arXiv subjects

Maribel Fernández

Publications and source records attributed to Maribel Fernández.

At least 19 recordsLinked to original sources

arXiv2025

Dependently Sorted Nominal Signatures

We investigate an extension of nominal many-sorted signatures in which abstraction has a form of instantiation, called generalised concretion, as elimination operator (similarly to lambda-calculi). Expressions are then classified using a system of sorts and sort families that respects alpha-conversion (similarly to dependently-typed lambda-calculi) but not allowing names to carry abstraction sorts, thus constituting a first-order dependent sort system. The system can represent forms of judgement and rules of inference of several interesting calculi. We present rules and properties of the system as well as experiments of representation, and discuss how it constitutes a basis on which to build a type theory where raw expressions with alpha-equivalence are given a completely formal treatment.

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arXiv2025

Nominal Equational Rewriting and Narrowing

Narrowing is a well-known technique that adds to term rewriting mechanisms the required power to search for solutions to equational problems. Rewriting and narrowing are well-studied in first-order term languages, but several problems remain to be investigated when dealing with languages with binders using nominal techniques. Applications in programming languages and theorem proving require reasoning modulo alpha-equivalence considering structural congruences generated by equational axioms, such as commutativity. This paper presents the first definitions of nominal rewriting and narrowing modulo an equational theory. We establish a property called nominal E-coherence and demonstrate its role in identifying normal forms of nominal terms. Additionally, we prove the nominal E-Lifting theorem, which ensures the correspondence between sequences of nominal equational rewriting steps and narrowing, crucial for developing a correct algorithm for nominal equational unification via nominal equational narrowing. We illustrate our results using the equational theory for commutativity.

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arXiv2025

Nominal Equational Narrowing: Rewriting for Unification in Languages with Binders

Narrowing extends term rewriting with the ability to search for solutions to equational problems. While first-order rewriting and narrowing are well studied, significant challenges arise in the presence of binders, freshness conditions and equational axioms such as commutativity. This is problematic for applications in programming languages and theorem proving, where reasoning modulo renaming of bound variables, structural congruence, and freshness conditions is needed. To address these issues, we present a framework for nominal rewriting and narrowing modulo equational theories that intrinsically incorporates renaming and freshness conditions. We define and prove a key property called nominal E-coherence under freshness conditions, which characterises normal forms of nominal terms modulo renaming and equational axioms. Building on this, we establish the nominal E-lifting theorem, linking rewriting and narrowing sequences in the nominal setting. This foundational result enables the development of a nominal unification procedure based on equational narrowing, for which we provide a correctness proof. We illustrate the effectiveness of our approach with examples including symbolic differentiation and simplification of first-order formulas.

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arXiv2025

Equational Reasoning Modulo Commutativity in Languages with Binders (Extended Version)

Many formal languages include binders as well as operators that satisfy equational axioms, such as commutativity. Here we consider the nominal language, a general formal framework which provides support for the representation of binders, freshness conditions and $α$-renaming. Rather than relying on the usual freshness constraints, we introduce a nominal algebra which employs permutation fixed-point constraints in $α$-equivalence judgements, seamlessly integrating commutativity into the reasoning process. We establish its proof-theoretical properties and provide a sound and complete semantics in the setting of nominal sets. Additionally, we propose a novel algorithm for nominal unification modulo commutativity, which we prove terminating and correct. By leveraging fixed-point constraints, our approach ensures a finitary unification theory, unlike standard methods relying on freshness constraints. This framework offers a robust foundation for structural induction and recursion over syntax with binders and commutative operators, enabling reasoning in settings such as first-order logic and the $π$-calculus.

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arXiv2024

Strong Nominal Semantics for Fixed-Point Constraints

Nominal algebra includes $α$-equality and freshness constraints on nominal terms endowed with a nominal set semantics that facilitates reasoning about languages with binders. Nominal unification is decidable and unitary, however, its extension with equational axioms such as Commutativity (which has a finitary first-order unification type) is no longer finitary unless permutation fixed-point constraints are used. In this paper, we extend the notion of nominal algebra by introducing fixed-point constraints and provide a sound semantics using strong nominal sets. We show, by providing a counter-example, that the class of nominal sets is not a sound denotation for this extended nominal algebra. To recover soundness we propose two different formulations of nominal algebra, one obtained by restricting to a class of fixed-point contexts that are in direct correspondence with freshness contexts and another obtained by using a different set of derivation rules.

