MD Alain Lescoat
email: alain.lescoat@chu-rennes.fr

MD Guillaume Coiffier

MD Marine De Carlan

MD Catherine Droitcourt

Alice Ballerie

MD Claire Cazalets

MD Aleth Perdriger

Patrick Jego

MD Patrick Jégo

Combination of Capillaroscopic and Ultrasonographic Evaluations in Systemic Sclerosis Results of a Cross-Sectional Study

Keywords: Systemic sclerosis, Scleroderma, Digital Ulcers, Acro-osteolysis, Calcinosis, Vasculopathy, Power Doppler Ultrasonography, Capillaroscopy, Ulnar artery, Digital ischemia

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Introduction:

Vascular involvement in Systemic sclerosis (SSc) is characterized by two main mechanisms.

The first one is an early destructive vasculopathy with progressive loss of capillaries. The second one is an obliterative vasculopathy due to intimal hyperplasia with proliferation of vascular cells and intimal fibrosis. Microvascular damages result in digital ulcers (DUs) secondary to chronic hypoxemia, and pulmonary arterial hypertension (PAH) caused by fibroproliferative and obliterative vasculopathy. If PAH is one of the main causes of mortality in SSc, hand involvement and DUs are major aspects of the disease and are responsible for a high morbidity.

Microvascular damages of the hand can easily be evaluated using nailfold capillaroscopy (NC). Among the capillaroscopic features, the number of capillaries per millimetre in the middle finger of the dominant hand seems to be a reproducible and reliable predictive parameter to assess the risk of DU recurrence in SSc 1. Digital manifestations of SSc also include sub-cutaneous calcinosis and acro-osteolysis. There is a lack of therapeutic measures to tackle these digital manifestations of the disease and a better characterization of the mechanisms underlying acro-osteolysis and calcinosis is therefore needed. Recent cross-sectional studies have reported an association of these digital manifestations with the Cutolo's late capillaroscopic pattern defined by severe capillary loss and proliferative neo-vascularization, supporting a vascular etiology of both acro-osteolysis and calcinosis 2,3. Ultrasonographic (US) evaluation has dramatically improved joint and tendon evaluation in rheumatoid arthritis and other rheumatic diseases. US assessment of the hand is now therefore used in daily practice in many rheumatic disorders. B-mode analysis and power Doppler evaluation are thus widely available. Recent articles have highlighted the relevance of Doppler US evaluation to assess the severity of hand involvement and digital vasculopathy in SSc 4-8. More specifically, these

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articles have supported that US evaluation may help to better characterize macrovascular involvement. Although micro-vessel alterations have been largely described, macrovascular involvement is also frequent in SSc. Macrovascular damages specifically involve narrowing or occlusions of proper palmar digital arteries (PPDA) and ulnar artery 4-7. On the contrary, radial artery is rarely concerned. Ulnar artery occlusion (UAO) assessed by Power Doppler Ultrasonography (PDUS) has proven to be predictive of the onset of new ischemic DUs in two longitudinal studies 4,6. PDUS could also be a reliable tool to evaluate finger pulp blood flow (FPBF) 6,7. Only few studies have explored the association between macrovascular damages evaluated by PDUS and microvascular involvement assessed by NC 9,10. The association between macrovascular disease and calcinosis or acro-osteolysis is still to be determined in SSc. Cutolo and colleagues have recently insisted on the necessity of conducting further surveys evaluating the relevance of macrovascular involvement as a reliable marker of severe vasculopathy in SSc 11.

The aim of this study was to further evaluate the relationship between microvascular damages assessed by NC and macrovascular features evaluated by PDUS of the hand, and to assess the associations of these damages with the main digital manifestations of the disease represented by DUs, acro-osteolysis and Calcinosis.

Methods:

Patients

Between November 2014 and November 2015, 64 unselected consecutive SSc patients referred to the rheumatology unit were included in this observational cross-sectional study. Previous history of DUs was noted using medical records of patients and clinical examination (pitting scars) at inclusion. The diagnosis of SSc was initially based on LeRoy's classification criteria but 93.8% of the patients (n=60) also fulfilled the ACR/EULAR 2013 classification criteria for SSc 12.

The ethics committee of Rennes Hospital approved this observational study (approvals 14.53 and 15.09). The study complied with the recommendations of the Declaration of Helsinki. Informed consent of all patients was obtained prior to investigations.

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PDUS evaluation:

The same trained rheumatologist (GC) (8 years of experience in musculoskeletal and vascular imaging) performed all PDUS evaluations as previously described 6. A standardized US evaluation of FPBF on the third and fourth fingers of both hands was performed after 15 minutes of acclimatization in our US laboratory with an ambient temperature ranging from 19 to 22°C.

Pathologic FPBF was defined objectively as a decrease of doppler signal on the sub-hypodermal part of finger pulp or on the entire finger pulp recorded at least on one of the two evaluated fingers. Ulnar artery blood flow was measured on the wrist using a transversal view of Guyon's canal including the Pisiform bone. UAO was defined as an abolition of blood flow assessed by PDUS. An Allen test was also performed and UAO was confirmed when deep palmar arch showed no PDUS signal when radial artery was temporarily compressed by the examiner. US measurements were performed using the MyLab TM Class C system (Esaote, Florence Italy) equipped with a 6-18 MHz dedicated linear-array probe. Power Doppler settings were standardized (Doppler frequency 10 MHz, Gain 55%, PRF 750 Hz). Kappa coefficients of inter and intra-rater agreements of this method have already been published 6. The investigator performing PDUS evaluation was blinded for the results of NC and X-ray evaluations.

Capillaroscopic evaluation:

NC were performed by the same examiner (AL) at inclusion, with a DermLite dermatoscope (Heine Delta TM 20). Microvascular damages were classified using Cutolo's classification. The number of capillaries per millimetre in the middle finger of the dominant hand was specifically noted. A severe capillary loss was defined by a count of less than 4 capillaries per millimetre. The results of PDUS features with NC analysis were combined to select the patients with a more severe vasculopathy, characterized by an association of both macro and microvascular damages.

X-Ray assessments:

Standard postero-anterior X-rays of both hands were obtained for all patients at inclusion.

Calcinosis was defined by the presence of at least one calcification in soft tissues. Acro-osteolysis was defined as any bone resorption of at least one distal phalanx. The investigator assessing X-ray and NC was also blinded for the results of PDUS evaluations.

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Statistics

Qualitative data associations were analysed conducting Chi-square test or Fisher exact test and expressed with odds ratio (OR) and 95% confidence intervals. Quantitative data were analyzed conducting the unpaired two-tailed student-t-test or Mann and Whitney U test depending on Gaussian distribution. We performed all tests with a significance level of P<0.05. Statistical analysis was performed using SPSS 20.0 software.

Results :

Patient characteristics:

Patient characteristics are summarized in Table 1; 50% of the patients had a history of DU.

Acro-osteolysis and calcinosis were present in respectively 34.4% and 43.8% of patients. Thirty-one patients (48.4%) had UAO and 33 had a pathologic FPBF (51.6%). Association of UAO and pathologic FPBF was present in 24 patients (37.5%). In NC, 17 (26.6%) patients had a normal or early pattern, 22 (34.4%) an active pattern and 25 (39.0%) a late pattern. A severe capillary loss was found in 18 (28.1%) patients.

