On the confluence of lambda-calculus with conditional rewriting

The confluence of untyped \lambda-calculus with unconditional rewriting is now well un- derstood. In this paper, we investigate the confluence of \lambda-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of M\"uller and Dougherty for unconditional rewriting. Two cases are considered, whether \beta-reduction is allowed or not in the evaluation of conditions. Moreover, Dougherty's result is improved from the assumption of strongly normalizing \beta-reduction to weakly normalizing \beta-reduction. We also provide examples showing that outside these conditions, modularity of confluence is difficult to achieve. Second, we go beyond the algebraic framework and get new confluence results using a restricted notion of orthogonality that takes advantage of the conditional part of rewrite rules

The seeds of divergence: the economy of French North America, 1688 to 1760

Generally, Canada has been ignored in the literature on the colonial origins of divergence with most of the attention going to the United States. Late nineteenth century estimates of income per capita show that Canada was relatively poorer than the United States and that within Canada, the French and Catholic population of Quebec was considerably poorer. Was this gap long standing? Some evidence has been advanced for earlier periods, but it is quite limited and not well-suited for comparison with other societies. This thesis aims to contribute both to Canadian economic history and to comparative work on inequality across nations during the early modern period. With the use of novel prices and wages from Quebec—which was then the largest settlement in Canada and under French rule—a price index, a series of real wages and a measurement of Gross Domestic Product (GDP) are constructed. They are used to shed light both on the course of economic development until the French were defeated by the British in 1760 and on standards of living in that colony relative to the mother country, France, as well as the American colonies. The work is divided into three components. The first component relates to the construction of a price index. The absence of such an index has been a thorn in the side of Canadian historians as it has limited the ability of historians to obtain real values of wages, output and living standards. This index shows that prices did not follow any trend and remained at a stable level. However, there were episodes of wide swings—mostly due to wars and the monetary experiment of playing card money. The creation of this index lays the foundation of the next component. The second component constructs a standardized real wage series in the form of welfare ratios (a consumption basket divided by nominal wage rate multiplied by length of work year) to compare Canada with France, England and Colonial America. Two measures are derived. The first relies on a “bare bones” definition of consumption with a large share of land-intensive goods. This measure indicates that Canada was poorer than England and Colonial America and not appreciably richer than France. However, this measure overestimates the relative position of Canada to the Old World because of the strong presence of land-intensive goods. A second measure is created using a “respectable” definition of consumption in which the basket includes a larger share of manufactured goods and capital-intensive goods. This second basket better reflects differences in living standards since the abundance of land in Canada (and Colonial America) made it easy to achieve bare subsistence, but the scarcity of capital and skilled labor made the consumption of luxuries and manufactured goods (clothing, lighting, imported goods) highly expensive. With this measure, the advantage of New France over France evaporates and turns slightly negative. In comparison with Britain and Colonial America, the gap widens appreciably. This element is the most important for future research. By showing a reversal because of a shift to a different type of basket, it shows that Old World and New World comparisons are very sensitive to how we measure the cost of living. Furthermore, there are no sustained improvements in living standards over the period regardless of the measure used. Gaps in living standards observed later in the nineteenth century existed as far back as the seventeenth century. In a wider American perspective that includes the Spanish colonies, Canada fares better. The third component computes a new series for Gross Domestic Product (GDP). This is to avoid problems associated with using real wages in the form of welfare ratios which assume a constant labor supply. This assumption is hard to defend in the case of Colonial Canada as there were many signs of increasing industriousness during the eighteenth and nineteenth centuries. The GDP series suggest no long-run trend in living standards (from 1688 to circa 1765). The long peace era of 1713 to 1740 was marked by modest economic growth which offset a steady decline that had started in 1688, but by 1760 (as a result of constant warfare) living standards had sunk below their 1688 levels. These developments are accompanied by observations that suggest that other indicators of living standard declined. The flat-lining of incomes is accompanied by substantial increases in the amount of time worked, rising mortality and rising infant mortality. In addition, comparisons of incomes with the American colonies confirm the results obtained with wages— Canada was considerably poorer. At the end, a long conclusion is provides an exploratory discussion of why Canada would have diverged early on. In structural terms, it is argued that the French colony was plagued by the problem of a small population which prohibited the existence of scale effects. In combination with the fact that it was dispersed throughout the territory, the small population of New France limited the scope for specialization and economies of scale. However, this problem was in part created, and in part aggravated, by institutional factors like seigneurial tenure. The colonial origins of French America’s divergence from the rest of North America are thus partly institutional