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arXiv2022

Nominal Matching Logic

We introduce Nominal Matching Logic (NML) as an extension of Matching Logic with names and binding following the Gabbay-Pitts nominal approach. Matching logic is the foundation of the $\mathbb{K}$ framework, used to specify programming languages and automatically derive associated tools (compilers, debuggers, model checkers, program verifiers). Matching logic does not include a primitive notion of name binding, though binding operators can be represented via an encoding that internalises the graph of a function from bound names to expressions containing bound names. This approach is sufficient to represent computations involving binding operators, but has not been reconciled with support for inductive reasoning over syntax with binding (e.g., reasoning over $λ$-terms). Nominal logic is a formal system for reasoning about names and binding, which provides well-behaved and powerful principles for inductive reasoning over syntax with binding, and NML inherits these principles. We discuss design alternatives for the syntax and the semantics of NML, prove meta-theoretical properties and give examples to illustrate its expressive power. In particular, we show how induction principles for $λ$-terms ($α$-structural induction) can be defined and used to prove standard properties of the $λ$-calculus.

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arXiv2021

EVL: a typed functional language for event processing

We define EVL, a minimal higher-order functional language to deal with generic events. The notion of generic event extends the well-known notion of event traditionally used in a variety of areas, such as database management, concurrency, reactive systems and cybersecurity. Generic events were introduced in the context of a metamodel to specify obligations in access control systems. Event specifications are represented as records and we use polymorphic record types to type events in EVL. We show how the higher-order capabilities of EVL can be used in the context of Complex Event Processing (CEP), to define higher-order parameterised functions that deal with the usual CEP techniques.

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arXiv2020

On Nominal Syntax and Permutation Fixed Points

We propose a new axiomatisation of the alpha-equivalence relation for nominal terms, based on a primitive notion of fixed-point constraint. We show that the standard freshness relation between atoms and terms can be derived from the more primitive notion of permutation fixed-point, and use this result to prove the correctness of the new $α$-equivalence axiomatisation. This gives rise to a new notion of nominal unification, where solutions for unification problems are pairs of a fixed-point context and a substitution. Although it may seem less natural than the standard notion of nominal unifier based on freshness constraints, the notion of unifier based on fixed-point constraints behaves better when equational theories are considered: for example, nominal unification remains finitary in the presence of commutativity, whereas it becomes infinitary when unifiers are expressed using freshness contexts. We provide a definition of $α$-equivalence modulo equational theories that take into account A, C and AC theories. Based on this notion of equivalence, we show that C-unification is finitary and we provide a sound and complete C-unification algorithm, as a first step towards the development of nominal unification modulo AC and other equational theories with permutative properties.

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arXiv2019

Proceedings Joint International Workshop on Linearity & Trends in Linear Logic and Applications

This volume contains a selection of papers presented at Linearity/TLLA 2018: Joint Linearity and TLLA workshops (part of FLOC 2018) held on July 7-8, 2018 in Oxford. Linearity has been a key feature in several lines of research in both theoretical and practical approaches to computer science. On the theoretical side there is much work stemming from linear logic dealing with proof technology, complexity classes and more recently quantum computation. On the practical side there is work on program analysis, expressive operational semantics for programming languages, linear programming languages, program transformation, update analysis and efficient implementation techniques. Linear logic is not only a theoretical tool to analyse the use of resources in logic and computation. It is also a corpus of tools, approaches, and methodologies (proof nets, exponential decomposition, geometry of interaction, coherent spaces, relational models, etc.) that were originally developed for the study of linear logic's syntax and semantics and are nowadays applied in several other fields.

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arXiv2019

Proceedings Tenth International Workshop on Computing with Terms and Graphs

This volume contains a selection of the papers presented at TERMGRAPH 2018, the tenth edition of the international workshop on computing with terms and graphs. Graphs, and graph transformation systems, are used in many areas within Computer Science: to represent data structures and algorithms, to define computation models, as a general modelling tool to study complex systems, etc. Research in this area addresses a range of theoretical and practical issues, including the modelling of first- and higher-order term rewriting by (acyclic or cyclic) graph rewriting, graphical frameworks such as interaction nets and sharing graphs (optimal reduction), rewrite calculi for the analysis of functional programs, graph reduction implementations of programming languages, graphical calculi modelling concurrent and mobile computations, object-oriented systems, graphs as a model of biological or chemical systems, and automated reasoning and symbolic computation systems working on shared structures. Previous editions of TERMGRAPH took place in Barcelona (2002), Rome (2004), Vienna (2006), Braga (2007), York (2009), Saarbrucken (2011), Rome (2013), Vienna (2014) and Eindhoven (2016). TERMGRAPH 2018 is affiliated with FSCD, which is part of FLOC.

