SEPIA: Search for Proofs Using Inferred Automata

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show that SEPIA provides a useful complement to existing automated tactics in Coq.Comment: To appear at 25th International Conference on Automated Deductio

The Tactician (extended version): A Seamless, Interactive Tactic Learner and Prover for Coq

We present Tactician, a tactic learner and prover for the Coq Proof Assistant. Tactician helps users make tactical proof decisions while they retain control over the general proof strategy. To this end, Tactician learns from previously written tactic scripts and gives users either suggestions about the next tactic to be executed or altogether takes over the burden of proof synthesis. Tactician's goal is to provide users with a seamless, interactive, and intuitive experience together with robust and adaptive proof automation. In this paper, we give an overview of Tactician from the user's point of view, regarding both day-to-day usage and issues of package dependency management while learning in the large. Finally, we give a peek into Tactician's implementation as a Coq plugin and machine learning platform.Comment: 19 pages, 2 figures. This is an extended version of a paper published in CICM-2020. For the project website, see https://coq-tactician.github.i

ENIGMA: Efficient Learning-based Inference Guiding Machine

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance.Comment: Submitted to LPAR 201

Adaptive learning through technology: a technical review and implementation

Purpose There is an increase globally of students using technology to support their learning. The purpose of this paper is to outline the technical aspects of adaptive learning and contribute to the development of pedagogy that incorporates this method in teaching and learning. Design/methodology/approach This is a technical review article that summarises key guidance on the application of adaptive learning and then reflects on its application in a UK and Vietnamese context. Findings Initial analysis demonstrates that learning can occur asynchronously because of students engaging with adaptive learning. Issues and recommendations were derived from the reflections and practice of both UK and Vietnamese practitioners. Recommendations focussed on the more practical elements of constructing and maintaining adaptive learning. Questions were then constructed to make the decision of whether to implement adaptive learning into teaching and learning practices. Originality/value This academic commentary reflects on the implementation of asynchronous learning adaptive technologies in both the UK and Vietnam, specifically exploring the use of a “mastery path” and “computerised adaptive testing” to enhance student understanding

ProofWatch: Watchlist Guidance for Large Theories in E

Watchlist (also hint list) is a mechanism that allows related proofs to guide a proof search for a new conjecture. This mechanism has been used with the Otter and Prover9 theorem provers, both for interactive formalizations and for human-assisted proving of open conjectures in small theories. In this work we explore the use of watchlists in large theories coming from first-order translations of large ITP libraries, aiming at improving hammer-style automation by smarter internal guidance of the ATP systems. In particular, we (i) design watchlist-based clause evaluation heuristics inside the E ATP system, and (ii) develop new proof guiding algorithms that load many previous proofs inside the ATP and focus the proof search using a dynamically updated notion of proof matching. The methods are evaluated on a large set of problems coming from the Mizar library, showing significant improvement of E's standard portfolio of strategies, and also of the previous best set of strategies invented for Mizar by evolutionary methods.Comment: 19 pages, 10 tables, submitted to ITP 2018 at FLO

Serotype-specific mortality from invasive Streptococcus pneumoniae disease revisited

BACKGROUND: Invasive infection with Streptococcus pneumoniae (pneumococci) causes significant morbidity and mortality. Case series and experimental data have shown that the capsular serotype is involved in the pathogenesis and a determinant of disease outcome. METHODS: Retrospective review of 464 cases of invasive disease among adults diagnosed between 1990 and 2001. Multivariate Cox proportional hazard analysis. RESULTS: After adjustment for other markers of disease severity, we found that infection with serotype 3 was associated with an increased relative risk (RR) of death of 2.54 (95% confidence interval (CI): 1.22–5.27), whereas infection with serotype 1 was associated with a decreased risk of death (RR 0.23 (95% CI, 0.06–0.97)). Additionally, older age, relative leucopenia and relative hypothermia were independent predictors of mortality. CONCLUSION: Our study shows that capsular serotypes independently influenced the outcome from invasive pneumococcal disease. The limitations of the current polysaccharide pneumococcal vaccine warrant the development of alternative vaccines. We suggest that the virulence of pneumococcal serotypes should be considered in the design of novel vaccines

Genomic epidemiology of SARS-CoV-2 in a UK university identifies dynamics of transmission

AbstractUnderstanding SARS-CoV-2 transmission in higher education settings is important to limit spread between students, and into at-risk populations. In this study, we sequenced 482 SARS-CoV-2 isolates from the University of Cambridge from 5 October to 6 December 2020. We perform a detailed phylogenetic comparison with 972 isolates from the surrounding community, complemented with epidemiological and contact tracing data, to determine transmission dynamics. We observe limited viral introductions into the university; the majority of student cases were linked to a single genetic cluster, likely following social gatherings at a venue outside the university. We identify considerable onward transmission associated with student accommodation and courses; this was effectively contained using local infection control measures and following a national lockdown. Transmission clusters were largely segregated within the university or the community. Our study highlights key determinants of SARS-CoV-2 transmission and effective interventions in a higher education setting that will inform public health policy during pandemics.</jats:p

Proof Mining with Dependent Types

Several approaches exist to data-mining big corpora of formal proofs. Some of these approaches are based on statistical machine learning, and some -- on theory exploration. However, most are developed for either untyped or simply-typed theorem provers. In this paper, we present a method that combines statistical data mining and theory exploration in order to analyse and automate proofs in dependently typed language of Coq.Comment: Accepted at CICM'17, Edinburgh, 17-21 July 201