Calcinosis and acro-osteolysis were both associated with DU history (respectively, OR=3.74 (1.31-10.62); p<0.05 and OR=9.00 (2.55-31.70); p<0.0001) and pitting scars on clinical examination at inclusion (respectively OR=7.3 (2.42-22.67); p<0.0001 and OR=10.88 (3.20-37.00); p<0.0001).

Acro-osteolysis was associated with dSSc (OR=3.38 (1.14-10.01); p<0.05). Acro-osteolysis and UAO were both associated with the presence of skin telangiectasia (respectively; OR=12.92 (1.58-105.59); p<0.01 and OR=12.08 (2.47-59.15); p<0.0001). UAO was not associated with smoking (OR=1.12 (0.05-1.44) p=0.814).

Association between capillaroscopic findings and PDUS features (Table 2):

UAO was significantly associated with the late NC pattern (OR=3.80 (1.31-11.01); p<0.05) and a severe capillary loss (OR=4.04 (1.23-13.29); p<0.05). A normal or early NC pattern tended to be protective from UAO (OR=0.34 (0.10-1.11); p=0.06). A pathologic FPBF was associated with severe capillary loss in NC (OR=3.38 (1.03-11.05) p<0.05) but was not associated with any of the NC patterns.

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.

Associations of NC or PDUS features with the main digital complications of SSc (Table 3):

History of DU and pitting scars were significantly associated with UAO, pathologic FPBF on PDUS evaluation, late pattern and severe capillary loss on NC (Table 3A and3B). On the contrary, normal or early NC patterns tended to be associated with less DU history (OR=0.31 (0.09-1.02); p=0.05). Acro-osteolysis was significantly associated with UAO, pathologic FPBF, late NC pattern and severe capillary loss (Table 3C). Calcinosis were associated with late NC pattern, severe capillary loss and UAO but were not associated with pathologic FPBF (Table 3D).

Combinations of PDUS features with NC findings and their associations with digital complications of SSc (supplementary Table 1):

The combination of UAO and severe capillary loss in a same patient was associated with pitting scars (OR=28.8 (3.43-241.64); p<0.0001), DU history (OR=18.60 (2.24-154.34); p=0.001), acro-osteolysis (OR=10.83 (2.56-45.88); p=0.001) and to a lesser extent with calcinosis (OR=6.11

(1.49-25.08); p=0.007). This combination of UAO on PDUS and severe capillary loss on NC showed higher associations with pitting scars, DU and acro-osteolysis than severe capillary loss on NC evaluation taken alone (Table 3). The combination of UAO, pathologic FPBF and severe capillary loss altogether in a same patient was also associated with pitting scars (OR=24.75 (2.94-208.30);

Discussion :

The results of this cross-sectional study suggest that microvascular damages evaluated by NC and some of the macrovascular features of SSc assessed by PDUS show concordant associations with the main digital manifestations of the disease. The proliferative obliterative vasculopathy characterizing Cutolo's late NC pattern is especially associated with UAO in our study, supporting the hypothesis that micro and macrovascular damages could be linked in SSc. Rosato et al. had previously reported a correlation between macrovascular features in the hands of SSc patients evaluated by PDUS and micro-vessel involvement assessed by laser Doppler perfusion imaging or digital photoplethysmography 9,10. Our cross-sectional study reveals associations of macrovascular damages with DUs but also with other digital manifestations of SSc such as acro-osteolysis and calcinosis, both supposed to be the consequences of microvascular damages 2. We can hypothesize that the same pathogenic pathways may partly support micro and macrovascular involvement,

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however the cross-sectional design of this study limits any conclusions about causality. Only prospective longitudinal studies with long-term follow-up will allow us to draw conclusions regarding any common causal factors of micro and macro-vascular involvement.

Two recent studies have highlighted the associations of calcinosis with digital ischemia and late NC pattern in SSc 2,3. Morardet et al. have also reported an association between acro-osteolysis and late NC pattern 2. Our results are consistent with these data and further support an implication of SSc vasculopathy in the pathogenesis of these digital manifestations of the disease. The association of acro-osteolysis on X-Rays and UAO assessed by PDUS in our study may suggest an involvement of macro-vascular disease in the pathogenesis of acro-osteolysis. However, any direct pathogenic links emerged from our study should be taken cautiously given its cross-sectional design that limits causal conclusions. Acro-osteolysis is associated with a neovascularization and an angiogenesis that remain insufficient to balance chronic ischemia. The reasons why this neo-angiogenesis remains ineffective are still to be determined. We could hypothesize that this endothelial proliferation may contribute to the macrovascular obliterative damages reflected by UAO and could therefore maintain chronic ischemia. In our study, the association of UAO with the presence of skin telangiectasia also supports the hypothesis of a link between macrovascular obliterative damages and neo-angiogenesis.

These results are consistent with other studies considering skin telangiectasia as a marker of severe vascular disease in SSc 13. As suggested by Lüders et al, a further characterization of other macrovessels of the hand such as PPDA would also be relevant to support this hypothesis 5.

Detecting patients with a severe vascular involvement and at higher risk of DU is a major issue in SSc. The combination of macrovascular and microvascular evaluations by PDUS and NC respectively may help to detect patients with a more severe vasculopathy. In our study, combining PDUS and NC results reveals highly significant associations with the main digital manifestations of the disease. The association of both macro and microvascular damages in a same patient might therefore be a relevant marker reflecting the severity of the vasculopathy in SSc. The odds ratios assessing these associations are quite high but with wide confidence interval, highlighting the need for future studies with larger sample size to characterize these associations more precisely. Moreover we have not performed multivariable analyses in this exploratory cross-sectional study, given the small sample size that would have strongly limited the strength and relevance of a multivariable logistic regression model. Therefore even if clinical parameters such as smoking and disease duration were not associated with macrovascular features in univariable analyses, such factors may nonetheless constitute confounding factors that will need to be further studied in multivariable models based on wider SSc populations.

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One of the limitations of our study is the heterogeneity of vasodilator treatments taken by the patients. It was recently reported that Calcium channel blockers (CCB) were inversely associated with calcinosis in a retrospective study including a large number of patients (n=1305) 3. In our study, 65.6% of the patients had CCB at inclusion. This is less than reported in the study by Morardet et al 2; this difference may explain the higher prevalence of calcinosis found in our work as compared to the prevalence reported by Morardet et al. The prevalence of calcinosis in our study is nonetheless consistent with the results of Johnstone et al 14. Treatments may have also influenced PDUS evaluation of FPBF and this could explain some inconsistent associations of pathologic FPBF with digital manifestations of SSc in our study. The small sample size of this single-center study may have also resulted in a lack of power to reveal some other relevant associations. Multi-center studies are warranted to confirm our data, to better characterize the impact of vasodilating therapies on FPBF and to evaluate more precisely the associations of calcinosis or acro-osteolysis with FPBF evaluated by PDUS or by other perfusion assessment tools such as laser Doppler perfusion imaging and laser speckled contrast analysis 10,15.

