An Approach to Call-by-Name Delimited Continuations

International audienceWe show that a variant of Parigot's λμ-calculus, originally due to de Groote and proved to satisfy Böhm's theorem by Saurin, is canonically interpretable as a call-by-name calculus of delim- ited control. This observation is expressed using Ariola et al's call-by-value calculus of delimited control, an extension of λμ-calculus with delimited control known to be equationally equivalent to Danvy and Filinski's calculus with shift and reset. Our main result then is that de Groote and Saurin's variant of λμ-calculus is equivalent to a canonical call-by-name variant of Ariola et al's calculus. The rest of the paper is devoted to a comparative study of the call-by-name and call-by-value variants of Ariola et al's calculus, covering in particular the questions of simple typing, operational semantics, and continuation-passing-style semantics. Finally, we discuss the relevance of Ariola et al's calculus as a uniform framework for representing different calculi of delimited continuations, including "lazy" variants such as Sabry's shift and lazy reset calculus

Use of Virtual Reality as Therapeutic Tool for Behavioural Exposure in the Ambit of Social

We hereby present a study whose aim is to evaluate the efficiency and flexibility of virtual reality as a therapeutic tool in the confines of a social phobia behavioural therapeutic program. Our research protocol, accepted by the ethical commission of the cantonal hospices’ psychiatry service, is identical in content and structure for each patient. This study’s second goal is to use the confines of virtual exposure to objectively evaluate a specific parameter present in social phobia, namely eye contact avoidance, by using an eyetracking system. Analysis of our results shows that there is a tendency to improvement in both the questionnaires and eye contact avoidance

Refocusing generalised normalisation

When defined with general elimination/application rules, natural deduction and $\lambda$-calculus become closer to sequent calculus. In order to get real isomorphism, normalisation has to be defined in a ``multiary'' variant, in which reduction rules are necessarily non-local (reason: nomalisation, like cut-elimination, acts at the \emph{head} of applicative terms, but natural deduction focuses at the \emph{tail} of such terms). Non-local rules are bad, for instance, for the mechanization of the system. A solution is to extend natural deduction even further to a \emph{unified calculus} based on the unification of cut and general elimination. In the unified calculus, a sequent term behaves like in the sequent calculus, whereas the reduction steps of a natural deduction term are interleaved with explicit steps for bringing heads to focus. A variant of the calculus has the symmetric role of improving sequent calculus in dealing with tail-active permutative conversions

Characterising strongly normalising intuitionistic sequent terms

This paper gives a characterisation, via intersection types, of the strongly normalising terms of an intuitionistic sequent calculus (where LJ easily embeds). The soundness of the typing system is reduced to that of a well known typing system with intersection types for the ordinary lambda-calculus. The completeness of the typing system is obtained from subject expansion at root position. This paper's sequent term calculus integrates smoothly the lambda-terms with generalised application or explicit substitution. Strong normalisability of these terms as sequent terms characterises their typeability in certain "natural'' typing systems with intersection types. The latter are in the natural deduction format, like systems previously studied by Matthes and Lengrand et al., except that they do not contain any extra, exceptional rules for typing generalised applications or substitution

Forcing-based cut-elimination for Gentzen-style intuitionistic sequent calculus

International audienceWe give a simple intuitionistic completeness proof of Kripke semantics for intuitionistic logic with implication and universal quantification with respect to cut-free intuitionistic sequent calculus. The Kripke semantics is ``simplified'' in the way that the domain remains constant. The proof has been formalised in the Coq proof assistant and by combining soundness with completeness, we obtain an executable cut-elimination procedure. The proof easily extends to the case of the absurdity connective using Kripke models with exploding nodes à la Veldman

A calibration method for broad-bandwidth cavity enhanced absorption spectroscopy performed with supercontinuum radiation

An efficient calibration method has been developed for broad-bandwidth cavity enhanced absorption spectroscopy. The calibration is performed using phase shift cavity ring-down spectroscopy, which is conveniently implemented through use of an acousto-optic tunable filter (AOTF). The AOTF permits a narrowband portion of the SC spectrum to be scanned over the full high-reflectivity bandwidth of the cavity mirrors. After calibration the AOTF is switched off and broad-bandwidth CEAS can be performed with the same light source without any loss of alignment to the set-up. We demonstrate the merits of the method by probing transitions of oxygen molecules O-2 and collisional pairs of oxygen molecules (O-2)(2) in the visible spectral range

Impact of Vitamin D Supplementation on Arterial Vasomotion, Stiffness and Endothelial Biomarkers in Chronic Kidney Disease Patients

