Computaçãao quântica pode ser entendida como transformação da informação codificada no estado de um sistema físico quântico. A idéia básica da computação quântica é codificar dados utilizando bits quânticos (qubits). Diferentemente do bit clássico, o qubit pode existir em uma superposição dos seus estados básicos permitindo o “paralelismo quântico”, o qual é uma característica importante da computação quântica visto que pode aumentar consideravelmente a velocidade de processamento dos algoritmos. Entretanto, tipos de dados quânticos são bastante poderosos não somente por causa da superposição de estados. Existem outras propriedades ímpares como medida e emaranhamento. Nesta tese, nós discutimos que um modelo realístico para computações quânticas deve ser geral com respeito a medidas, e completo com respeito a comunicação entre o mundo quântico e o mundo clássico. Nós, então, explicamos e estruturamos computações quânticas gerais e completas em Haskell utilizando construções conhecidas da área de semântica e linguagens de programação clássicas, como mônadas e setas. Em mais detalhes, esta tese se concentra nas seguintes contribuições. Mônadas e Setas. Paralelismo quântico, emaranhamento e medida quântica certamente vão além do escopo de linguagens funcionais “puras”. Nós mostramos que o paralelismo quântico pode ser modelado utilizando-se uma pequena generalização de mônadas, chamada mônadas indexadas ou estruturas Kleisli. Além disso, nós mostramos que a medida quântica pode ser explicada utilizando-se uma generalização mais radical de mônadas, as assim chamadas setas, mais especificamente, setas indexadas, as quais definimos nesta tese. Este resultado conecta características quânticas “genéricas” e “completas” `a construções semânticas de linguagens de programação bem fundamentadas. Entendendo as Interpretações da Mecânica Quântica como Efeitos Computacionais. Em um experimento hipotético, Einstein, Podolsky e Rosen demonstraram algumas consequências contra-intuitivas da mecânica quântica. A idéia básica é que duas partículas parecem sempre comunicar alguma informação mesmo estando separadas por uma distância arbitrariamente grande. Existe muito debate e muitos artigos sobre esse tópico, mas é interessante notar que, como proposto por Amr Sabry, essas características estranhas podem ser essencialmente modeladas por atribuições a variáveis globais. Baseados nesta idéia nós modelamos este comportamento estranho utilizando noções gerais de efeitos computacionais incorporados nas noções de mônadas e setas. Provando Propriedades de Programas Quânticos Utilizando Leis Algébricas. Nós desenvolvemos um trabalho preliminar para fazer provas equacionais sobre algoritmos quânticos escritos em uma sublinguagem pura de uma linguagem de programação funcional quântica, chamada QML. / Quantum computation can be understood as transformation of information encoded in the state of a quantum physical system. The basic idea behind quantum computation is to encode data using quantum bits (qubits). Differently from the classical bit, the qubit can be in a superposition of basic states leading to “quantum parallelism”, which is an important characteristic of quantum computation since it can greatly increase the speed processing of algorithms. However, quantum data types are computationally very powerful not only due to superposition. There are other odd properties like measurement and entangled. In this thesis we argue that a realistic model for quantum computations should be general with respect to measurements, and complete with respect to the information flow between the quantum and classical worlds. We thus explain and structure general and complete quantum programming in Haskell using well known constructions from classical semantics and programming languages, like monads and arrows. In more detail, this thesis focuses on the following contributions. Monads and Arrows. Quantum parallelism, entanglement, and measurement certainly go beyond “pure” functional programming. We have shown that quantum parallelism can be modelled using a slightly generalisation of monads called indexed monads, or Kleisli structures. We have also build on this insight and showed that quantum measurement can be explained using a more radical generalisation of monads, the so-called arrows, more specifically, indexed arrows, which we define in this thesis. This result connects “generic” and “complete” quantum features to well-founded semantics constructions and programming languages. Understanding of Interpretations of QuantumMechanics as Computational Effects. In a thought experiment, Einsten, Podolsky, and Rosen demonstrate some counter-intuitive consequences of quantum mechanics. The basic idea is that two entangled particles appear to always communicate some information even when they are separated by arbitrarily large distances. There has been endless debate and papers on this topic, but it is interesting that, as proposed by Amr Sabry, this strangeness can be essentially modelled by assignments to global variables. We build on that, and model this strangeness using the general notions of computational effects embodied in monads and arrows. Reasoning about Quantum Programs Using Algebraic Laws. We have developed a preliminary work to do equational reasoning about quantum algorithms written in a pure sublanguage of a functional quantum programming language, called QML.

