The syntactic side of autonomous categories enriched over generalised metric spaces

Programs with a continuous state space or that interact with physical processes often require notions of equivalence going beyond the standard binary setting in which equivalence either holds or does not hold. In this paper we explore the idea of equivalence taking values in a quantale V, which covers the cases of (in)equations and (ultra)metric equations among others. Our main result is the introduction of a V-equational deductive system for linear λ-calculus together with a proof that it is sound and complete. In fact we go further than this, by showing that linear λ-theories based on this V-equational system form a category equivalent to a category of autonomous categories enriched over ‘generalised metric spaces’. If we instantiate this result to inequations, we get an equivalence with autonomous categories enriched over partial orders. In the case of (ultra)metric equations, we get an equivalence with autonomous categories enriched over (ultra)metric spaces. Additionally, we show that this syntax-semantics correspondence extends to the affine setting. We use our results to develop examples of inequational and metric equational systems for higher-order programming in the setting of real-time, probabilistic, and quantum computing.This work is financed by National Funds through FCT - Fundação para a Ciência e a Tecnologia, I.P. (Portuguese Foundation for Science and Technology) within project IBEX, with reference PTDC/CCI-COM/4280/2021. We are also thankful for the reviewers’ helpful feedback

Hybrid programs

The MAP-i Doctoral Programme in Informatics, of the Universities of Minho, Aveiro and PortoThis thesis studies hybrid systems, an emerging family of devices that combine in their models digital computations and physical processes. They are very quickly becoming a main concern in software engineering, which is explained by the need to develop software products that closely interact with physical attributes of their environment e. g. velocity, time, energy, temperature – typical examples range from micro-sensors and pacemakers, to autonomous vehicles, transport infrastructures and district-wide electric grids. But even if already widespread, these systems entail different combinations of programs with physical processes, and this renders their development a challenging task, still largely unmet by the current programming practices. Our goal is to address this challenge at its core; we wish to isolate the basic interactions between discrete computations and physical processes, and bring forth the programming paradigm that naturally underlies them. In order to do so in a precise and clean way, we resort to monad theory, a well established categorical framework for developing program semantics systematically. We prove the existence of a monad that naturally encodes the aforementioned interactions, and use it to develop and examine the foundations of the paradigm alluded above, which we call hybrid programming: we show how to build, in a methodical way, different programming languages that accommodate amplifiers, differential equations, and discrete assignments – the basic ingredients of hybrid systems – we list all program operations available in the paradigm, introduce if-then-else constructs, abort operations, and different types of feedback. Hybrid systems bring several important aspects of control theory into computer science. One of them is the notion of stability, which refers to a system’s capacity of avoiding significant changes in its output if small variations in its state or input occur. We introduce a notion of stability to hybrid programming, explore it, and show how to analyse hybrid programs with respect to it in a compositional manner. We also introduce hybrid programs with internal memory and show that they form the basis of a component-based software development discipline in hybrid programming. We develop their coalgebraic theory, namely languages, notions of behaviour, and bisimulation. In the process, we introduce new theoretical results on Coalgebra, including improvements of well-known results and proofs on the existence of suitable notions of behaviour for non-deterministic transition systems with infinite state spaces.Esta tese estuda sistemas híbridos, uma família emergente de dispositivos que envolvem diferentes interações entre computações digitais e processos físicos. Estes sistemas estão rapidamente a tornar-se elementos-chave da engenharia de software, o que é explicado pela necessidade de desenvolver produtos que interagem com os atributos físicos do seu ambiente e. g. velocidade, tempo, energia, e temperatura – exemplos típicos variam de micro-sensores e pacemakers, a veículos autónomos, infra-estruturas de transporte, e redes eléctricas distritais. Mas ainda que amplamente usados, estes sistemas são geralmente desenvolvidos de forma pouco sistemática nas prácticas de programação atuais. O objetivo deste trabalho é isolar as interações básicas entre computações digitais e processos físicos, e subsequentemente desenvolver o paradigma de programação subjacente. Para fazer isto de forma precisa, a nossa base de trabalho irá ser a teoria das mónadas, uma estrutura categórica para o desenvolvimento sistemático de semânticas na programação. A partir desta base, provamos a existência de uma mónada que capta as interações acima mencionadas, e usamo-la para desenvolver e examinar os fundamentos do paradigma de programação correspondente a que chamamos programação híbrida: mostramos como construir, de maneira metódica, diferentes linguagens de programação que acomodam amplificadores, equações diferenciais, e atribuições - os ingredientes básicos dos sistemas híbridos - caracterizamos todas as operações sobre programas disponíveis, introduzimos construções if-then-else, operações para lidar com excepções, e diferentes tipos de feedback. Os sistemas híbridos trazem vários aspectos da teoria de controlo para a ciência da computação. Um destes é a noção de estabilidade, que se refere à capacidade de um sistema de evitar mudanças drásticas no seu output se pequenas variações no seu estado ou input ocorrerem. Neste trabalho, desenvolvemos uma noção composicional de estabilidade para a programação híbrida. Introduzimos também programas híbridos com memória interna, que formam a base de uma disciplina de desenvolvimento de software baseado em componentes. Desenvolvemos a sua teoria coalgébrica, nomeadamente linguagens, noções de comportamento e bisimulação. Neste processo, introduzimos também novos resultados teóricos sobre Coalgebra, incluindo melhorias a resultados conhecidos e provas acerca da existência de noções de comportamento para sistemas de transição não determinísiticos com espaço de estados infinitos.The present work was financed by FCT – Fundação para a Ciência e a Tecnologia – with the grant SFRH/BD/52234/2013. Additional support was provided by the PTFLAD Chair on Smart Cities & Smart Governance and by project Dalí (POCI-01-0145-FEDER-016692), the latter funder by ERDF – European Regional Development Fund – through COMPETE 2020 – Operational Programme for Competitiveness and Internationalisation – together with FCT

