Decomposing Probabilistic Lambda-Calculi

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Continuation-Passing Style and Strong Normalisation for Intuitionistic Sequent Calculi

The intuitionistic fragment of the call-by-name version of Curien and Herbelin's \lambda\_mu\_{\~mu}-calculus is isolated and proved strongly normalising by means of an embedding into the simply-typed lambda-calculus. Our embedding is a continuation-and-garbage-passing style translation, the inspiring idea coming from Ikeda and Nakazawa's translation of Parigot's \lambda\_mu-calculus. The embedding strictly simulates reductions while usual continuation-passing-style transformations erase permutative reduction steps. For our intuitionistic sequent calculus, we even only need "units of garbage" to be passed. We apply the same method to other calculi, namely successive extensions of the simply-typed λ-calculus leading to our intuitionistic system, and already for the simplest extension we consider (λ-calculus with generalised application), this yields the first proof of strong normalisation through a reduction-preserving embedding. The results obtained extend to second and higher-order calculi

An Inheritance-Based Theory of the Lexicon in Combinatory Categorial Grammar

Institute for Communicating and Collaborative SystemsThis thesis proposes an extended version of the Combinatory Categorial Grammar (CCG) formalism, with the following features: 1. grammars incorporate inheritance hierarchies of lexical types, defined over a simple, feature-based constraint language 2. CCG lexicons are, or at least can be, functions from forms to these lexical types This formalism, which I refer to as ‘inheritance-driven’ CCG (I-CCG), is conceptualised as a partially model-theoretic system, involving a distinction between category descriptions and their underlying category models, with these two notions being related by logical satisfaction. I argue that the I-CCG formalism retains all the advantages of both the core CCG framework and proposed generalisations involving such things as multiset categories, unary modalities or typed feature structures. In addition, I-CCG: 1. provides non-redundant lexicons for human languages 2. captures a range of well-known implicational word order universals in terms of an acquisition-based preference for shorter grammars This thesis proceeds as follows: Chapter 2 introduces the ‘baseline’ CCG formalism, which incorporates just the essential elements of category notation, without any of the proposed extensions. Chapter 3 reviews parts of the CCG literature dealing with linguistic competence in its most general sense, showing how the formalism predicts a number of language universals in terms of either its restricted generative capacity or the prioritisation of simpler lexicons. Chapter 4 analyses the first motivation for generalising the baseline category notation, demonstrating how certain fairly simple implicational word order universals are not formally predicted by baseline CCG, although they intuitively do involve considerations of grammatical economy. Chapter 5 examines the second motivation underlying many of the customised CCG category notations — to reduce lexical redundancy, thus allowing for the construction of lexicons which assign (each sense of) open class words and morphemes to no more than one lexical category, itself denoted by a non-composite lexical type. Chapter 6 defines the I-CCG formalism, incorporating into the notion of a CCG grammar both a type hierarchy of saturated category symbols and an inheritance hierarchy of constrained lexical types. The constraint language is a simple, feature-based, highly underspecified notation, interpreted against an underlying notion of category models — this latter point is crucial, since it allows us to abstract away from any particular inference procedure and focus on the category notation itself. I argue that the partially model-theoretic I-CCG formalism solves the lexical redundancy problem fairly definitively, thereby subsuming all the other proposed variant category notations. Chapter 7 demonstrates that the I-CCG formalism also provides the beginnings of a theory of the CCG lexicon in a stronger sense — with just a small number of substantive assumptions about types, it can be shown to formally predict many implicational word order universals in terms of an acquisition-based preference for simpler lexical inheritance hierarchies, i.e. those with fewer types and fewer constraints. Chapter 8 concludes the thesis

Component library retrieval using property models

The re-use of products such as code, specifications, design decisions and documentation has been proposed as a method for increasing software productivity and reliability. A major problem that has still to be adequately solved is the storage and retrieval of re-usable 'components'. Current methods, such as keyword retrieval and catalogues, rely on the use of names to describe components or categories. This is inadequate for all but a few well established components and categories; in the majority of cases names do not convey sufficient information on which to base a decision to retrieve. One approach to this problem is to describe components using a formal specification. However this is impractical for two reasons; firstly, the limitations of theorem proving would severely restrict the complexity of components that could be retrieved and secondly the retrieval mechanism would need to have a method of retrieving components with 'similar' specifications. This thesis proposes the use of formal 'property' models to represent the key functionality of components. Retrieval of components can then take place on the basis of a property model produced by the library's users. These models only describe the key properties of a component, thereby making the task of comparing properties feasible. Views are introduced as a method of relating similar, non identical property models, and the use of these views facilitates the re-use of components with similar properties. The language Miramod has been developed for the purpose of describing components, and a Miramod compiler and property prover which allow Miramod models to be compared for similarity, have been designed and implemented. These tools have indicated that model based component library retrieval is feasible at relatively low levels of the programming process, and future work is suggested to extend the method to encompass earlier stages in the development of large systems

Curry and Howard Meet Borel

International audienceWe show that an intuitionistic version of counting propositional logic corresponds, in the sense of Curry and Howard, to an expressive type system for the probabilistic event λ-calculus, a vehicle calculus in which both call-by-name and call-by-value evaluation of discrete randomized functional programs can be simulated. In this context, proofs (respectively, types) do not guarantee that validity (respectively, termination) holds, but reveal the underlying probability. We finally show how to obtain a system precisely capturing the probabilistic behavior of λ-terms, by endowing the type system with an intersection operator

Language Reform by Lebanese Lexicographers in the Nahḍa: The case of Saʻīd al-Ḫūrī aš-Šartūnī

This article provides an overview of the social and literary revival and linguistic regeneration of the nineteenth century in Arab countries, especially in the Syro-Lebanese region. After outlining the work of the most important Lebanese lexicographers, this research focuses on the author Saʻīd al-Ḫūrī aš-Šartūnī and his multiple interests. The aim of this paper is to understand the role of this author in a reform carried out by two groups of intellectuals, one conservative and one reformist, in the period called Nahḍa