Computaçãao quântica pode ser entendida como transformação da informação codificada no estado de um sistema físico quântico. A idéia básica da computação quântica é codificar dados utilizando bits quânticos (qubits). Diferentemente do bit clássico, o qubit pode existir em uma superposição dos seus estados básicos permitindo o “paralelismo quântico”, o qual é uma característica importante da computação quântica visto que pode aumentar consideravelmente a velocidade de processamento dos algoritmos. Entretanto, tipos de dados quânticos são bastante poderosos não somente por causa da superposição de estados. Existem outras propriedades ímpares como medida e emaranhamento. Nesta tese, nós discutimos que um modelo realístico para computações quânticas deve ser geral com respeito a medidas, e completo com respeito a comunicação entre o mundo quântico e o mundo clássico. Nós, então, explicamos e estruturamos computações quânticas gerais e completas em Haskell utilizando construções conhecidas da área de semântica e linguagens de programação clássicas, como mônadas e setas. Em mais detalhes, esta tese se concentra nas seguintes contribuições. Mônadas e Setas. Paralelismo quântico, emaranhamento e medida quântica certamente vão além do escopo de linguagens funcionais “puras”. Nós mostramos que o paralelismo quântico pode ser modelado utilizando-se uma pequena generalização de mônadas, chamada mônadas indexadas ou estruturas Kleisli. Além disso, nós mostramos que a medida quântica pode ser explicada utilizando-se uma generalização mais radical de mônadas, as assim chamadas setas, mais especificamente, setas indexadas, as quais definimos nesta tese. Este resultado conecta características quânticas “genéricas” e “completas” `a construções semânticas de linguagens de programação bem fundamentadas. Entendendo as Interpretações da Mecânica Quântica como Efeitos Computacionais. Em um experimento hipotético, Einstein, Podolsky e Rosen demonstraram algumas consequências contra-intuitivas da mecânica quântica. A idéia básica é que duas partículas parecem sempre comunicar alguma informação mesmo estando separadas por uma distância arbitrariamente grande. Existe muito debate e muitos artigos sobre esse tópico, mas é interessante notar que, como proposto por Amr Sabry, essas características estranhas podem ser essencialmente modeladas por atribuições a variáveis globais. Baseados nesta idéia nós modelamos este comportamento estranho utilizando noções gerais de efeitos computacionais incorporados nas noções de mônadas e setas. Provando Propriedades de Programas Quânticos Utilizando Leis Algébricas. Nós desenvolvemos um trabalho preliminar para fazer provas equacionais sobre algoritmos quânticos escritos em uma sublinguagem pura de uma linguagem de programação funcional quântica, chamada QML. / Quantum computation can be understood as transformation of information encoded in the state of a quantum physical system. The basic idea behind quantum computation is to encode data using quantum bits (qubits). Differently from the classical bit, the qubit can be in a superposition of basic states leading to “quantum parallelism”, which is an important characteristic of quantum computation since it can greatly increase the speed processing of algorithms. However, quantum data types are computationally very powerful not only due to superposition. There are other odd properties like measurement and entangled. In this thesis we argue that a realistic model for quantum computations should be general with respect to measurements, and complete with respect to the information flow between the quantum and classical worlds. We thus explain and structure general and complete quantum programming in Haskell using well known constructions from classical semantics and programming languages, like monads and arrows. In more detail, this thesis focuses on the following contributions. Monads and Arrows. Quantum parallelism, entanglement, and measurement certainly go beyond “pure” functional programming. We have shown that quantum parallelism can be modelled using a slightly generalisation of monads called indexed monads, or Kleisli structures. We have also build on this insight and showed that quantum measurement can be explained using a more radical generalisation of monads, the so-called arrows, more specifically, indexed arrows, which we define in this thesis. This result connects “generic” and “complete” quantum features to well-founded semantics constructions and programming languages. Understanding of Interpretations of QuantumMechanics as Computational Effects. In a thought experiment, Einsten, Podolsky, and Rosen demonstrate some counter-intuitive consequences of quantum mechanics. The basic idea is that two entangled particles appear to always communicate some information even when they are separated by arbitrarily large distances. There has been endless debate and papers on this topic, but it is interesting that, as proposed by Amr Sabry, this strangeness can be essentially modelled by assignments to global variables. We build on that, and model this strangeness using the general notions of computational effects embodied in monads and arrows. Reasoning about Quantum Programs Using Algebraic Laws. We have developed a preliminary work to do equational reasoning about quantum algorithms written in a pure sublanguage of a functional quantum programming language, called QML.

