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

Proving Type Class Laws for Haskell

Type classes in Haskell are used to implement ad-hoc polymorphism, i.e. a way to ensure both to the programmer and the compiler that a set of functions are defined for a specific data type. All instances of such type classes are expected to behave in a certain way and satisfy laws associated with the respective class. These are however typically just stated in comments and as such, there is no real way to enforce that they hold. In this paper we describe a system which allows the user to write down type class laws which are then automatically instantiated and sent to an inductive theorem prover when declaring a new instance of a type class.Comment: Presented at the Symposium for Trends in Functional Programming, 201

Pressure dependence of the Verwey transition in magnetite: an infrared spectroscopic point of view

We investigated the electronic and vibrational properties of magnetite at temperatures from 300 K down to 10 K and for pressures up to 10 GPa by far-infrared reflectivity measurements. The Verwey transition is manifested by a drastic decrease of the overall reflectance and the splitting of the phonon modes as well as the activation of additional phonon modes. In the whole studied pressure range the down-shift of the overall reflectance spectrum saturates and the maximum number of phonon modes is reached at a critical temperature, which sets a lower bound for the Verwey transition temperature T$_{\mathrm{v}}$. Based on these optical results a pressure-temperature phase diagram for magnetite is proposed.Comment: 5 pages, 4 figures; accepted for publication in J. Appl. Phy

GPs' recognition of death in the foreseeable future and diagnosis of a fatal condition: a national survey

Background: Nowadays, palliative care is considered as a care continuum that may start early in the course of the disease. In order to address the evolving needs of patients for palliative care in time, GPs should be aware in good time of the diagnosis and of the imminence of death. The aim of the study was to gain insight into how long before a non-sudden death the diagnosis of the disease ultimately leading to death is made and on what kind of information the diagnosis is based. In addition, we aimed to explore when, and based on what kind of information, GPs become aware that death of a patient will be in the foreseeable future. Methods: A written questionnaire focusing on the GPs' experiences with their last patient who died non-suddenly was sent to a random representative sample of 850 GPs in the Netherlands. Results: The data were analysed of the 297 GPs who responded. 76% of the reported cases were cancer patients and 24% were patients with another non-sudden cause of death. The diagnosis was made only in the last week of life for 15% of the non-cancer patients and 1% of the patients with cancer. GPs were most likely to have been informed of the diagnosis by the medical specialist, although particularly in the case of non-cancer patients GPs also relied on their own assessment of the diagnosis or on other information sources. The GP remained unaware that the patient would die in the foreseeable future until the last week of life in 26% of the non-cancer group, while this was the case for only 6% of the cancer patients. GP's awareness was most likely to be based on the GP's own observations of problems and/or symptoms. Conclusions: The GP often only becomes aware of a fatal diagnosis and of death in the foreseeable future at a late stage in the disease trajectory, particularly in the case of non-cancer patients. It can be assumed that if the diagnosis and the nearing death are only recognised at a late stage, palliative care is either started at a very late stage or not at all

Strictly One-Dimensional Electron System in Au Chains on Ge(001) Revealed By Photoelectron K-Space Mapping

Atomic nanowires formed by Au on Ge(001) are scrutinized for the band topology of the conduction electron system by k-resolved photoemission. Two metallic electron pockets are observed. Their Fermi surface sheets form straight lines without undulations perpendicular to the chains within experimental uncertainty. The electrons hence emerge as strictly confined to one dimension. Moreover, the system is stable against a Peierls distortion down to 10 K, lending itself for studies of the spectral function. Indications for unusually low spectral weight at the chemical potential are discussed.Comment: 4 pages, 4 figures - revised version with added Fig. 2e) and additional reference

Pressure-induced insulator-to-metal transition in low-dimensional TiOCl

We studied the transmittance and reflectance of the low-dimensional Mott-Hubbard insulator TiOCl in the infrared and visible frequency range as a function of pressure. The strong suppression of the transmittance and the abrupt increase of the near-infrared reflectance above 12 GPa suggest a pressure-induced insulator-to-metal transition. The pressure-dependent frequency shifts of the orbital excitations, as well as the pressure dependences of the charge gap and the spectral weight of the optical conductivity above the phase transition are presented.Comment: 4 pages, 6 figure

Muon-spin relaxation measurements on the dimerized spin-1/2 chains NaTiSi2O6 and TiOCl

We report muon spin relaxation (muSR) and magnetic susceptibility investigations of two Ti3+ chain compounds which each exhibit a spin gap at low temperature, NaTiSi2O6 and TiOCl. From these we conclude that the spin gap in NaTiSi2O6 is temperature independent, with a value of 2*Delta=660(50)K, arising from orbital ordering at Too = 210K; the associated structural fluctuations activate the muon spin relaxation rate up to temperatures above 270K. In TiOCl we find thermally activated spin fluctuations corresponding to a spin gap 2*Delta=420(40)K below Tc1=67K. We also compare the methods used to extract the spin gap and the concentration of free spins within the samples from muSR and magnetic susceptibility data.Comment: 4 pages, 3 figure

Finding Finite Models in Multi-Sorted First-Order Logic

This work extends the existing MACE-style finite model finding approach to multi-sorted first order logic. This existing approach iteratively assumes increasing domain sizes and encodes the related ground problem as a SAT problem. When moving to the multi-sorted setting each sort may have a different domain size, leading to an explosion in the search space. This paper focusses on methods to tame that search space. The key approach adds additional information to the SAT encoding to suggest which domains should be grown. Evaluation of an implementation of techniques in the Vampire theorem prover shows that they dramatically reduce the search space and that this is an effective approach to find finite models in multi-sorted first order logic.Comment: SAT 201