algebra, dynamic evaluation can be used for applying programs which have been written for matrices with coefficients in a field to matrices with coefficients in a ring. Thus, a proof system for computer algebra should include a treatement of exceptions, which must rely on a careful description of a semantics of exceptions. The categorical notion of monad can be used for formalizing the raising of exceptions: this has been proposed by Moggi and implemented in Haskell. In this paper, we provide a proof system for exceptions which involves both raising and handling, by extending Moggi's approach. Moreover, the core part of this proof system is dual to a proof system for side effects in imperative languages, which relies on the categorical notion of comonad. Both proof systems are implemented in the Coq proof assistant.

cs.LO↗
arXiv2014

Breaking a monad-comonad symmetry between computational effects

Computational effects may often be interpreted in the Kleisli category of a monad or in the coKleisli category of a comonad. The duality between monads and comonads corresponds, in general, to a symmetry between construction and observation, for instance between raising an exception and looking up a state. Thanks to the properties of adjunction one may go one step further: the coKleisli-on-Kleisli category of a monad provides a kind of observation with respect to a given construction, while dually the Kleisli-on-coKleisli category of a comonad provides a kind of construction with respect to a given observation. In the previous examples this gives rise to catching an exception and updating a state. However, the interpretation of computational effects is usually based on a category which is not self-dual, like the category of sets. This leads to a breaking of the monad-comonad duality. For instance, in a distributive category the state effect has much better properties than the exception effect. This remark provides a novel point of view on the usual mechanism for handling exceptions. The aim of this paper is to build an equational semantics for handling exceptions based on the coKleisli-on-Kleisli category of the monad of exceptions. We focus on n-ary functions and conditionals. We propose a programmer's language for exceptions and we prove that it has the required behaviour with respect to n-ary functions and conditionals.

cs.LO↗
arXiv2014

Transformation of Attributed Structures with Cloning (Long Version)

Copying, or cloning, is a basic operation used in the specification of many applications in computer science. However, when dealing with complex structures, like graphs, cloning is not a straightforward operation since a copy of a single vertex may involve (implicitly)copying many edges. Therefore, most graph transformation approaches forbid the possibility of cloning. We tackle this problem by providing a framework for graph transformations with cloning. We use attributed graphs and allow rules to change attributes. These two features (cloning/changing attributes) together give rise to a powerful formal specification approach. In order to handle different kinds of graphs and attributes, we first define the notion of attributed structures in an abstract way. Then we generalise the sesqui-pushout approach of graph transformation in the proposed general framework and give appropriate conditions under which attributed structures can be transformed. Finally, we instantiate our general framework with different examples, showing that many structures can be handled and that the proposed framework allows one to specify complex operations in a natural way.

cs.SE↗
arXiv2013

Patterns for computational effects arising from a monad or a comonad

This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used for proving properties of different effects. The first pattern provides inference rules which can be interpreted in the Kleisli category of a monad and the coKleisli category of the associated comonad. In a dual way, the second pattern provides inference rules which can be interpreted in the coKleisli category of a comonad and the Kleisli category of the associated monad. The logics combine a 3-tier effect system for terms consisting of pure terms and two other kinds of effects called 'constructors/observers' and 'modifiers', and a 2-tier system for 'up-to-effects' and 'strong' equations. Each pattern provides generic rules for dealing with any monad (respectively comonad), and it can be extended with specific rules for each effect. The paper presents two use cases: a language with exceptions (using the standard monadic semantics), and a language with state (using the less standard comonadic semantics). Finally, we prove that the obtained inference system for states is Hilbert-Post complete.

cs.LO↗
arXiv2013

Formal verification in Coq of program properties involving the global state effect

The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we present a framework for the verification in Coq of properties of programs manipulating the global state effect. These properties are expressed in a proof system which is close to the syntax, as in effect systems, in the sense that the state does not appear explicitly in the type of expressions which manipulate it. Rather, the state appears via decorations added to terms and to equations. In this system, proofs of programs thus present two aspects: properties can be verified {\em up to effects} or the effects can be taken into account. The design of our Coq library consequently reflects these two aspects: our framework is centered around the construction of two inductive and dependent types, one for terms up to effects and one for the manipulation of decorations.

cs.LO↗
arXiv2013

Scalability using effects

This note is about using computational effects for scalability. With this method, the specification gets more and more complex while its semantics gets more and more correct. We show, from two fundamental examples, that it is possible to design a deduction system for a specification involving an effect without expliciting this effect.

cs.LO↗
arXiv2012

Adjunctions for exceptions

An algebraic method is used to study the semantics of exceptions in computer languages. The exceptions form a computational effect, in the sense that there is an apparent mismatch between the syntax of exceptions and their intended semantics. We solve this apparent contradiction by efining a logic for exceptions with a proof system which is close to their syntax and where their intended semantics can be seen as a model. This requires a robust framework for logics and their morphisms, which is provided by categorical tools relying on adjunctions, fractions and limit sketches.

cs.LO↗
arXiv2012

Decorated proofs for computational effects: States

The syntax of an imperative language does not mention explicitly the state, while its denotational semantics has to mention it. In this paper we show that the equational proofs about an imperative language may hide the state, in the same way as the syntax does.

cs.PL↗