Hybrid automata as coalgebras

Publicado em "Theoretical aspects of computing - ICTAC 2016: 13th International Colloquium, Taipei, Taiwan, ROC, October 24–31, 2016, Proceedings". ISBN 978-3-319-46749-8Able to simultaneously encode discrete transitions and continuous behaviour, hybrid automata are the de facto framework for the formal specification and analysis of hybrid systems. The current paper revisits hybrid automata from a coalgebraic point of view. This allows to interpret them as state-based components, and provides a uniform theory to address variability in their definition, as well as the corresponding notions of behaviour, bisimulation, and observational semantics.FCT grants SFRH/BD/52234/2013, SFRH/BSAB/ 113890/2015ERDF - European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT within project PTDC/EEI-CTP/4836/201

Languages and models for hybrid automata: A coalgebraic perspective

article in pressWe study hybrid automata from a coalgebraic point of view. We show that such a perspective supports a generic theory of hybrid automata with a rich palette of definitions and results. This includes, among other things, notions of bisimulation and behaviour, state minimisation techniques, and regular expression languages.POCI-01-0145-FEDER-016692. RDF — European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation — COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT — Fundação para a Ciência e a Tecnologia within project POCI-01-0145-FEDER-016692 and by the PT-FLAD Chair on Smart Cities & Smart Governance at Universidade do Minh

A method for rigorous design of reconfigurable systems

Reconfigurability, understood as the ability of a system to behave differently in different modes of operation and commute between them along its lifetime, is a cross-cutting concern in modern Software Engineering. This paper introduces a specification method for reconfigurable software based on a global transition structure to capture the system's reconfiguration space, and a local specification of each operation mode in whatever logic (equational, first-order, partial, fuzzy, probabilistic, etc.) is found expressive enough for handling its requirements. In the method these two levels are not only made explicit and juxtaposed, but formally interrelated. The key to achieve such a goal is a systematic process of hybridisation of logics through which the relationship between the local and global levels of a specification becomes internalised in the logic itself.This work is financed by the ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation – COMPETE 2020 Programme and by National Funds through the Portuguese funding agency, FCT – Fundação para a Ciência e a Tecnologia within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013. The first author is further supported by the BPD FCT Grant SFRH/BPD/103004/2014, and R. Neves is sponsored by FCT Grant SFRH/BD/52234/2013. M.A. Martins is also funded by the EU FP7 Marie Curie PIRSESGA-2012-318986 project GeTFun: Generalizing Truth-Functionality

Reuse and integration of specification logics: the hybridisation perspective

Hybridisation is a systematic process along which the characteristic features of hybrid logic, both at the syntactic and the semantic levels, are developed on top of an arbitrary logic framed as an institution. It also captures the construction of first-order encodings of such hybridised institutions into theories in first-order logic. The method was originally developed to build suitable logics for the specification of reconfigurable software systems on top of whatever logic is used to describe local requirements of each system’s configuration. Hybridisation has, however, a broader scope, providing a fresh example of yet another development in combining and reusing logics driven by a problem from Computer Science. This paper offers an overview of this method, proposes some new extensions, namely the introduction of full quantification leading to the specification of dynamic modalities, and exemplifies its potential through a didactical application. It is discussed how hybridisation can be successfully used in a formal specification course in which students progress from equational to hybrid specifications in a uniform setting, integrating paradigms, combining data and behaviour, and dealing appropriately with systems evolution and reconfiguration.This work is financed by the ERDF—European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation—COMPETE 2020 Programme, and by National Funds through the FCT (Portuguese Foundation for Science and Technology) within project POCI-01-0145-FEDER-006961. M. Martins was further supported by project UID/MAT/04106/2013. A. Madeira and R. Neves research was carried out in the context of a post-doc and a Ph.D. grant with references SFRH/BPD/103004/2014 and SFRH/BD/52234/2013, respectively. L.S. Barbosa is also supported by SFRH/BSAB/ 113890/2015