In a recent study conducted by our group and using the same methodology, Kappa coefficients of inter-rater agreement were 0.94 for the presence of pathologic FPBF and 0.97 for the presence of UAO on PDUS images. Kappa coefficients of intra-rater agreement were 0.90 for the presence of pathologic FPBF and 0.93 for the presence of UAO 6. These results are close to the performances of other assessment tools of peripheral blood perfusion such as laser speckle contrast analysis 15. Macro-vascular evaluation using these PDUS parameters thus seems to be reproducible.

As PDUS is a widely available non-invasive tool, used in daily practice by an increasing number of rheumatologists, it may therefore prove to be relevant to detect patients with a more severe vasculopathy in daily practice 4-6. Recent clinical trials, evaluating therapeutic measures supposed to prevent new DU occurrence have failed to reach their primary outcome 16,17. Therefore, both macro and microvascular evaluations of the hand may help to better identify patients at high risk of DUs for future studies evaluating DU prevention strategies in SSc.

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  p<0.0001), DU history (OR=16.24 (1.95-135.38); p=0.001) and to a lesser extent with acro-osteolysis (OR=9.00 (2.11-38.35); p=0.002) and calcinosis (5.21 (1.25-21.63); p=0.015); (other combinations shown in supplementary data available at Arthritis Care & Research online).

Table 1 .

 1 Demographic and clinical characteristics at inclusion

	Patients characteristics at inclusion (%/ SD)	SSc (n=64)
	Demographics
	Female	47 (73.4)
	Mean age at inclusion, years (SD)	58.6 (11.5)
	Clinical characteristics
	Fulfilling ACR 2013 SSc classification criteria	60 (93.8)
	Disease form
	lSSc	41 (64.1)
	dSSc	23 (35.9)
	Mean disease duration since first non-RP symptom, years	7.4 (8.8)
	(SD)
	Mean modified Rodnan Skin Score (SD)	8.7 (8.0)
	Telengiectasia	47 (73.4)
	Puffy fingers	18 (28.1)
	Antibodies
	ACA	30 (46.9)
	ATA	17 (26.6)
	ARNAPIII	4 (6.3)
	Other	13 (20.3)
	DU Characteristics
	DU History	32 (50.0)
	Multiple episodes of DU	21 (32.8)
	Ischemic DU	27 (42.2)
	Calcinosis related DU	8 (12.5)
	Pitting scars	27 (42,2)
	X-ray Features
	Acro-osteolysis	22 (34.4)
	Calcinosis	28 (43.8)
	PDUS Features
	UAO	31 (48.4)
	bilateral	21 (32.8)
	Pathologic FPBF	33 (51.6)
	bilateral	27 (42.2)
	Association of UAO and Pathologic FPBF	24 (37.5)
	Capillaroscopic Features
	Normal or early pattern	17 (26.6)
	Active pattern	22 (34.4)
	Late pattern	25 (39.0)

Table 2 :

 2 Association between capillaroscopic patterns and PDUS features (n=64) A. Association of Capillaroscopic patterns with Ulnar Artery Occlusion

	Ulnar Artery Occlusion
	OR (95%CI)	p

Table 3 :

 3 Association between NC or PDUS features and main clinical manifestations involving hand in 64 SSc.A. Association of capillaroscopic or PDUS features with DU history . Association of capillaroscopic or PDUS features with Acro-osteolysis on X-Ray

	DU history
	OR (95%CI)	p

C

Khanna D, Denton CP, Merkel PA, Krieg T, Le Brun FO, Marr Aet al. Effect of Macitentan on the Development of New Ischemic Digital Ulcers in Patients With Systemic Sclerosis: DUAL-1 and DUAL-2 Randomized Clinical Trials. JAMA. 2016 May 10;315(18):1975-88.

Acknowledgments:

The authors gratefully acknowledge all patients and investigators involved in this study. The authors also thank Dr M. Sebillot, Dr J.D. Albert and Dr A. Rouil for their comments.

This work was not supported by any funding agency. , M de Carlan, A Perdriger report no conflict of interest. P Jégo received speaking fees from Actelion Pharmaceuticals

Accepted Article


Andre Luiz Appel
email: alappel@gmail.com

Ivonne Lujano
email: ivonne.lujano@gmail.com

Sarita Albagli
email: sarita.albagli@gmail.com

Open Science Practices Adopted by Latin American & Caribbean Open Access Journals

Keywords: open access, open science, open access journals, Latin America and the Caribbean, Directory

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

This study is part of a research which aims to investigate to what extent and how open science (OS) values and practices have influenced open access (OA) journals publishers. It focuses on Latin American and the Caribbean countries (LA&C), considering that this region has adopted OA as the main scholarly publishing model since the late 1990s due the fact that their scientific research and scholarly communication infrastructures are mainly publicly funded.

For this study, we selected a set of OS values and practices based on a previous work on scientific journals [START_REF] Appel | Open scientific journals: Emerging practices and approaches[END_REF], as well as on an update of the literature review. They include the adoption of: alternative metrics for measuring journals' influence and diffusion, open peer-review, open research data, Creative Commons licenses, articles' full-text in machine-readable formats, and emerging OA business models. Considering this scenario, this research aims to contribute to answer the following question: to what extent are these practices being adopted by LA&C journals?

In order to get an overview of the opinions of LA&C journals publishers about the aforementioned issue, we conducted a survey with a sample of LA&C journals selected from the Directory of Open Access Journals (DOAJ) database. The design and methodology to select this sample and to carry out the survey are described in the section Design and Methodology of this paper. The results reveal that many journals are somewhat aware of 7 Some initiatives are responsible for "translating" and systematising OS principles and practices to journal's editorial standards and policies. The most significant we can point out, at the moment, are the works of DOAJ, which establishes a criteria range to define OA journals [START_REF] Olijhoek | Criteria for Open Access and publishing[END_REF]-which include many concepts and values being advocated as open science-and the work of [START_REF] Björk | Opening academic publishing: Development and application of systematic evaluation criteria[END_REF] for the Open Science and Research Initiative in Finland.

8

DOAJ is the largest database of fully OA scientific journals. On the date the DOAJ database was consulted for this study (11 January 2018) it registered 10,845 records of OA published journals in 123 countries. Each record in DOAJ provides basic information about the journal and its editorial process, content licensing and copyright policy. The current criteria for indexing journals in DOAJ were established in 2013 following the Principles of Transparency and Best Practice in Scholarly Publishing, which is a list of recommendations provided by DOAJ in collaboration with the Committee on Publication Ethics (COPE), the Open Access Scholarly Publishers Association (OASPA), and the World Association of Medical Editors (WAME) [START_REF] Olijhoek | Criteria for Open Access and publishing[END_REF]. This list 3 includes some criteria related to open science principles, such as the need for adoption of Creative Commons Licenses, depositing and copyright policies, the promotion of machine readable full-text formats for publication (such as HTML and XML), voluntary adoption of open peer-review among others.

9

The work of [START_REF] Björk | Opening academic publishing: Development and application of systematic evaluation criteria[END_REF] is aimed at the construction of an "applicable scorecard that can provide a tool for standardized systematic evaluation, and benchmarking of the openness of academic publishers". The study focused on criteria such as fraction of OA journals among total publication output, costs, use of CC-licensing, self-archiving policies, text and data mining (TDM), openness of citation data, and accessibility of information relating to OA practices. Within the results, the authors present the outcomes from the evaluation of nine "big publishers" under the proposed scorecard.