Background: Cardiovascular events are frequent and vascular endothelial function is abnormal in patients with chronic kidney disease (CKD). We demonstrated endothelial dysfunction with vitamin D deficiency in CKD patients; however the impact of cholecalciferol supplementation on vascular stiffness and vasomotor function, endothelial and bone biomarkers in CKD patients with low 25-hydroxy vitamin D [25(OH)D] is unknown, which this study investigated. Methods: We assessed non-diabetic patients with CKD stage 3/4, age 17–80 years and serum 25(OH)D ,75 nmol/L. Brachial artery Flow Mediated Dilation (FMD), Pulse Wave Velocity (PWV), Augmentation Index (AI) and circulating blood biomarkers were evaluated at baseline and at 16 weeks. Oral 300,000 units cholecalciferol was administered at baseline and 8-weeks. Results: Clinical characteristics of 26 patients were: age 50614 (mean61SD) years, eGFR 41611 ml/min/1.73 m2, males 73%, dyslipidaemia 36%, smokers 23% and hypertensives 87%. At 16-week serum 25(OH)D and calcium increased (43616 to 84629 nmol/L, p,0.001 and 2.3760.09 to 2.4260.09 mmol/L; p = 0.004, respectively) and parathyroid hormone decreased (10.868.6 to 7.464.4; p = 0.001). FMD improved from 3.163.3% to 6.163.7%, p = 0.001. Endothelial biomarker concentrations decreased: E-Selectin from 566662123 to 525662058 pg/mL; p = 0.032, ICAM-1, 3.4560.01 to 3.1061.04 ng/mL; p = 0.038 and VCAM-1, 54633 to 42633 ng/mL; p = 0.006. eGFR, BP, PWV, AI, hsCRP, von Willebrand factor and Fibroblast Growth Factor-23, remained unchanged. Conclusion: This study demonstrates for the first time improvement of endothelial vasomotor and secretory functions with vitamin D in CKD patients without significant adverse effects on arterial stiffness, serum calcium or FGF-23. Trial Registration: ClinicalTrials.gov NCT0200571

Towards a canonical classical natural deduction system

This paper studies a new classical natural deduction system, presented as a typed calculus named \lml. It is designed to be isomorphic to Curien-Herbelin's calculus, both at the level of proofs and reduction, and the isomorphism is based on the correct correspondence between cut (resp. left-introduction) in sequent calculus, and substitution (resp. elimination) in natural deduction. It is a combination of Parigot's $\lambda\mu$-calculus with the idea of ``coercion calculus'' due to Cervesato-Pfenning, accommodating let-expressions in a surprising way: they expand Parigot's syntactic class of named terms. This calculus aims to be the simultaneous answer to three problems. The first problem is the lack of a canonical natural deduction system for classical logic. \lml is not yet another classical calculus, but rather a canonical reflection in natural deduction of the impeccable treatment of classical logic by sequent calculus. The second problem is the lack of a formalization of the usual semantics of Curien-Herbelin's calculus, that explains co-terms and cuts as, respectively, contexts and hole-filling instructions. The mentioned isomorphism is the required formalization, based on the precise notions of context and hole-expression offered by \lml. The third problem is the lack of a robust process of ``read-back'' into natural deduction syntax of calculi in the sequent calculus format, that affects mainly the recent proof-theoretic efforts of derivation of $\lambda$-calculi for call-by-value. An isomorphic counterpart to the $Q$-subsystem of Curien-Herbelin's-calculus is derived, obtaining a new $\lambda$-calculus for call-by-value, combining control and let-expressions.Fundação para a Ciência e a Tecnologia (FCT

Forcing-based cut-elimination for Gentzen-style intuitionistic sequent calculus

International audienceWe give a simple intuitionistic completeness proof of Kripke semantics for intuitionistic logic with implication and universal quantification with respect to cut-free intuitionistic sequent calculus. The Kripke semantics is ``simplified'' in the way that the domain remains constant. The proof has been formalised in the Coq proof assistant and by combining soundness with completeness, we obtain an executable cut-elimination procedure. The proof easily extends to the case of the absurdity connective using Kripke models with exploding nodes à la Veldman

Sound and Complete Typing for lambda-mu

In this paper we define intersection and union type assignment for Parigot's calculus lambda-mu. We show that this notion is complete (i.e. closed under subject-expansion), and show also that it is sound (i.e. closed under subject-reduction). This implies that this notion of intersection-union type assignment is suitable to define a semantics.Comment: In Proceedings ITRS 2010, arXiv:1101.410