Premise Selection and External Provers for HOL4

Learning-assisted automated reasoning has recently gained popularity among the users of Isabelle/HOL, HOL Light, and Mizar. In this paper, we present an add-on to the HOL4 proof assistant and an adaptation of the HOLyHammer system that provides machine learning-based premise selection and automated reasoning also for HOL4. We efficiently record the HOL4 dependencies and extract features from the theorem statements, which form a basis for premise selection. HOLyHammer transforms the HOL4 statements in the various TPTP-ATP proof formats, which are then processed by the ATPs. We discuss the different evaluation settings: ATPs, accessible lemmas, and premise numbers. We measure the performance of HOLyHammer on the HOL4 standard library. The results are combined accordingly and compared with the HOL Light experiments, showing a comparably high quality of predictions. The system directly benefits HOL4 users by automatically finding proofs dependencies that can be reconstructed by Metis

A method to estimate trends in distributions of 1 min rain rates from numerical weather prediction data

It is known that the rain rate exceeded 0.01% of the time in the UK has experienced an increasing trend over the last 20 years. It is very likely that rain fade and outage experience a similar trend. This paper presents a globally applicable method to estimate these trends, based on the widely accepted Salonen-Poiares Baptista model. The input data are parameters easily extracted from numerical weather prediction reanalysis data. The method is verified using rain gauge data from the UK, and the predicted trend slopes of 0.01% exceeded rain rate are presented on a global grid

Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla

Introduction to the computational structural mechanics testbed

The Computational Structural Mechanics (CSM) testbed software system based on the SPAR finite element code and the NICE system is described. This software is denoted NICE/SPAR. NICE was developed at Lockheed Palo Alto Research Laboratory and contains data management utilities, a command language interpreter, and a command language definition for integrating engineering computational modules. SPAR is a system of programs used for finite element structural analysis developed for NASA by Lockheed and Engineering Information Systems, Inc. It includes many complementary structural analysis, thermal analysis, utility functions which communicate through a common database. The work on NICE/SPAR was motivated by requirements for a highly modular and flexible structural analysis system to use as a tool in carrying out research in computational methods and exploring computer hardware. Analysis examples are presented which demonstrate the benefits gained from a combination of the NICE command language with a SPAR computational modules

Case 10 : Youth as Change Agents

Kadugondanahalli (KG Halli), a neighbourhood within the urban slums of Bangalore, India, is riddled with barriers and challenges to navigation within the healthcare system. Residents, faced with a multitude of problems, including chronic conditions, primarily Type 2 diabetes and hypertension, have poor access to healthcare services and are, thereby, faced with high out-ofpocket expenditure. The youth, especially, are confronted with extremely challenging living conditions. Healthcare services at KG Halli are not integrated, quality of care is poor, and these trends are perpetuated by the strong power dynamics that exist at both state and national levels. For the past three years, Dr. Thriveni, Urban Health Systems project manager and Public Health Specialist at the Institute of Public Health (IPH), has been advocating on behalf of the local youth to improve their living circumstances

Rubidium and lead abundances in giant stars of the globular clusters M 13 and NGC 6752

We present measurements of the neutron-capture elements Rb and Pb in five giant stars of the globular cluster NGC 6752 and Pb measurements in four giants of the globular cluster M 13. The abundances were derived by comparing synthetic spectra with high resolution, high signal-to-noise ratio spectra obtained using HDS on the Subaru telescope and MIKE on the Magellan telescope. The program stars span the range of the O-Al abundance variation. In NGC 6752, the mean abundances are [Rb/Fe] = -0.17 +/- 0.06 (sigma = 0.14), [Rb/Zr] = -0.12 +/- 0.06 (sigma = 0.13), and [Pb/Fe] = -0.17 +/- 0.04 (sigma = 0.08). In M 13 the mean abundance is [Pb/Fe] = -0.28 +/- 0.03 (sigma = 0.06). Within the measurement uncertainties, we find no evidence for a star-to-star variation for either Rb or Pb within these clusters. None of the abundance ratios [Rb/Fe], [Rb/Zr], or [Pb/Fe] are correlated with the Al abundance. NGC 6752 may have slightly lower abundances of [Rb/Fe] and [Rb/Zr] compared to the small sample of field stars at the same metallicity. For M 13 and NGC 6752 the Pb abundances are in accord with predictions from a Galactic chemical evolution model. If metal-poor intermediate-mass asymptotic giant branch stars did produce the globular cluster abundance anomalies, then such stars do not synthesize significant quantities of Rb or Pb. Alternatively, if such stars do synthesize large amounts of Rb or Pb, then they are not responsible for the abundance anomalies seen in globular clusters.Comment: Accepted for publication in Ap

Machine-Checked Proofs For Realizability Checking Algorithms

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions, assume/guarantee contracts, and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. For these proofs to be meaningful, each leaf-level component contract must be realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. We have recently proposed (in [1]) a contract-based realizability checking algorithm for assume/guarantee contracts over infinite theories supported by SMT solvers such as linear integer/real arithmetic and uninterpreted functions. In that work, we used an SMT solver and an algorithm similar to k-induction to establish the realizability of a contract, and justified our approach via a hand proof. Given the central importance of realizability to our virtual integration approach, we wanted additional confidence that our approach was sound. This paper describes a complete formalization of the approach in the Coq proof and specification language. During formalization, we found several small mistakes and missing assumptions in our reasoning. Although these did not compromise the correctness of the algorithm used in the checking tools, they point to the value of machine-checked formalization. In addition, we believe this is the first machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur

Formalising Mathematics in Simple Type Theory

Despite the considerable interest in new dependent type theories, simple type theory (which dates from 1940) is sufficient to formalise serious topics in mathematics. This point is seen by examining formal proofs of a theorem about stereographic projections. A formalisation using the HOL Light proof assistant is contrasted with one using Isabelle/HOL. Harrison's technique for formalising Euclidean spaces is contrasted with an approach using Isabelle/HOL's axiomatic type classes. However, every formal system can be outgrown, and mathematics should be formalised with a view that it will eventually migrate to a new formalism