Hierarchical hybrid logic

We introduce HHL, a hierarchical variant of hybrid logic. We study first order correspondence results and prove a Hennessy-Milner like theorem relating (hierarchical) bisimulation and modal equivalence for HHL. Combining hierarchical transition structures with the ability to refer to specific states at different levels, this logic seems suitable to express and verify properties of hierarchical transition systems, a pervasive semantic structure in Computer Science.ERDF European Regional Development Fund, through the COMPETE Programme, and by National Funds through FCT - Portuguese Foundation for Science and Technology - within projects POCI-01-0145-FEDER-016692 and UID/MAT/04106/2013, as well by project “SmartEGOV: Harnessing EGOV for Smart Governance (Foundations, Methods, Tools) / NORTE-01-0145-FEDER-000037”, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL 2020 Partnership Agreement. A. Madeira and R. Neves are further supported by the FCT individual grants SFRH/BPD/103004/2014 and SFRH/BD/52234/201

Pervasive gaps in Amazonian ecological research

Biodiversity loss is one of the main challenges of our time,1,2 and attempts to address it require a clear un derstanding of how ecological communities respond to environmental change across time and space.3,4 While the increasing availability of global databases on ecological communities has advanced our knowledge of biodiversity sensitivity to environmental changes,5–7 vast areas of the tropics remain understudied.8–11 In the American tropics, Amazonia stands out as the world’s most diverse rainforest and the primary source of Neotropical biodiversity,12 but it remains among the least known forests in America and is often underrepre sented in biodiversity databases.13–15 To worsen this situation, human-induced modifications16,17 may elim inate pieces of the Amazon’s biodiversity puzzle before we can use them to understand how ecological com munities are responding. To increase generalization and applicability of biodiversity knowledge,18,19 it is thus crucial to reduce biases in ecological research, particularly in regions projected to face the most pronounced environmental changes. We integrate ecological community metadata of 7,694 sampling sites for multiple or ganism groups in a machine learning model framework to map the research probability across the Brazilian Amazonia, while identifying the region’s vulnerability to environmental change. 15%–18% of the most ne glected areas in ecological research are expected to experience severe climate or land use changes by 2050. This means that unless we take immediate action, we will not be able to establish their current status, much less monitor how it is changing and what is being lostinfo:eu-repo/semantics/publishedVersio

ATLANTIC EPIPHYTES: a data set of vascular and non-vascular epiphyte plants and lichens from the Atlantic Forest

Epiphytes are hyper-diverse and one of the frequently undervalued life forms in plant surveys and biodiversity inventories. Epiphytes of the Atlantic Forest, one of the most endangered ecosystems in the world, have high endemism and radiated recently in the Pliocene. We aimed to (1) compile an extensive Atlantic Forest data set on vascular, non-vascular plants (including hemiepiphytes), and lichen epiphyte species occurrence and abundance; (2) describe the epiphyte distribution in the Atlantic Forest, in order to indicate future sampling efforts. Our work presents the first epiphyte data set with information on abundance and occurrence of epiphyte phorophyte species. All data compiled here come from three main sources provided by the authors: published sources (comprising peer-reviewed articles, books, and theses), unpublished data, and herbarium data. We compiled a data set composed of 2,095 species, from 89,270 holo/hemiepiphyte records, in the Atlantic Forest of Brazil, Argentina, Paraguay, and Uruguay, recorded from 1824 to early 2018. Most of the records were from qualitative data (occurrence only, 88%), well distributed throughout the Atlantic Forest. For quantitative records, the most common sampling method was individual trees (71%), followed by plot sampling (19%), and transect sampling (10%). Angiosperms (81%) were the most frequently registered group, and Bromeliaceae and Orchidaceae were the families with the greatest number of records (27,272 and 21,945, respectively). Ferns and Lycophytes presented fewer records than Angiosperms, and Polypodiaceae were the most recorded family, and more concentrated in the Southern and Southeastern regions. Data on non-vascular plants and lichens were scarce, with a few disjunct records concentrated in the Northeastern region of the Atlantic Forest. For all non-vascular plant records, Lejeuneaceae, a family of liverworts, was the most recorded family. We hope that our effort to organize scattered epiphyte data help advance the knowledge of epiphyte ecology, as well as our understanding of macroecological and biogeographical patterns in the Atlantic Forest. No copyright restrictions are associated with the data set. Please cite this Ecology Data Paper if the data are used in publication and teaching events. © 2019 The Authors. Ecology © 2019 The Ecological Society of Americ