Sequent Calculus and Equational Programming

Proof assistants and programming languages based on type theories usually come in two flavours: one is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style. We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus. A typed functional language is presented, based on a sequent calculus, that we relate to the syntax and internal language of Agda. In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.Comment: In Proceedings LFMTP 2015, arXiv:1507.0759

Inexperienced sonographers can successfully visualize and assess a three-dimensional image of the fetal face using a standardized ultrasound protocol

Introduction: A standardized three-dimensional ultrasonographic (3DUS) protocol is described that allows fetal face reconstruction. Ability to identify cleft lip with 3DUS using this protocol was assessed by operators with minimal 3DUS experience. Material and Methods: 260 stored volumes of fetal face were analyzed using a standardized protocol by operators with different levels of competence in 3DUS. The outcomes studied were: (1) the performance of post-processing 3D face volumes for the detection of facial clefts; (2) the ability of a resident with minimal 3DUS experience to reconstruct the acquired facial volumes, and (3) the time needed to reconstruct each plane to allow proper diagnosis of a cleft. Results: The three orthogonal planes of the fetal face (axial, sagittal and coronal) were adequately reconstructed with similar performance when acquired by a maternal-fetal medicine specialist or by residents with minimal experience (72 vs. 76%, p = 0.629). The learning curve for manipulation of 3DUS volumes of the fetal face corresponds to 30 cases and is independent of the operator's level of experience. Discussion: The learning curve for the standardized protocol we describe is short, even for inexperienced sonographers. This technique might decrease the length of anatomy ultrasounds and improve the ability to visualize fetal face anomalies

Focused Proof Search for Linear Logic in the Calculus of Structures

The proof-theoretic approach to logic programming has benefited from the introduction of focused proof systems, through the non-determinism reduction and control they provide when searching for proofs in the sequent calculus. However, this technique was not available in the calculus of structures, known for inducing even more non-determinism than other logical formalisms. This work in progress aims at translating the notion of focusing into the presentation of linear logic in this setting, and use some of its specific features, such as deep application of rules and fine granularity, in order to improve proof search procedures. The starting point for this research line is the multiplicative fragment of linear logic, for which a simple focused proof system can be built

Borders, Nationalism, and Representations: Imagined French India in the Era of Decolonisation, 1947–1962

French India consisted of five small, non-contiguous, defenceless, and economically insignificant territories, remnants of old trading posts scattered along the Indian coastline. The territories nevertheless had distinct cultural, historical, social, and linguistic characteristics. The independence of India in August 1947 brought into sharp focus the presence of France on the subcontinent and her territorial sovereignty over the French Indian territories. The issue was exacerbated by the new French constitution that made French India, like other French overseas territories, an indivisible part of the Fourth Republic (1946-1958) that could only secede through a referendum. This thesis suggests that France’s status as a subaltern coloniser, which had been defined by the historical dimensions of Franco-British relations in India, resulted in France’s creation of a myth of French India. This myth was part of the formation of a French national identity, and consequently French India was imagined to be greater than it really was. These considerations prevented France’s swift withdrawal from the subcontinent after India’s independence. In addition, a post-war colonial policy based on national grandeur, historical continuity, and a belief in the strategic value of French India in relation to the rest of the empire, in particular Indochina, led to France’s determination to remain in India - where it had a presence since 1663 - despite India’s territorial claims over European territories on the subcontinent and rising anti-colonial criticism. India’s own construct of French India as part of the Indian homeland drove both France and India to use French India as a political showcase for their own nationalist agendas. Diplomatic negotiations to decide the future of the French Indian territories dragged on for seven years; at the local level, pro-merger, anti-merger, and separatist factions, all of whom had been influenced by political, social, and historical factors, undermined both the arguments that French India should merge with India, and the arguments that she should remain within the French colonial framework. The factions, it will be argued, challenged both India’s nation-building process and France’s last attempt at regaining past colonial grandeur

I Need MORE Help : A Rise in Demand for Special Education in Ontario

According to regulation 298 of the Ontario Education Act (1990), a primary role of educators is to ‘effectively’ instruct the students they have been assigned. It is my understanding that ‘effective’ teaching is more than simply giving the lesson of the day that aligns with the curriculum. As a teacher, I try to support my pupils’ learning by taking into consideration the best possible way to serve their diverse abilities. Furthermore, I acknowledge that students may require personalized and tailored school supports in order to fully benefit from their educational experience. In my own practice, I have utilized special education programs and services as resources to individualize my pedagogy. That said, working in the realm of special education has its challenges. This major paper has the purpose of exploring these barriers while understanding special education as a growing tool to cater to the diversity of students in 20th century classrooms

