Hipster: Integrating Theory Exploration in a Proof Assistant

This paper describes Hipster, a system integrating theory exploration with the proof assistant Isabelle/HOL. Theory exploration is a technique for automatically discovering new interesting lemmas in a given theory development. Hipster can be used in two main modes. The first is exploratory mode, used for automatically generating basic lemmas about a given set of datatypes and functions in a new theory development. The second is proof mode, used in a particular proof attempt, trying to discover the missing lemmas which would allow the current goal to be proved. Hipster's proof mode complements and boosts existing proof automation techniques that rely on automatically selecting existing lemmas, by inventing new lemmas that need induction to be proved. We show example uses of both modes

Mining State-Based Models from Proof Corpora

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will lead to a successful proof requires a significant amount of human intervention. This paper presents an automated technique that takes as input examples of successful proofs and infers an Extended Finite State Machine as output. This can in turn be used to generate proofs of new conjectures. Our preliminary experiments show that the inferred models are generally accurate (contain few false-positive sequences) and that representing existing proofs in such a way can be very useful when guiding new ones.Comment: To Appear at Conferences on Intelligent Computer Mathematics 201

Improved cross-validation for classifiers that make algorithmic choices to minimise runtime without compromising output correctness

Our topic is the use of machine learning to improve software by making choices which do not compromise the correctness of the output, but do affect the time taken to produce such output. We are particularly concerned with computer algebra systems (CASs), and in particular, our experiments are for selecting the variable ordering to use when performing a cylindrical algebraic decomposition of $n$-dimensional real space with respect to the signs of a set of polynomials. In our prior work we explored the different ML models that could be used, and how to identify suitable features of the input polynomials. In the present paper we both repeat our prior experiments on problems which have more variables (and thus exponentially more possible orderings), and examine the metric which our ML classifiers targets. The natural metric is computational runtime, with classifiers trained to pick the ordering which minimises this. However, this leads to the situation were models do not distinguish between any of the non-optimal orderings, whose runtimes may still vary dramatically. In this paper we investigate a modification to the cross-validation algorithms of the classifiers so that they do distinguish these cases, leading to improved results.Comment: 16 pages. Accepted into the Proceedings of MACIS 2019. arXiv admin note: text overlap with arXiv:1906.0145

How to follow the guidelines, when the appropriate fluid is missing?

Intravenous maintenance fluid therapy (IV-MFT) is probably the most prescribed drug in paediatric hospital care. Recently paediatric societies have produced evidence-based practice guidelines that recommend the use of balanced isotonic fluid when prescribing IV-MFT in both acute and critical paediatric care. Unfortunately, the applicability of these guidelines could be called into question when a ready-to-use glucose-containing balanced isotonic fluid is not available. The main objective of this study was to describe the availability of glucose-containing balanced isotonic fluids in European and Middle Eastern paediatric acute and critical care settings. This work is an ancillary study of the survey dedicated to IV-MFT practices in the paediatric acute and critical care settings in Europe and Middle East, a cross-sectional electronic 27-item survey, emailed in April–May 2021 to paediatric critical care physicians across 34 European and Middle East countries. The survey was developed by an expert multi-professional panel within the European Society of Peadiatric and Neonatal Intensive Care (ESPNIC). Balanced isotonic fluid with glucose 5% was available for only 32/153 (21%) responders. Balanced isotonic fluid with glucose 5% was consistently available in the UK (90%) but not available in France, Greece, The Netherlands and Turkey.    Conclusion: Ready-to-use isotonic balanced IV solutions containing glucose in sufficient amount exist but are inconsistently available throughout Europe. National and European Medication Safety Incentives should guarantee the availability of the most appropriate and safest IV-MFT solution for all children. What is Known:• Intravenous maintenance fluid therapy (IV-MFT) is probably the most prescribed drug in paediatric hospital care.• Balanced isotonic fluid is recommended when prescribing IV-MFT in both acute and critical paediatric care. What is New:• Balanced isotonic fluid with glucose 5% is available for less than 25% of the prescribers in Europe and the Middle East. Availability of balanced isotonic fluid with glucose 5% varies from one country to another but can also be inconsistent within the same country.• Clinicians who have access to a ready-to-use balanced isotonic fluid with glucose 5% are more likely to consider its use than clinicians who do not have access to such an IV solution

Comparing machine learning models to choose the variable ordering for cylindrical algebraic decomposition

There has been recent interest in the use of machine learning (ML) approaches within mathematical software to make choices that impact on the computing performance without affecting the mathematical correctness of the result. We address the problem of selecting the variable ordering for cylindrical algebraic decomposition (CAD), an important algorithm in Symbolic Computation. Prior work to apply ML on this problem implemented a Support Vector Machine (SVM) to select between three existing human-made heuristics, which did better than anyone heuristic alone. The present work extends to have ML select the variable ordering directly, and to try a wider variety of ML techniques. We experimented with the NLSAT dataset and the Regular Chains Library CAD function for Maple 2018. For each problem, the variable ordering leading to the shortest computing time was selected as the target class for ML. Features were generated from the polynomial input and used to train the following ML models: k-nearest neighbours (KNN) classifier, multi-layer perceptron (MLP), decision tree (DT) and SVM, as implemented in the Python scikit-learn package. We also compared these with the two leading human constructed heuristics for the problem: Brown's heuristic and sotd. On this dataset all of the ML approaches outperformed the human made heuristics, some by a large margin.Comment: Accepted into CICM 201

ESPNIC clinical practice guidelines: intravenous maintenance fluid therapy in acute and critically ill children- a systematic review and meta-analysis

PURPOSE Intravenous maintenance fluid therapy (IV-MFT) prescribing in acute and critically ill children is very variable among pediatric health care professionals. In order to provide up to date IV-MFT guidelines, the European Society of Pediatric and Neonatal Intensive Care (ESPNIC) undertook a systematic review to answer the following five main questions about IV-MFT: (i) the indications for use (ii) the role of isotonic fluid (iii) the role of balanced solutions (iv) IV fluid composition (calcium, magnesium, potassium, glucose and micronutrients) and v) and the optimal amount of fluid. METHODS A multidisciplinary expert group within ESPNIC conducted this systematic review using the Scottish Intercollegiate Guidelines Network (SIGN) grading method. Five databases were searched for studies that answered these questions, in acute and critically children (from 37 weeks gestational age to 18 years), published until November 2020. The quality of evidence and risk of bias were assessed, and meta-analyses were undertaken when appropriate. A series of recommendations was derived and voted on by the expert group to achieve consensus through two voting rounds. RESULTS 56 papers met the inclusion criteria, and 16 recommendations were produced. Outcome reporting was inconsistent among studies. Recommendations generated were based on a heterogeneous level of evidence, but consensus within the expert group was high. "Strong consensus" was reached for 11/16 (69%) and "consensus" for 5/16 (31%) of the recommendations. CONCLUSIONS Key recommendations are to use isotonic balanced solutions providing glucose to restrict IV-MFT infusion volumes in most hospitalized children and to regularly monitor plasma electrolyte levels, serum glucose and fluid balance

Learning2Reason

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