Impuretés et compromis de l'expertise, une difficile reconnaissance. A propos des risques collectifs et des situations d'incertitude

A partir d'une discussion d'un certain nombre de travaux actuels sur les pratiques d'expertise dans le domaine des risques collectifs, cet article suggère quelques déplacements qui sont autant de pistes de réflexion visant à rompre avec les analyses les plus convenues sur ces questions. Un premier déplacement concerne le statut accordé au modèle abstrait et idéalisé de l'expertise scientifique (neutralité, indépendance, etc.) : plutôt que de se contenter de dénoncer les écarts observables entre ce modèle et les pratiques concrètes de l'expertise scientifique, nous proposons de l'analyser également comme une ressource mobilisée par les acteurs eux-mêmes afin de maintenir leur identité professionnelle et la spécificité de leur rôle, et ce en dépit des impuretés et transgressions diverses qui caractérisent ce genre de pratiques. Le deuxième déplacement consiste à envisager l'expertise scientifique dans le domaine des risques collectifs, et plus particulièrement dans les situations d'incertitude, comme une recherche de plus en plus explicite de compromis entre savoirs techniques, règles juridiques, et intérêts politiques et économiques

Le corps de l’esclave en Grèce ancienne : espace de la représentation ou représentation d’un espace ?.

The objective for this paper is to show and tell the slave’s body from a transdisciplinary perspective which will combine in a unique way Ancient History and Geography. If slavery has created a great interest amongst Ancient historians, it would seem that the slave’s body has remained invisible in the field. How could this be explained ? We will grasp this subject from the assumption that it has been an unthought cultural thought : a non mentioned or non explicit reality. We thus went looking for this denied body in the fields of representations. Where and how is the slave’s body shown ? What signs or indicators show the bodies of slavery ? How do we recognize the slave in figurative and discourse representations ? We will highlight a gradient in how the slave’s body is visible/ invisible based on a chosen corpus of texts and iconography.Esta ponencia tiene como objetivo enseñar y hablar del el cuerpo del esclavo, a partir de una reflexión interdisciplinar que asocia de manera insólita la historia antigua y la geografía. Si bien el tema de la esclavitud ha suscitado un verdadero interés por parte de los historiadores de la Antigüedad, el cuerpo del esclavo parece ser un verdadero ángulo muerto en el campo de estos estudios. ¿ Cuál podría ser la explicación de tal ausencia ? Abordamos este tema partiendo del postulado que el cuerpo del esclavo permanece impensado o, dicho de otra manera, que se trata de una realidad siempre presente pero escasamente explicitada o evocada. Estaremos buscando este cuerpo renegado a través el campo de las representaciones. ¿ Cómo y dónde se muestra el cuerpo del esclavo ? ¿ Cuáles son los signos, los marcadores corporales de la esclavitud ? ¿ Cómo se reconoce al esclavo en las representaciones figuradas o discursivas ? Se pondrá en evidencia un abanico de visibilidad/ invisibilidad del cuerpo del esclavo a partir de un corpus de textos y de representaciones iconográficas seleccionadas.Barthe-Deloizy Francine, Charpentier Marie-Claude. Le corps de l’esclave en Grèce ancienne : espace de la représentation ou représentation d’un espace ?.. In: Los espacios de la esclavitud y la dependecia desde la antigüedad. Madrid, 28-30 novembre 2012. Actats del XXXV coloquio del GIREA. Homenaje a Domingo Placido. Besançon : Presses Universitaires de Franche-Comté, 2015. pp. 79-95. (Actes des colloques du Groupe de recherche sur l'esclavage dans l'antiquité, 35

Le corps de l’esclave en Grèce ancienne : espace de la représentation ou représentation d’un espace ?.

