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

Фотографія як вид мистецтва

Фотографія - це найдемократичніший вид мистецтва. Історія фотографії розпочалася близько 1816 року, коли Джезеф Нісефор Ньєпс винайшов спосіб отримання зображень предметів за допомогою камери-обскури. Першу в історії фотографію "вид з вікна" він отримав у 1826 році. Весь подальший розвиток фотографії відбувався в напрямі отримання більш досконалих знімків. При цитуванні документа, використовуйте посилання http://essuir.sumdu.edu.ua/handle/123456789/3300

Encoding monomorphic and polymorphic types

Most automatic theorem provers are restricted to untyped logics, and existing translations from typed logics are bulky or unsound. Recent research proposes monotonicity as a means to remove some clutter. Here we pursue this approach systematically, analysing formally a variety of encodings that further improve on efficiency while retaining soundness and completeness. We extend the approach to rank-1 polymorphism and present alternative schemes that lighten the translation of polymorphic symbols based on the novel notion of “cover”. The new encodings are implemented, and partly proved correct, in Isabelle/HOL. Our evaluation finds them vastly superior to previous schemes

Structural Examination of Au/Ge(001) by Surface X-Ray Diffraction and Scanning Tunneling Microscopy

The one-dimensional reconstruction of Au/Ge(001) was investigated by means of autocorrelation functions from surface x-ray diffraction (SXRD) and scanning tunneling microscopy (STM). Interatomic distances found in the SXRD-Patterson map are substantiated by results from STM. The Au coverage, recently determined to be 3/4 of a monolayer of gold, together with SXRD leads to three non-equivalent positions for Au within the c(8x2) unit cell. Combined with structural information from STM topography and line profiling, two building blocks are identified: Au-Ge hetero-dimers within the top wire architecture and Au homo-dimers within the trenches. The incorporation of both components is discussed using density functional theory and model based Patterson maps by substituting Germanium atoms of the reconstructed Ge(001) surface.Comment: 5 pages, 3 figure

Two-Spinon and Orbital Excitations of the Spin-Peierls System TiOCl

We combine high-resolution resonant inelastic x-ray scattering with cluster calculations utilizing a recently derived effective magnetic scattering operator to analyze the polarization, excitation energy, and momentum dependent excitation spectrum of the low-dimensional quantum magnet TiOCl in the range expected for orbital and magnetic excitations (0 - 2.5 eV). Ti 3d orbital excitations yield complete information on the temperature-dependent crystal-field splitting. In the spin-Peierls phase we observe a dispersive two-spinon excitation and estimate the inter- and intra-dimer magnetic exchange coupling from a comparison to cluster calculations

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

Terahertz Conductivity at the Verwey Transition in Magnetite

The complex conductivity at the (Verwey) metal-insulator transition in Fe_3O_4 has been investigated at THz and infrared frequencies. In the insulating state, both the dynamic conductivity and the dielectric constant reveal a power-law frequency dependence, the characteristic feature of hopping conduction of localized charge carriers. The hopping process is limited to low frequencies only, and a cutoff frequency nu_1 ~ 8 meV must be introduced for a self-consistent description. On heating through the Verwey transition the low-frequency dielectric constant abruptly decreases and becomes negative. Together with the conductivity spectra this indicates a formation of a narrow Drude-peak with a characteristic scattering rate of about 5 meV containing only a small fraction of the available charge carriers. The spectra can be explained assuming the transformation of the spectral weight from the hopping process to the free-carrier conductivity. These results support an interpretation of Verwey transition in magnetite as an insulator-semiconductor transition with structure-induced changes in activation energy.Comment: 6 Pages, 3 Figure

Raman and fluorescence contributions to resonant inelastic soft x-ray scattering on LaAlO3_3/SrTiO3_3 heterostructures

We present a detailed study of the Ti 3$d$ carriers at the interface of LaAlO$_3$/SrTiO$_3$ heterostructures by high-resolution resonant inelastic soft x-ray scattering (RIXS), with special focus on the roles of overlayer thickness and oxygen vacancies. Our measurements show the existence of interfacial Ti 3$d$ electrons already below the critical thickness for conductivity and an increase of the total interface charge up to a LaAlO$_3$ overlayer thickness of 6 unit cells before it levels out. By comparing stoichiometric and oxygen deficient samples we observe strong Ti 3$d$ charge carrier doping by oxygen vacancies. The RIXS data combined with photoelectron spectroscopy and transport measurements indicate the simultaneous presence of localized and itinerant charge carriers. However, it is demonstrated that the relative amount of localized and itinerant Ti $3d$ electrons in the ground state cannot be deduced from the relative intensities of the Raman and fluorescence peaks in excitation energy dependent RIXS measurements, in contrast to previous interpretations. Rather, we attribute the observation of either the Raman or the fluorescence signal to the spatial extension of the intermediate state reached in the RIXS excitation process.Comment: 9 pages, 6 figure