Submitted by Renata Lopes (renatasil82@gmail.com) on 2016-04-28T17:14:15Z No. of bitstreams: 1 felipezschaberalvespassos.pdf: 18204607 bytes, checksum: e54236349361337a64d57bb931e9010b (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2016-05-02T01:12:46Z (GMT) No. of bitstreams: 1 felipezschaberalvespassos.pdf: 18204607 bytes, checksum: e54236349361337a64d57bb931e9010b (MD5) / Made available in DSpace on 2016-05-02T01:12:46Z (GMT). No. of bitstreams: 1 felipezschaberalvespassos.pdf: 18204607 bytes, checksum: e54236349361337a64d57bb931e9010b (MD5) Previous issue date: 2015-02-26 / Em nosso trabalho, estudaremos um produto jornalístico que se assemelha à reportagem, mas que é, a sua vez, praticado na Web: trata-se do especial multimídia. Alinhamos essa prática aos materiais produzidos pelos gêneros jornalísticos interpretativo e literário, que veem sua faceta sendo adaptada ao meio da Web. Percebemos que esse meio possui qualidades específicas, modificando, a sua maneira, alguns pontos da prática tradicional. Acreditamos que essas reportagens na Web podem oferecer ao usuário diversos percursos de leitura e, desse modo, possibilitar distintas construções de significados, de acordo com os conteúdos midiáticos que são explorados por meio do percurso trilhado. Nossa hipótese aponta para a configuração de sua estrutura, das relações entre os seus meios – as formas que se encontram – e entre meiosusuários – no nível dos conteúdos e da interface – como pontos determinantes nesse material. Também cremos que é possível conferir uma viabilidade estrutural em seu planejamento e produção, utilizando nessa oportunidade o conceito das “mônadas abertas”, cunhado por Pernisa Júnior e Alves (2012). No estudo, colocaremos esses conceitos em relação aos resultados encontrados na fase empírica, na qual analisaremos três casos de webreportagens. Nessa ocasião, pretendemos encontrar padrões e tendências e, dessa forma, alcançar conclusões acerca da presente temática, inferindo o que foi estudado na teoria com aquilo identificado na prática. / In our work, we study a journalistic product that resembles the journalistic feature, but, which is, in turn, practiced on the Web: it is the multimedia special. We align this practice to the materials produced by the interpretative and literary journalistic genres, which see their facet being adapted to the environment of the Web. We realized that this medium has specific qualities, modifying, in its way, some points of the traditional practice. We believe that these web features (reports) can provide many reading paths to the user, and thereby enable different constructions of meanings, according to the media content which are explored by means of the covered path. Our hypothesis points to the configuration of its structure, the relationship between their medium – the way they meet – and between medium and users – in the level of content and interface – as key points in this material. We also believe that is possible to give a structural viability in their planning and production, using in this opportunity the concept of “opened monads”, coined by Pernisa Júnior and Alves (2012). In the study, we put these concepts in relation to the results found in the empirical phase, in which we analyze three cases of web features. In this occasion we intend to find patterns and trends and thus reach conclusions about this subject, inferring what was studied by theory with what has been identified in practice.

The main goal of this thesis was to implement a functional programming (FP) library named Funk that extends C# with support for concepts present in functional programming languages, such as F# and Scala. Funk utilizes many functional programming concepts, including immutability, pattern matching, and various types of monads, together with stronger typing. Introduction of these concepts into C# helps in avoiding many runtime errors and boilerplate code, and it also lets developers write C# code in a declarative rather than in an imperative way, making the day-to-day software development easier and less error-prone. Additionally, the thesis analyzes and compares Funk with existing functional programming libraries such as Language-ext and FuncSharp. Finally, it analyzes the new features of C# 8, which include nullable reference types and pattern matching and compares them with the functionalities of the Funk library.