It is also worth to mention the initiative from the Scholarly Publishing and Academic Resources Coalition (SPARC) named Open Access Spectrum Evaluation Tool 4 (OAS). which is aimed at ranking journals according to degrees of openness, considering criteria such as reader rights, reuse rights, copyrights, author posting rights, automatic posting, and machine readability. To the moment, OAS lists 1,022 journals with their respective score.

OA and OS in LA&C

In this section, we briefly describe some proposed and ongoing open science and open access initiatives and policies developed in six LA&C countries, which have played a significant role in this area.

Brazil pioneered the OA journals landscape with the launching of the Scientific Electronic Library Online 5 (SciELO) in 1997. SciELO started as a platform aggregating 275 OA journals and today counts with 1.285 OA journals. Its methodology and infrastructure support fifteen LA&C countries along with Portugal, Spain, and South Africa. Since 2000, the Brazilian Institute of Information in Science and Technology (Ibict) led a strong open access movement, providing capacity building and infrastructure for this purpose. At the regulatory level, some Brazilian legislators with the support of the academic community and research institutes, proposed two bills to the House of Representatives-to the Congress in 2007 and to the Senate in 2011-demanding the deposit of all research outputs resulting from public funding in institutional repositories. The first bill was archived, and the latter one was rejected in 2015 due to unconstitutionality, for interfering in university autonomy granted by Brazilian legislation. In 2014, Ibict organised an international seminar that brought together a representative group of In Argentina, in 2013 the Congress passed a law 6 , requiring that the outcomes of public funded research must be freely available in open access institutional repositories. Also in Argentina, Fressoli & Arza (2017) and Arza & Fressoli (2017) worked on the characterization and documentation of OS projects and initiatives in terms of a bidimensional framework to identify and measure degrees of access and collaboration.

In 2013, Peru passed the Act No. 30035 7 that regulates the National Digital Repository for Open Access Science, Technology and Innovation. This Act establishes that the National Council of Science, Technology and Technological Innovation (Concytec) is responsible for implementing, integrating, standardizing, storing, preserving and managing the national repository that gathers the scientific production publicly funded, or private entities that wish to share their information in open access.

Colombia established the National System of Open Access to Knowledge (SNAAC) in 2015, which is an initiative promoted by the Ministry of Education, the Administrative Department of Science, Technology and Innovation (Colciencias), universities, the National Academic Network of Advanced Technology (RENATA), and other stakeholders. Its objective is "to promote and strengthen the conditions and capacities for the production, articulation, organization, visibility, promotion of the use and visibility of Colombian scientific production in open access." Institutions wishing to join this initiative provide information on their repositories on the SNAAC website.

In 2014, the Mexican Congress approved amendments in the Science and Technology legislation, the General Education legislation, and the Organic Law of the National Council for Science and Technology to introduce open access requirements and the development of the national repository 8 . Mexico launched, in 2017, an open science policy 9 that includes a classification system for open access journals along with a set of OS guidelines aiming to subsidize policies, resources, and initiatives of the National Council of Science and Technology (Conacyt) in this field. It represents a precedent towards OS policy design in the region. Mexico also hosts two important databases for regional journals indexing, namely RedAlyc 10 and Latindex 11 . Besides indexation, these databases are also responsible for promoting "best practices" for the adoption of quality standards by scientific journals in the region (Alperin & Fischman, 2015).

In Chile, the initiative Datos Científicos 12 (Scientific Data) has been conducted by the National Commission of Scientific and Technological Research (Conicyt), requiring that all data derived from research funded by Conicyt must be deposited in open repositories in adequate formats. The website of the initiative also presents complementary guidelines as well as FAQ and best practice sections related to open data publication. Chile is also the hosting country of LA Referencia 13 , a Latin American federated network of OA repositories, currently aggregating nearly a million and a half of full-text open access publications from nine countries as national nodes.

In the beginning of 2018, four LA&C institutions (Clacso, Ibict, Latindex, and Redalyc) signed a joint declaration 14 reinforcing the importance of the adoption of the CC BY-NC-SA license by LA&C journals and repositories in order to promote the open access to scientific production in the region, as well to guarantee its protection from commercial exploitation and appropriation. This declaration constitutes a political statement and a general guideline regarding licensing practices in the region. Nevertheless, it conflicts with the prevailing view in the international open science movement that recommends the adoption of CC BY. CC BY-NC-SA is one of the most rectrict model of CC licensing, requiring attributing the work in the manner specified by the author or licensor (BY), with non-commercial purposes (NC), and under the same license specified by the author or licensor (SA) while CC BY, the most open, only requires attributing the work in the manner specified by the author or licensor.

Design and Methodology

The identification of 19LA&C countries was based on information from UNESCO website 15 . We extracted data from the complete DOAJ database about open access journals located in LA&C countries, resulting in a list of 2,010 journals distributed in 19 countries. Subsequently, we removed journals not validated by DOAJ after 2014 16 , which resulted in a list of 1,990 journals, corresponding to our research universe (N). The next sampling stage involved the selection of a simple random sample (confidence interval = 95%, margin of error = 5%), resulting in a list of 322 journals (n = 322). We then distributed this sample proportionally to each of the 19 countries, according to the proportions given by the universe of journals, finally reaching a sample of 322 periodicals distributed in 14 LA&C countries.

To send the questionnaires, we have collected the email addresses of those responsible for each journal, directly on each journal's website. The questionnaire was developed and distributed in Google Forms platform and has been made available for completion between March 13 and 20, 2018. This short timespan provided for completion resulted from unforeseen changes on the survey methodology, which has shortened our study schedule. At the end of the deadline, we received a total of 55 responses, corresponding to 17% of our sample. Although this result can not be considered sufficiently representative, due to a high margin of error resulting from the estimated level of confidence, it allows observations that may help to understand the LA&C scholarly journals' attitudes towards OA and OS new demands. It is also worth to take into consideration the occurence of participation bias due to the fact that the journals that answered the questionnaire may be more knowledgeable or interested about the topic in question.

Results and Discussion

Research results are organised and presented in two main groups. The first group (Table 1) comprises general data on and characterization of selected journals. Data on the levels of knowledge about OS practices and the willingness to adopt them are represented in Figure 1 and are discussed afterwards. Other data are not represented graphically, such as:

a. the organizational nature of selected journals' publishers, being 73% institutional, 23% scientific societies or research institutes, only 1 commercial and 1 non-governmental organisation (NGO); b. the funding sources, being 85% institutional funding, 9% article processing charges, and 4% grants.