The Focused Calculus of Structures

The focusing theorem identifies a complete class of sequent proofs that have no inessential non-deterministic choices and restrict the essential choices to a particular normal form. Focused proofs are therefore well suited both for the search and for the representation of sequent proofs. The calculus of structures is a proof formalism that allows rules to be applied deep inside a formula. Through this freedom it can be used to give analytic proof systems for a wider variety of logics than the sequent calculus, but standard presentations of this calculus are too permissive, allowing too many proofs. In order to make it more amenable to proof search, we transplant the focusing theorem from the sequent calculus to the calculus of structures. The key technical contribution is an incremental treatment of focusing that avoids trivializing the calculus of structures. We give a direct inductive proof of the completeness of the focused calculus of structures with respect to a more standard unfocused form. We also show that any focused sequent proof can be represented in the focused calculus of structures, and, conversely, any proof in the focused calculus of structures corresponds to a focused sequent proof

Focused Linear Logic and the λ-calculus

International audienceLinear logic enjoys strong symmetries inherited from classical logic while providing a constructive framework comparable to intuitionistic logic. However, the computational interpretation of sequent calculus presentations of linear logic remains problematic, mostly because of the many rule permutations allowed in the sequent calculus. We address this problem by providing a simple interpretation of focused proofs, a complete subclass of linear sequent proofs known to have a much stronger structure than the standard sequent calculus for linear logic. Despite the classical setting, the interpretation relates proofs to a refined linear λ-calculus, and we investigate its properties and relation to other calculi, such as the usual λ-calculus, the λµ-calculus, and their variants based on sequent calculi

Entre ethos professionnel et logiques d’entreprises : La recherche et l’innovation dans les agences d’architecture

Encouragés par une politique publique, incitative et de réforme, les dirigeants d’agences montrent un intérêt certain pour l’intégration de pratiques de recherche ou d’innovation dans leurs structures. Cependant, les dispositifs de droit commun ouverts aux agences d’architecture et prévus pour valoriser la recherche et l’innovation sont jugés insuffisamment investis par le champ de l’architecture (CIR, CII, CIFRE). Pour participer à la compréhension de ce phénomène, nous interrogeons les manières dont les architectes dirigeants appréhendent ces notions, les pratiques qu’ils leur associent et leur possible intégration au sein des structures. Nous avons pu vérifier ainsi la dualité à laquelle ils se confrontent : penser l’évolution des pratiques professionnelles et des structures qui les accueillent en réponse aux multiples défis auxquels est confronté le champ de l’architecture, tout en respectant les codes, valeurs et normes hérités d’une profession libérale.Encouraged by an incentive and reforming public policy, agency executives are showing a real interest in integrating research or innovation practices into their structures. However, the common law mechanisms open to architecture agencies and designed to promote research and innovation are considered to have received insufficient investments by the field of architecture (CIR, CII, CIFRE). In order to participate in the understanding of this phenomenon, we wanted to question the ways in which architect directors apprehend these notions, the practices they associate with them as well as their integration into structures. By doing so, we have been able to test the duality they are confronted with: building the evolution of professional practices and the structures that accommodate them, while satisfying the precepts and values inherited from a liberal profession

A Climate for Change in the UN Security Council? Member States' Approaches to the Climate-Security Nexus

This research report is the first to systematically engage with the growing political agenda of the climate-security nexus and to place a particular focus on the relationship between the state and the only international organ with a mandate to maintain international peace and security: the United Nations Security Council (UNSC). Discussions that have been ongoing since 2007, scattered governmental positions and the difficulty of achieving an overview of the various understandings, topics, concerns and responses of the UNSC member states in relation to the climate-security nexus all indicate a need to address this topic. This report therefore assesses and maps if and how the UNSC members acknowledge the linkages between climate change and security and how they position themselves with respect to these debates in the UNSC. With a large international network of interdisciplinary and country-specialized partner scientists, the analysis relies on an extensive spectrum of official primary sources from member state governments, various ministry strategies (such as those addressing security and climate change), UNSC documents and interdisciplinary academic literature on the climate-security nexus. It is located in the context of substantiated planetary climate emergencies and existential threats as well as urgent calls for action from the UN and member state representatives, scientific networks in Earth System Sciences and youth protests. Based on broad empirical research findings, this report concludes that all 15 current UNSC member states acknowledge the climate-security nexus in complex, changing and partly country-dependent ways. The report formulates an outlook and recommendations for decision-makers and scholars with a particular focus on strengthening the science-policy interface and dialogue and emphasizing the urgent need for institutional, multilateral and scientifically informed change. It also illustrates how essential it is for the UNSC to recognize and adapt institutional working methods to the interrelations of climate change and security and their effects as a cross-cutting issue