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arXiv2018

Attributed Hierarchical Port Graphs and Applications

We present attributed hierarchical port graphs (AHP) as an extension of port graphs that aims at facilitating the design of modular port graph models for complex systems. AHP consist of a number of interconnected layers, where each layer defines a port graph whose nodes may link to layers further down the hierarchy; attributes are used to store user-defined data as well as visualisation and run-time system parameters. We also generalise the notion of strategic port graph rewriting (a particular kind of graph transformation system, where port graph rewriting rules are controlled by user-defined strategies) to deal with AHP following the Single Push-out approach. We outline examples of application in two areas: functional programming and financial modelling.

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arXiv2017

Nominal C-Unification

Nominal unification is an extension of first-order unification that takes into account the α-equivalence relation generated by binding operators, following the nominal approach. We propose a sound and complete procedure for nominal unification with commutative operators, or nominal C-unification for short, which has been formalised in Coq. The procedure transforms nominal C-unification problems into simpler (finite families) of fixpoint problems, whose solutions can be generated by algebraic techniques on combinatorics of permutations.

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arXiv2017

Proceedings Fourth International Workshop on Linearity

This volume contains the papers presented at LINEARITY 2016, the Fourth International Workshop on Linearity, held on June 26, 2016 in Porto, Portugal. The workshop was a one-day satellite event of FSCD 2016, the first International Conference on Formal Structures for Computation and Deduction. The aim of this workshop was to bring together researchers who are developing theory and applications of linear calculi, to foster their interaction and provide a forum for presenting new ideas and work in progress, and enable newcomers to learn about current activities in this area. Of interest were new results that made a central use of linearity, ranging from foundational work to applications in any field. This included: sub-linear logics, linear term calculi, linear type systems, linear proof-theory, linear programming languages, applications to concurrency, interaction-based systems, verification of linear systems, and biological and chemical models of computation.

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arXiv2016

Linear Recursion

We define two extensions of the typed linear lambda-calculus that yield minimal Turing-complete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both approaches are compatible with linearity and typeability constraints. Both extensions of the typed linear lambda-calculus are minimal, in the sense that taking out any of the components breaks the universality of the system. We discuss implementation techniques that exploit the linearity of the calculi. Finally, we apply the results to languages with fixpoint operators: we give a compilation of the programming language PCF into a linear lambda-calculus with linear unbounded recursion.

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arXiv2015

From nominal to higher-order rewriting and back again

We present a translation function from nominal rewriting systems (NRSs) to combinatory reduction systems (CRSs), transforming closed nominal rules and ground nominal terms to CRSs rules and terms, respectively, while preserving the rewriting relation. We also provide a reduction-preserving translation in the other direction, from CRSs to NRSs, improving over a previously defined translation. These tools, together with existing translations between CRSs and other higher-order rewriting formalisms, open up the path for a transfer of results between higher-order and nominal rewriting. In particular, techniques and properties of the rewriting relation, such as termination, can be exported from one formalism to the other.

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arXiv2014

Static Enforcement of Role-Based Access Control

We propose a new static approach to Role-Based Access Control (RBAC) policy enforcement. The static approach we advocate includes a new design methodology, for applications involving RBAC, which integrates the security requirements into the system's architecture. We apply this new approach to policies restricting calls to methods in Java applications. We present a language to express RBAC policies on calls to methods in Java, a set of design patterns which Java programs must adhere to for the policy to be enforced statically, and a description of the checks made by our static verifier for static enforcement.

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arXiv2014

Strategic Port Graph Rewriting: An Interactive Modelling and Analysis Framework

We present strategic portgraph rewriting as a basis for the implementation of visual modelling and analysis tools. The goal is to facilitate the specification, analysis and simulation of complex systems, using port graphs. A system is represented by an initial graph and a collection of graph rewriting rules, together with a user-defined strategy to control the application of rules. The strategy language includes constructs to deal with graph traversal and management of rewriting positions in the graph. We give a small-step operational semantics for the language, and describe its implementation in the graph transformation and visualisation tool PORGY.

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arXiv2014

General dynamic recovery for compensating CSP

Compensation is a technique to roll-back a system to a consistent state in case of failure. Recovery mechanisms for compensating calculi specify the order of execution of compensation sequences. Dynamic recovery means that the order of execution is determined at runtime. In this paper, we define an extension of Compensating CSP, called DEcCSP, with general dynamic recovery. We provide a formal, operational semantics for the calculus, and illustrate its expressive power with a case study. In contrast with previous versions of Compensating CSP, DEcCSP provides mechanisms to replace or discard compensations at runtime. Additionally, we bring back to DEcCSP standard CSP operators that are not available in other compensating CSP calculi, and introduce channel communication.

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