Table 1. General characteristics of selected journals. Source: Survey data. Source: Survey data 22 According to the DOAJ database, most of the Latin American journals have adopted blind peer-review process. On the other hand, 71% of our respondents stated to be highly informed about open peer review (OPR). It is important to highlight that 35% (19) of the surveyed journals affirmed that they have already adopted some kind of OPR and other 35% affirmed that it is fairly likely that they will adopt this type of peer review system in the future. Most of the journals (78%) that have adopted OPR belong to Arts & Humanities and Social Sciences fields, which shows that among Natural Sciences, Engineering and Technology, Medicine and Life Sciences & Agriculture and Veterinary disciplines the traditional blind peer-review system is still the prefered system. On the other hand, 15% of the surveyed journals indicated that adopting OPR would be unlikely. One of the reasons presented for the avoidance of this practice refers to a possible decrease in the amount of reviewers, since most of them would not be willing to disclose their reviews.

Dimensions

Another justification presented reveals that editors are more willing to adopt OPR after its "consolidation", since its early adoption would impose "adverse repercussions". A third given reason refers to "the weakness of academic respect" on a literal translation, which could be understood as the possible violation of the "academic etiquette" in commentary or review sections. These survey results show that OPR is not yet considered a reliable system by journals in LA&C. OPR must be analysed in further and more comprehensive studies, since it involves not only editors but also the authors and reviewers. have adopted it. In Latin America, the adoption of CC licenses has been advocated by some of the main OA promoters. SciELO, for instance, adopted the most open license (CC BY) in 2015, by emphasizing its advantages in allowing unrestricted information reuse as well as in maximising the dissemination of research results [START_REF] Santos | SciELO adopts CC-BY as main Open Access attribution[END_REF]. However, only 30% of journals surveyed for this study have already adopted CC BY. On the other hand, 25% of them have adopt CC BY-NC-ND, 16% CC BY-NC, and 14% CC BY-NC-SA.

In other words, the majority of journals surveyed are seeking to prevent the reuse of scholarly information for commercial purposes, and this does not vary across the disciplines. There is an ongoing debate on which licensing model should be the most appropriate for the LA&C OA context. Different LA&C organizations in the field of science and technology-including Redalyc, Latindex, CLACSO (Latin American Council of Social Sciences), and Ibict-are advocating the adoption of CC BY-NC-SA license not only for journals but also for "courses, workshops, conferences, videoconferences and in any type of communication or academic material" in order to "protect the OA ecosystem" ("Declaración de México a Favor del Ecosistema Latinoamericano de Acceso Abierto no Comercial", 2018). On the other hand, this statement is contradictory to the major orientation of the open science movement, which encourages the adoption of CC BY in order to maximize information reuse regardless the commercial purpose. It is important to highlight that, to the moment, most of the conceptions about those licenses are based on the assumptions of their advocates, reflecting the strong opposition to the copyrights model, with little or no evidence of their implications or impact. This calls for the realization of in-depth studies about authors, publishers, and readers' opinions on this issue.

25 Regarding the practice of altmetrics (ALM), most of the respondents indicated low and moderate levels of awareness of this practice (82%). However, the survey also reveals that a large number of journals are very interested in adopting altmetrics (35%). The percentage of journals that already provide altmetrics is very low (9%) and, combined with the low level of awareness of the practice, it is contradictory to the fact that most of the surveyed journals use the OJS platform (75%), considering such platform allows at least the dissemination of article-level metrics with a combination of plugins. We did not observe significant differences in the levels of awareness between the different fields of knowledge. Regarding implementation difficulties, many surveyed journals mentioned

Open Science Practices Adopted by Latin American & Caribbean Open Access Jour...

ELPUB 2018

cost as a barrier. This factor, combined with the low levels of awareness and the low levels of adoption, may be related to the fact that editors still associate the practice of altmetrics exclusively with the service provided by the Altmetric.com 17 platformspecialised in measuring the diffusion of articles in social media-while altmetrics is also related to the promotion of article-level metrics, such as number of views and downloads of articles etc., which would be more easily adoptable and manageable by the editors themselves. Other difficulties mentioned relate to the lack of awareness and to technical barriers, which may also refer to cost.

As for the practice of providing articles' full-texts in machine-readable formats (MRFT), the surveyed journals indicated a high level of awareness of it (64%), which also corresponds to its level of adoption (65%). In addition, among the journals that have not yet adopted this practice, our survey also reveals the great interest in future adoption.

The fields of Natural Sciences, Engineering, Agriculture and Veterinary, and Medicine (STEM) combined demonstrated high levels of awareness (78% on average). On the other hand, more than half Humanities and Social Sciences journals (56%) also indicated a high level of awareness of the practice. The surveyed journals also pointed out the MRFT complexity and the lack of time and technical support as difficulties for its adoption.

Regarding open research data (ORD), half of the respondents indicated high level of awareness of it, while the other half is virtually divided between the moderate and low levels of awareness. The potential for the adoption of this practice is significantly high: 20% of selected journals have already implemented it, 38% indicated a high possibility of its adoption, and 29% indicated a moderate interest in adopting it. Only 5% indicated that they would not adopt such practice. Regarding the association of this practice with fields of knowledge, Medicine, Life and Natural Sciences have the lowest number of surveyed journals unaware of opening research data (6%), while journals in Arts, Humanities and Social Sciences are divided in levels of awareness (high, moderate, low). Regarding the difficulties or issues impeding the adoption of this practice, the justification of one of the journal's editors encompasses the (ethical) risk of disclosure of low quality material (texts and data) due to the lack of a previous filter performed by reviewers througouth doubleblind review. Other editors pointed out that the practice of opening research data is not directly related to the fields of knowledge of their journals, but it is mainly due to the rare production of quantitative research in the field, which, in turn, results in a low volume of data to be openly disclosed.

Conclusion

With the conclusion of this study, we highlight that the question we have initially posed could be, to some extent, answered. Based on the research results, it is possible to emphasize that journals in LA&C are somewhat aware of, or informed about, most of open science practices being discussed, and some of those journals have already even successfully implemented some practice.

Regarding the decision-making process about the adoption of the practices in question, it is possible to reassure the predominantly institutional nature of the journals in LA&C, a condition that encourage journals to avoid the possibility of "outsourcing" their core processes. However, this characteristic would also pose as a barrier to the development or adoption of new practices, since institutions could not always be prepared to provide the necessary support for publishing activities, resulting in barriers of cost, time, technical support among others.

On the other hand, the implementation of APC as a guarantee of self-funding is not considered by journal publishers in LA&C either, since this practice is seen in the region as a barrier to authors and, consequently, impacting the free and open dissemination of knowledge. Hence the funding model based on the distribution of grants for journals would emerge as an alternative. The results, otherwise, indicate that the number of journals which benefits of such type of fund is still very small. By increasing funds for this type of expenditure and by serving a larger and more diverse universe of journals seem to be most suitable route to avoid the proliferation of APC, to attenuate institutional dependency, and to encourage journals' development. BIBLIOGRAPHY

  foreign and local OS and OA experts and advocates, addressing topics such as open data, open hardware, academic open source software, citizen science and open notebook science.

Figure 1 .

 1 Figure 1. Levels of knowledge about and willingness to adopt Open Science practices by LA&C journals (n = 55).

  a) Levels of awareness; (b) Possibility of adoption; NA: No answer; ALM: Altmetrics; OPR: Open Peer Review; ORD: Open Research Data; CC: Creative Commons; MRFT: Machine Readable Full-Text; APC: Article Processing Charges.