In this work we introduce some category-theoretical concepts and techniques to study probability distributions on metric spaces and ordered metric spaces. In Chapter 1 we give an overview of the concept of a probability monad, first defined by Giry. Probability monads can be interpreted as a categorical tool to talk about random elements of a space X. We can consider these random elements as formal convex combinations, or mixtures, of elements of X. Spaces where the convex combinations can be actually evaluated are called algebras of the probability monad. In Chapter 2 we define a probability monad on the category of complete metric spaces and 1-Lipschitz maps called the Kantorovich monad, extending a previous construction due to van Breugel. This monad assigns to each complete metric space X its Wasserstein space PX. It is well-known that finitely supported probability measures with rational coefficients, or empirical distributions of finite sequences, are dense in the Wasserstein space. This density property can be translated into categorical language as a colimit of a diagram involving certain powers of X. The monad structure of P, and in particular the integration map, is uniquely determined by this universal property. We prove that the algebras of the Kantorovich monad are exactly the closed convex subsets of Banach spaces. In Chapter 3 we extend the Kantorovich monad of Chapter 2 to metric spaces equipped with a partial order. The order is inherited by the Wasserstein space, and is called the stochastic order. Differently from most approaches in the literature, we define a compatibility condition of the order with the metric itself, rather then with the topology it induces. We call the spaces with this property L-ordered spaces. On L-ordered spaces, the stochastic order induced on the Wasserstein spaces satisfies itself a form of Kantorovich duality. The Kantorovich monad can be extended to the category of L-ordered metric spaces. We prove that its algebras are the closed convex subsets of ordered Banach spaces, i.e. Banach spaces equipped with a closed cone. The category of L-ordered metric spaces can be considered a 2-category, in which we can describe concave and convex maps categorically as the lax and oplax morphisms of algebras. In Chapter 4 we develop a new categorical formalism to describe operations evaluated partially. We prove that partial evaluations for the Kantorovich monad, or partial expectations, define a closed partial order on the Wasserstein space PA over every algebra A, and that the resulting ordered space is itself an algebra. We prove that, for the Kantorovich monad, these partial expectations correspond to conditional expectations in distribution. Finally, we study the relation between these partial evaluation orders and convex functions. We prove a general duality theorem extending the well-known duality between convex functions and conditional expectations to general ordered Banach spaces.

Ces travaux s’intéressent à la modélisation formelle de la sémantique des langues naturelles. Pour cela, nous suivons le principe de compositionnalité qui veut que le sens d’une expression complexe soit une fonction du sens de ses parties. Ces fonctions sont généralement formalisées à l’aide du [lambda]-calcul. Cependant, ce principe est remis en cause par certains usages de la langue, comme les pronoms anaphoriques ou les présuppositions. Ceci oblige à soit abandonner la compositionalité, soit modifier les structures du sens. Dans le premier cas, le sens n’est alors plus obtenu par un calcul qui correspond à des fonctions mathématiques, mais par un calcul dépendant du contexte, ce qui le rapproche des langages de programmation qui manipulent leur contexte avec des effets de bord. Dans le deuxième cas, lorsque les structures de sens sont ajustées, les nouveaux sens ont tendance à avoir une structure de monade. Ces dernières sont elles-mêmes largement utilisées en programmation fonctionnelle pour coder des effets de bord, que nous retrouvons à nouveau. Par ailleurs, s’il est souvent possible de proposer le traitement d’un unique phénomène, composer plusieurs traitements s’avère être une tâche complexe. Nos travaux proposent d’utiliser les résultats récents autour des langages de programmation pour parvenir à combiner ces modélisations par les effets de bord. Pour cela, nous étendons le [lambda]-calcul avec une monade qui implémente les effects et les handlers, une technique récente dans l’étude des effets de bord. Dans la première partie de la thèse, nous démontrons les propriétés fondamentales de ce calcul (préservation de type, confluence et terminaison). Dans la seconde partie, nous montrons comment utiliser le calcul pour le traitement de plusieurs phénomènes linguistiques : deixis, quantification, implicature conventionnelle, anaphore et présupposition. Enfin, nous construisons une unique grammaire qui gère ces phénomènes et leurs interactions. / In formal semantics, researchers assign meanings to sentences of a natural language. This work is guided by the principle of compositionality: the meaning of an expression is a function of the meanings of its parts. These functions are often formalized using the [lambda]-calculus. However, there are areas of language which challenge the notion of compositionality, e.g. anaphoric pronouns or presupposition triggers. These force researchers to either abandon compositionality or adjust the structure of meanings. In the first case, meanings are derived by processes that no longer correspond to pure mathematical functions but rather to context-sensitive procedures, much like the functions of a programming language that manipulate their context with side effects. In the second case, when the structure of meanings is adjusted, the new meanings tend to be instances of the same mathematical structure, the monad. Monads themselves being widely used in functional programming to encode side effects, the common theme that emerges in both approaches is the introduction of side effects. Furthermore, different problems in semantics lead to different theories which are challenging to unite. Our thesis claims that by looking at these theories as theories of side effects, we can reuse results from programming language research to combine them.This thesis extends [lambda]-calculus with a monad of computations. The monad implements effects and handlers, a recent technique in the study of programming language side effects. In the first part of the thesis, we prove some of the fundamental properties of this calculus: subject reduction, confluence and termination. Then in the second part, we demonstrate how to use the calculus to implement treatments of several linguistic phenomena: deixis, quantification, conventional implicature, anaphora and presupposition. In the end, we build a grammar that features all of these phenomena and their interactions.