The objective for this paper is to show and tell the slave’s body from a transdisciplinary perspective which will combine in a unique way Ancient History and Geography. If slavery has created a great interest amongst Ancient historians, it would seem that the slave’s body has remained invisible in the field. How could this be explained ? We will grasp this subject from the assumption that it has been an unthought cultural thought : a non mentioned or non explicit reality. We thus went looking for this denied body in the fields of representations. Where and how is the slave’s body shown ? What signs or indicators show the bodies of slavery ? How do we recognize the slave in figurative and discourse representations ? We will highlight a gradient in how the slave’s body is visible/ invisible based on a chosen corpus of texts and iconography.Esta ponencia tiene como objetivo enseñar y hablar del el cuerpo del esclavo, a partir de una reflexión interdisciplinar que asocia de manera insólita la historia antigua y la geografía. Si bien el tema de la esclavitud ha suscitado un verdadero interés por parte de los historiadores de la Antigüedad, el cuerpo del esclavo parece ser un verdadero ángulo muerto en el campo de estos estudios. ¿ Cuál podría ser la explicación de tal ausencia ? Abordamos este tema partiendo del postulado que el cuerpo del esclavo permanece impensado o, dicho de otra manera, que se trata de una realidad siempre presente pero escasamente explicitada o evocada. Estaremos buscando este cuerpo renegado a través el campo de las representaciones. ¿ Cómo y dónde se muestra el cuerpo del esclavo ? ¿ Cuáles son los signos, los marcadores corporales de la esclavitud ? ¿ Cómo se reconoce al esclavo en las representaciones figuradas o discursivas ? Se pondrá en evidencia un abanico de visibilidad/ invisibilidad del cuerpo del esclavo a partir de un corpus de textos y de representaciones iconográficas seleccionadas.Barthe-Deloizy Francine, Charpentier Marie-Claude. Le corps de l’esclave en Grèce ancienne : espace de la représentation ou représentation d’un espace ?.. In: Los espacios de la esclavitud y la dependecia desde la antigüedad. Madrid, 28-30 novembre 2012. Actats del XXXV coloquio del GIREA. Homenaje a Domingo Placido. Besançon : Presses Universitaires de Franche-Comté, 2015. pp. 79-95. (Actes des colloques du Groupe de recherche sur l'esclavage dans l'antiquité, 35

Le corps de l’esclave en Grèce ancienne : espace de la représentation ou représentation d’un espace ?.

The objective for this paper is to show and tell the slave’s body from a transdisciplinary perspective which will combine in a unique way Ancient History and Geography. If slavery has created a great interest amongst Ancient historians, it would seem that the slave’s body has remained invisible in the field. How could this be explained ? We will grasp this subject from the assumption that it has been an unthought cultural thought : a non mentioned or non explicit reality. We thus went looking for this denied body in the fields of representations. Where and how is the slave’s body shown ? What signs or indicators show the bodies of slavery ? How do we recognize the slave in figurative and discourse representations ? We will highlight a gradient in how the slave’s body is visible/ invisible based on a chosen corpus of texts and iconography.Esta ponencia tiene como objetivo enseñar y hablar del el cuerpo del esclavo, a partir de una reflexión interdisciplinar que asocia de manera insólita la historia antigua y la geografía. Si bien el tema de la esclavitud ha suscitado un verdadero interés por parte de los historiadores de la Antigüedad, el cuerpo del esclavo parece ser un verdadero ángulo muerto en el campo de estos estudios. ¿ Cuál podría ser la explicación de tal ausencia ? Abordamos este tema partiendo del postulado que el cuerpo del esclavo permanece impensado o, dicho de otra manera, que se trata de una realidad siempre presente pero escasamente explicitada o evocada. Estaremos buscando este cuerpo renegado a través el campo de las representaciones. ¿ Cómo y dónde se muestra el cuerpo del esclavo ? ¿ Cuáles son los signos, los marcadores corporales de la esclavitud ? ¿ Cómo se reconoce al esclavo en las representaciones figuradas o discursivas ? Se pondrá en evidencia un abanico de visibilidad/ invisibilidad del cuerpo del esclavo a partir de un corpus de textos y de representaciones iconográficas seleccionadas.Barthe-Deloizy Francine, Charpentier Marie-Claude. Le corps de l’esclave en Grèce ancienne : espace de la représentation ou représentation d’un espace ?.. In: Los espacios de la esclavitud y la dependecia desde la antigüedad. Madrid, 28-30 novembre 2012. Actats del XXXV coloquio del GIREA. Homenaje a Domingo Placido. Besançon : Presses Universitaires de Franche-Comté, 2015. pp. 79-95. (Actes des colloques du Groupe de recherche sur l'esclavage dans l'antiquité, 35

ABSTRACT Pure Patterns Type Systems

We introduce a new framework of algebraic pure type systems in which we consider rewrite rules as lambda terms with patterns and rewrite rule application as abstraction application with built-in matching facilities. This framework, that we call “Pure Pattern Type Systems”, is particularly well-suited for the foundations of programming (meta)languages and proof assistants since it provides in a fully unified setting higher-order capabilities and pattern matching ability together with powerful type systems. We prove some standard properties like confluence and subject reduction for the case of a syntactic theory and under a syntactical restriction over the shape of patterns. We also conjecture the strong normalization of typable terms. This work should be seen as a contribution to a formal connection between logics and rewriting, and a step towards new proof engines based on the Curry-Howard isomorphism