  It is also possible to observe that the practices are perceived or impacted differently according to different disciplines. Concerning open research data, e.g, the different needs of each discipline should be taken into account by institutions or funding agencies during the definition of open data policies. Certain disciplines do not require the development of extensive mandatory policies by their journals, however, brief guidelines and referrals to data repositories would address specific cases related to quantitative research.The study left some questions open for future exploration, such as:a. what are the corresponding decision-making processes of scientific publishers? b. are there any public policies in LA&C currently supporting the adoption of these practices? Also, one of the key questions still open concerns the possible positive and negative impacts arising from the adoption of OS practices. This will possibly lead to a more qualitative study.

With respect to the adoption of Creative Commons (CC) for content licensing, 82% of the surveyed journals stated high level of awareness of this practice. In fact, 95% of them

Only 33% of surveyed journals showed to be highly informed about article processing charges (APC), which could be justified by the fact that the predominant funding model for open access journals in LA&C is based on public and/or institutional resources. 65% of the respondents pointed out that it is unlikely that this practice will be adopted. However, 13% of the journals surveyed have already implemented APCs. The fields of knowledge of these journals are predominantly Medicine, Life and Natural Sciences as well as Agriculture and Veterinary. In contrast, 70% of respondents that stated that APC is unlikely to be adopted are from journals in Arts, Humanities and Social Sciences. Some of the comments received on why they will not likely charge authors are justified by ethical reasons. For instance, a respondent stated that given the precariousness of academic activity in Latin America, collecting fees from authors would create a divide between those who have conditions to bear these costs and those who do not. Another respondent mentioned that, arguing in consistency with the OA movement and in favour of the wide dissemination of LA&C scientific outputs, it is very unlikely for journals to charge authors any type of fee.

This work was partially funded by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES), Brasil-Bolsa de Doutorado Demanda Social (DS). We also thank the significant contributions of the reviewers.

Open Science Practices Adopted by Latin American & Caribbean Open Access Jour...

ABSTRACTS

The objective of this study is to investigate how Open Science (OS) values and practices have influenced open access (OA) journals publishers in Latin American and the Caribbean (LA&C) countries. Our key research question is: to what extent are these practices being adopted by LA&C journals? In order to address this question, we conducted a survey with a sample of LA&C journals listed on the Directory of Open Access Journals (DOAJ) database. The results reveal that many journals are somewhat aware of or informed about most of open science practices being discussed, but just some of them have already successfully adopted those practices.


Ulysse Gérard

Dale Miller

Functional programming with λ -tree syntax: a progress report

In this progress report, we highlight the design of the functional programming language MLTS which we have recently proposed elsewhere. This language uses the λ -tree syntax approach to encoding data structures that contain bindings. In this setting, bound variables never become free nor escape their scope: instead, binders in data structures are permitted to move into binding sites within programs. The concrete syntax of MLTS is based on the one for OCaml but includes additional binders within programs that directly support the mobility of bindings. The natural semantics of MLTS can be viewed as a logical theory within the logic G , which forms the basis of the Abella proof system and which includes nominal abstractions and the ∇-quantifier. Here, we provide several examples of MLTS programs. We also illustrate how many Abella relational specifications that are known to specify functions can be rewritten as functions in MLTS.

Introduction

The λ -tree syntax approach to encoding data structures that contain binders (which includes a wide range of syntactic expressions) has been successfully used in a wide range of specifications, programs, and reasoning systems. Most of these systems, however, are based on logic programming or, more generally, the proof search paradigms. One exception to that trend is Beluga [START_REF] Pientka | Beluga: A Framework for Programming and Reasoning with Deductive Systems (System Description)[END_REF], a functional programming language that is based on contextual modal logic [START_REF] Nanevski | Contextual Model Type Theory[END_REF]. Beluga provides first-class treatments for not only bindings but also contexts: the latter play important roles in mechanizing reasoning involving, for example, type systems.

In this progress report, we report on a recently designed functional programming language we call MLTS. With this language, we attempt a modest goal: can we extend an ML-like functional programming language in order to allow a first-class treatment to data structures containing bindings? We are focused on the specification of computation in a traditional sense: the concerns of supporting deduction (mechanized metatheory) are not an immediate goal. As a result, we have not attempted to build into this language some specific notion of context. For us, one criterion of a successful design would be that programs written on data structures without binding should be seen as programs in the original, non-extended programming language.

Accompanying this progress report is the TryMLTS website [START_REF] Gérard | TryMLTS[END_REF] which contains the following: a full length draft report [START_REF] Gérard | Functional programming with λ -tree syntax: Draft[END_REF] that describes MLTS in more detail, the full sources (λ Prolog, OCaml, JavaScript) as a git repository, and a web-browser-based environment in which one can create and execute MLTS programs online without needing to install any software. In our overview of MLTS, we repeat some of the material from [START_REF] Gérard | Functional programming with λ -tree syntax: Draft[END_REF] in sections 2 and 3

Design principles and new features

The programming language MLTS extends (the core of) the OCaml programming language with a treatment of the λ -tree syntax approach to encoding data structures containing binders [START_REF] Miller | Programming with Higher-Order Logic[END_REF]. Briefly, the λ -tree syntax approach to bindings involves the following three tenets: [START_REF]The Abella Prover[END_REF] Syntax is encoded as untyped λ -terms (although simple types can be used, for example, to distinguish different syntactic categories).

(2) Equality of syntax must include α, β 0 , and η conversion. 1 (3) Bound variables never become free: instead, their binding scope can move. This latter tenet introduces the most characteristic aspect of λ -tree syntax which is often called binder mobility [START_REF] Miller | Bindings, mobility of bindings, and the ∇-quantifier[END_REF]. MLTS is, in fact, an acronym for mobility and λ -tree syntax. (We do not use the term higher-order abstract syntax since the literature of functional programming and constructive type theory has used that term to also refer to the mapping of binding structures into function spaces [START_REF] Chlipala | Parametric higher-order abstract syntax for mechanized semantics[END_REF][START_REF] Despeyroux | Higher-order abstract syntax in Coq[END_REF][START_REF] Hofmann | Semantical analysis of higher-order abstract syntax[END_REF], which is a completely different approach to what we do here.) Note that the intent of the first tenet mentioned above is to de-emphasize typing in the core notion of λ -tree syntax: doing so allows it to be adapted to many different typing disciplines.

Our strategy for strengthening the expressiveness of ML-style languages has been to add to the language more binding sites to which bindings can move: in fact, MLTS contains three new binders to support the mobility needed for λ -tree syntax. In particular, MLTS has a syntax similar to that of OCaml [18] except that we add to OCaml the following four new features.

1. Datatypes can be extended to contain new nominal constants and the (new X in body) program phrase provides a binding that declares that the nominal X is new within the lexical scope given by body.

2. The backslash (\ as an infix symbol that associates to the right) is used to form an abstraction of a nominal over its scope. For example, (X\body) is a syntactic expression that hides the nominal X in the scope body. Thus the backslash introduces an abstraction. The @, conversely, eliminates an abstraction: for example, the expression ((X\body) @ Y) denotes the result of substituting the abstracted nominal X with the nominal Y in body. Expressions involving @ are restricted to be of the form (m @ X1 ... Xj) where m is a pattern (match) variable and X1, . . ., Xj are nominals bound within the scope of the pattern binding on m.