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Quantum computing is an emerging technology that, currently, has the challenge of developing programming languages, according to the rules of quantum mechanics, to support the creation, analysis, modeling and simulation of high-level quantum algorithms. Particularly, the focus is on the investigation of new semantic models to develop programming languages for quantum computing. In this context, one alternative is to use the semantic model of monads and arrows that abstracts both pure and mixed quantum states and also can express measures. This model however, was originally implemented as a library for the functional language Haskell, which not every programmer is family. This way, this study aims to provide a universal tool for high-level quantum programming, providing a library for Java. This library was implemented using the new features of closures present in the version 8 of the JDK (Java Development Kit), already available in developers preview. In addition, we present a specific syntax for the library to facilitate the development of quantum algorithms with a clearly structured notation. This syntax is described in a notation similar to the do-notation of Haskell and operates in conjunction with a parser implemented by ANTLR tool. / A computação quântica é uma tecnologia emergente e, atualmente, encontra-se no desafio de desenvolver linguagens de programação segundo as regras da mecânica quântica para a criação, análise, modelagem e simulação de algoritmos quânticos de alto nível. Particularmente, o foco é na investigação de novos modelos semânticos para elaborar linguagens de programação para a computação quântica. Nesse contexto, uma das alternativas é utilizar um modelo semântico de mônadas e setas capaz de abstrair tanto estados quânticos puros quanto mistos e ainda expressar operações de medidas. Esse modelo foi implementado como uma biblioteca para a linguagem funcional Haskell, contudo nem todo programador está familiarizado. Dessa forma, o presente trabalho objetiva oferecer uma ferramenta universal de alto nível para a programação quântica, apresentando uma biblioteca para o Java. Essa biblioteca foi implementada utilizando os novos recursos de closures presentes na versão 8 do JDK (Java Development Kit), já disponibilizados na prévia de desenvolvedores. Além disso, esse trabalho apresenta uma sintaxe específica para a biblioteca para facilitar a elaboração de algoritmos quânticos de forma clara e estruturada, descrita de uma maneira similar a notação-do do Haskell. A sintaxe criada opera em conjunto com um tradutor desenvolvido com a ferramenta ANTLR.

This work focuses on the meaning of dialectical method in the context of preceding parts of the dialogue Philebus (discourse about One and Many, asymmetrical ethical controversy, examining of the nature of pleasure) and in the context of some following parts (examples of application of the dialectical method, remembrance from a god connected with the agreement on three features of the good, sketch of the panta-ontology). This method has from its perspective the universal scope and its task is to solve difficulties. But its principle according to which it distinguishes One and Many and also Determinacy and Indeterminacy needs to be explained. The initial One has meaning of the genus which includes species or of the henad which includes monads. Limits of the dialectical method are marked with the ethical perspective based on the insight into nature of the good and with the ontological perpective which introduces the cause. The good and the cause can be identified with the pure One in order to make from them supplements of the dialectical method. This dialectical method can be applied only to One which is Many or to One which unifies Many (the pure One). It can't be applied to One which is without any relation to Many or to Many which is in no way One. In contrast to the dialectical method the...

Ce manuscrit présente une méthode de conception au niveau système reposant sur la programmation fonctionnelle typée et visant à atténuer certains des problèmes complexifiant le développement des systèmes numériques modernes, tels que leurs tailles importantes ou la grande variété des blocs les constituant. Nous proposons un ensemble de mécanismes permettant de mélanger au sein d'un même design plusieurs formalismes de description distincts («modèles de calcul») se situant potentiellement à des niveaux d'abstraction différents. De plus, nous offrons au concepteur la possibilité d'expliciter directement les paramètres explorables de chaque sous-partie du design, puis d'en déterminer des valeurs acceptables via une étape d'exploration partiellement ou totalement automatisée réalisée à l'échelle du système. Les gains qu'apportent ces stratégies nouvelles sont illustrés sur plusieurs exemples. / This work presents a novel system-level design method based on typed functional programming and aiming at mitigating some of the issues making the development of modern digital systems complex, such as their increasing sizes and the variety of their subcomponents. We propose a range of mechanisms allowing to mix within a single design several description formalisms (``models of computation''), possibly at different abstraction levels. Moreover, the designer is provided with means to directly express the explorable parameters of each part of their design, and to find acceptable values for them through a partially or totally automatic system-wide architectural exploration step. The advantages brought by those new strategies are illustrated on several examples.

No description available.