3. A new typing constructor => is used to type bindings within term structures. This constructor is in addition to the already familiar constructor -> used for typing functional expressions.

4. Rules within match-expressions can also contain the (nab X in rule) binder: in the scope of this binder, the symbol X can match existing nominals introduced by the new binder and the \ operator. Note that X is bound over the entire rule (including both the left and right-side of the rule).

All three bindings expressions-(X\body), (new X in body) and (nab X in rule)-are subject to alphabetic renaming of bound variables, just as the names of variables bound in let declarations and function definitions. Since nominals are best thought of as constructors, we follow the OCaml convention of capitalizing their names. We are assuming that in all parts of MLTS, the names of nominals (of bound variables in general) are not available to programs since α-conversion (the alphabetic change of bound variables) is always applicable. Thus, compilers are free to implement nominals in any number of ways, even ways in which they do not have, say, print names.

let rec size term = match term with | App (n , m ) -> 1 + ( size n ) + ( size m ) | Abs ( r ) -> 1 + ( new X in size ( r @ X ) ) | nab X in X -> 1;; size ( Abs ( X \ ( Abs ( Y \ ( App (X , Y ) ) ) ) ) ) ;; 1 + new X in ( size ( Abs ( Y \ ( App (X , Y ) ) ) ) ) ;; 1 + new X in 1 + new Y in ( size ( App (X , Y ) ) ) ;; 1 + new X in 1 + new Y in 1 + ( size X ) + ( size Y ) ;; 1 + new X in 1 + new Y in 1 + 1 + 1;; Figure 1: An MLTS program
for computing the size of untyped λ -terms along with a series of expressions that presents the naive computation that the size of a particular λ -term is 5.

The restriction on the structure of expressions of the form (m @ X1 ... Xj) are essentially the same as those required by pattern unification (a.k.a. L λ -unification) [START_REF] Miller | A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification[END_REF]: as a result, pattern matching in this setting is a simple generalization of usual first-order matching. Given the η-rule, if r is of => type, the expressions r and (X\ r @ X) are interchangeable.

Some MLTS example programs

We now present several examples of MLTS programs in this section. All of these examples are available via the website [START_REF] Gérard | TryMLTS[END_REF].

Untyped λ -terms can be defined in MLTS as the following datatype: The use of the => type constructor here indicates that the argument of Abs is an abstraction of a tm over a tm. Just as the type tm denotes a syntactic category of untyped λ -terms, the type tm => tm denotes the syntactic category of terms abstracted over such terms. The MLTS program in Figure 1 computes the size of an untyped λ -term and shows a sequence of rewritings that provides a naive model of how that function computes. For example, the expression (size (Abs(X\ (Abs(Y\ App(X, Y))))) evaluates to 5 (see Figure 1). In the second match rule in the definition of size, the match-variable r is bound to an expression built using the backslash. On the right of that rule, r is applied to a single argument which is a newly provided constructor of type tm. The first call to size will bind the pattern variable r to (X\ (Abs (Y\ (App(X,Y))))). The third match rule contains the nab binder that allows the token X to match any nominal. Note that in the evaluation (rewriting) steps denoting a size computation, no bound variable actually becomes free: instead, the binding within Abs-terms move to the binding in new expressions.

As a second example, consider a program that returns the boolean true if and only if its argument is a λ -abstraction for which the bound variable is vacuous in its scope; otherwise, it returns false. Figure 2 contains three implementations of this boolean-valued function. Note that, in the implementation of vacp2, once the outermost match rule determines that the argument is a λ -abstraction, a new nominal is created and used to play the role of the λ -abstracted variable. The internal aux function is then defined to search the body of that λ -abstraction for that new nominal. The third implementation, vacp3, is not (overtly) recursive since the entire effort of checking for the vacuous binding can be done during pattern matching. The first match rule of this third implementation is essentially asking the question: is there an instantiation for the (pattern) variable s so that the equation Abs(λ x.s) equals t? This question can be posed as asking if the logical formula ∃s.(Abs(λ x.s)) = t can be proved. In this latter form, it should be clear that since substitution is intended as a logical operation, the result of substituting for s never allows for variable capture. Hence, every instance of the existential quantifier yields an equation with a left-hand side that is a vacuous abstraction. For this kind of pattern matching to work as described, determining this match requires a recursive analysis of the term t. Of course, if one feels that pattern matching must execute in time independent of the terms being matched, then this use of a pattern variable could easily be made illegal (just as repeated pattern variables are made illegal in most pattern matching mechanisms).

let rec vacp1 t = match t with | Abs ( X \ X ) -> false | nab Y in Abs ( X \ Y ) -> true | Abs ( X \ App ( m @ X , n @ X ) ) -> ( vacp1 ( Abs m ) ) && ( vacp1 ( Abs n ) ) | Abs ( X \ Abs ( Y \ r @ X Y ) ) -> new Y in vacp1 ( Abs ( X \ r @ X Y ) ) | t -> false ;; let vacp2 t = match t with | Abs ( r ) -> new X in let rec aux term = match term with | X -> false | nab Y in Y -> true | App (m , n ) -> ( aux m ) && ( aux n ) | Abs ( u ) -> new Y in aux ( u @ Y ) in aux ( r @ X ) | t -
For the third and final example of this section, consider the simple and direct implementation of

let rec subst t x u = match (t , x ) with | nab X in (X , X ) -> u | nab X Y in (Y , X ) -> Y | ( App (m , n ) , x ) -> App ( subst m x u , subst n x u ) | ( Abs r , x ) -> Abs ( Y \ subst ( r @ Y ) x u )
Figure 3: An implementation of (capture-avoiding) substitution: subst t x u returns the result of replacing the nominal x in t with u.

substitution given in Figure 3. There are at least two features of this definition that are worth noting. First, the order of the clauses can be changed without affecting the function's computation. For example, a successful match using the second clause necessarily implies that X and Y are different nominals: thus, there is no overlap between the first and second clause. Second, this substitution is capture-avoiding because the MLTS rewriting mechanism is capture-avoiding: in particular, the binding on Y cannot capture any nominals that may appear in the argument u. Such rewriting is always possible since αconversion is available and the choice of Y can be picked to avoid all nominals in u.

4 Formal specifications of typing and natural semantic evaluation MLTS programs can be given types in much the same way as other ML-like programming languages are given types. As one expects, λ Prolog provides a simple implementation of type inference and type checking for MLTS programs. An actual λ Prolog implementation for type inference is about 50 lines of code (although it does not currently capture full let-polymorphism).

Typing is not used during evaluation but typing is an invariant of evaluation (as is usual for ML-style programming languages). A different kind of typing is, however, important to evaluation. In particular, we need to be able to distinguish between a syntactic category (say, denoting program expressions) and an abstraction of one such category over another. For this we adopt the notion of arity types from Martin-Löf [START_REF] Nordstrom | Programming in Martin-Löf's type theory : an introduction[END_REF]. Essentially, the backslash binder allows to raise the arity of an object by one. Conversely, the Abs constructor from Section 3 expects to be applied to an argument that has arity 1 and it returns an expression that is arity 0. If an MLTS program does not manipulate any data structures containing bindings, then all pattern variables in such programs will all have arity 0. Observe that this remains true even for higher-order programs such as map, foldr, etc: thus, expressions that have higher-order types (using ->) can still be of arity 0.

The natural semantic specification of MLTS evaluation [START_REF] Gérard | Functional programming with λ -tree syntax: Draft[END_REF] can be given as a small set of clauses within the G logic [START_REF] Gacek | Nominal abstraction[END_REF]. The nab and the new bindings correspond naturally to nominal abstraction and to the ∇-quantifier, both of which are available in G . Since λ Prolog does not contain any feature that corresponds to nab, our prototype implementation of natural semantics in λ Prolog was a bit more involved and is about 250 lines of code. The λ Prolog implementations of type inference and evaluation are both available from the website [START_REF] Gérard | TryMLTS[END_REF].

Similarities with Abella

It is often the case that a relation specified in, say, Prolog or λ Prolog, encodes a function. In the paper [START_REF] Gérard | Separating Functional Computation from Relations[END_REF], the authors used focusing to describe how functional computations can be performed using relational specification when those relational specifications are known to compute functions. A different question to consider in this setting, however, is: can we transform the syntax of a relational specification of a function and produce a functional program of that encoded function? For example, one can imagine transforming the usual Prolog [START_REF] Clocksin | Programming in Prolog[END_REF] append relation into a, say, OCaml function for computing the appending of two input lists. A possible additional ingredient to such a transformation might also be a formal proof that the append relational specification actually determines a function when we view the first two arguments as inputs and the third argument as output. We shall not attempt to formalize such a transformation here. Instead we consider how a naive approach to transforming, say, Prolog to OCaml might be extended in order to transform some Abella [START_REF]The Abella Prover[END_REF][START_REF] Baelde | Abella: A System for Reasoning about Relational Specifications[END_REF] specification to MLTS. For the examples below, we make the arbitrary assumption that if a relation is actually a function, it is the last argument of the relation that depends on the other arguments as inputs.

Figure 4 presents Abella relational specifications that correspond closely to functional specifications we have presented in Section 3. Whatever informal understanding one might have of transforming Prolog to OCaml, it seems that the following two observations can be added. If the Abella specification contains nabla-in-the-head, then the corresponding clause in the MLTS program contains a nab binder. If the Abella specification contains a nabla in the body of a clause, then the corresponding clause in the MLTS program contains either a new binder or an explicit λ -binder (the backslash).

Although details of pattern matching and the treatment of auxiliary definitions are different between Abella and functional programming, there are a number of similarities. We offer these similarities in part as a way to help motivate the particular choices used in the design of MLTS.

We have left one MLTS program in Section 3 without a corresponding specification in Abella, namely, the vacp3 function. The most natural Abella specification corresponding to that function would be the following. The relation defined here does not, in fact, encode a function since the first two clauses overlap. For example, it is possible to prove that this vacp3 relation is multi-valued. It seems the only way to specify the boolean valued function for determining vacuousness is via a recursion over syntax.

Conclusion and future work

In 1990, the second author proposed an extension to ML, called ML λ [START_REF] Miller | An Extension to ML to Handle Bound Variables in Data Structures: Preliminary Report[END_REF]. Although there is some overlap between that early proposal and the one for MLTS, ML λ did not have two critical features: nominals and nab binder in match patterns. The lack of these features greatly weakened that earlier proposal. Recent advances in proof-theoretic treatments of binding have allowed us to provide a greatly improved design.

Our immediate goals with MLTS are two fold. First, we wish to develop more examples in the metaprogramming areas of automating logic and building compilers. Second, we wish to explore whether or not an abstract machine such as the SECD machine [START_REF] Landin | The Mechanical Evaluation of Expressions[END_REF] can be built to provide an effective model of computation for MLTS.

One of the things we will most certainly encounter with applying MLTS to metaprogramming tasks is the need to encode and manipulate contexts. Currently, contexts are treated like any other data structures: list of nominals, list of pairs of nominals and type expression, etc. Almost certainly, we will find that many different kinds of contexts will share a number of features that we might wish to incorporate into MLTS: we plan to consider such extensions to the language as we gain familiarity with such applications. Define subst : tm -> tm -> tm -> tm -> prop by nabla x , subst x x U U ; nabla x y , subst y x ( U y ) y ; nabla x , subst ( app ( M x ) ( N x ) ) x U ( app SM SN ) := nabla x , subst ( M x ) x U SM /\ nabla x , subst ( N x ) x U SN ; nabla x , subst ( abs ( R x ) ) x U ( abs SR ) := nabla x y , subst ( R x y ) x ( U y ) ( SR y ) .

  type tm = | App of tm * tm | Abs of tm = > tm ;;

Figure 2 :

 2 Figure 2: Three implementations of the function that determines if its argument is a vacuous λ -term.

  Define vacp3 : tm -> bool -> prop by vacp3 ( abs x \ T ) tt ; vacp3 ( abs T ) ff ; vacp3 ( app M N ) ff ; nabla x , vacp3 x ff .

  Theorem v acp3-m ultiva lued : forall B , vacp3 ( abs x \ abs y \ y ) B -> ( B = tt \/ B = ff ) . intros . case H1 . left . search . right . search .

  Define size : tm -> nat -> prop by size ( app M N ) ( s S ) := exists S1 S2 , size M S1 /\ size N S2 /\ plus S1 S2 S ; size ( abs R ) ( s S ) := nabla x , size ( R x ) S ; nabla x , size x ( s z ) . Define vacp1 : tm -> bool -> prop by vacp1 ( abs x \ x ) ff ; nabla y , vacp1 ( abs x \ y ) tt ; vacp1 ( abs x \ app ( M x ) ( N x ) ) B := exists B1 B2 , vacp1 ( abs M ) B1 /\ vacp1 ( abs N ) B2 /\ and B1 B2 B ; vacp1 ( abs x \ abs y \ R x y ) B := nabla y , vacp1 ( abs x \ R x y ) B ; vacp1 ( app M N ) ff ; nabla x , vacp1 x ff . Define vacp2aux : tm -> tm -> bool -> prop by nabla x , vacp2aux x x ff ; nabla x y , vacp2aux x y tt ; nabla x , vacp2aux x ( app ( M x ) ( N x ) ) B := exists B1 B2 , nabla x , ( vacp2aux x ( M x ) B1 /\ vacp2aux x ( N x ) B2 ) /\ and B1 B2 B ; nabla x , vacp2aux x ( abs y \ R x y ) B := nabla x y , vacp2aux x ( R x y ) B . Define vacp2 : tm -> bool -> prop by vacp2 ( abs T ) B := nabla x , vacp2aux x ( T x ) B ; vacp2 ( app M N ) ff ; nabla x , vacp2 x ff .

Figure 4 :

 4 Figure 4: The Abella specification of four relations, which when viewed as MLTS could match the specifications in Section 3.

By β 0 conversion we mean the subset of β -conversion where β -redexes ((λ x.B)t) are restricted so that t is a bound variable that is not free in λ x.B[START_REF] Miller | A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification[END_REF].