Case-Analysis for Rippling and Inductive Proof

Rippling is a heuristic used to guide rewriting and is typically used for inductive theorem proving. We introduce a method to support case-analysis within rippling. Like earlier work, this allows goals containing if-statements to be proved automatically. The new contribution is that our method also supports case-analysis on datatypes. By locating the case-analysis as a step within rippling we also maintain the termination. The work has been implemented in IsaPlanner and used to extend the existing inductive proof method. We evaluate this extended prover on a large set of examples from Isabelle’s theory library and from the inductive theorem proving literature. We find that this leads to a significant improvement in the coverage of inductive theorem proving. The main limitations of the extended prover are identified, highlight the need for advances in the treatment of assumptions during rippling and when conjecturing lemmas

A recent rebuilding of most spirals ?

Re-examination of the properties of distant galaxies leads to the evidence that most present-day spirals have built up half of their stellar masses during the last 8 Gyr, mostly during several intense phases of star formation during which they took the appearance of luminous infrared galaxies (LIRGs). Distant galaxy morphologies encompass all of the expected stages of galaxy merging, central core formation and disk growth, while their cores are much bluer than those of present-day bulges. We have tested a spiral rebuilding scenario, for which 75+/-25% of spirals have experienced their last major merger event less than 8 Gyr ago. It accounts for the simultaneous decreases, during that period, of the cosmic star formation density, of the merger rate, of the number densities of LIRGs and of compact galaxies, while the densities of ellipticals and large spirals are essentially unaffected.Comment: (1) GEPI, Obs. Meudon, France ;(2)Max-Planck Institut fuer Astronomie, Germany (3) National Astronomical Observatories, CAS, China. Five pages, 1 figure. To be published in "Starbursts: From 30 Doradus to Lyman Break Galaxies", held in Cambridge, ed. R. de Grijs & R. M. Gonzalez Delgado (Dordrecht: Kluwer

Fitting the integrated Spectral Energy Distributions of Galaxies

Fitting the spectral energy distributions (SEDs) of galaxies is an almost universally used technique that has matured significantly in the last decade. Model predictions and fitting procedures have improved significantly over this time, attempting to keep up with the vastly increased volume and quality of available data. We review here the field of SED fitting, describing the modelling of ultraviolet to infrared galaxy SEDs, the creation of multiwavelength data sets, and the methods used to fit model SEDs to observed galaxy data sets. We touch upon the achievements and challenges in the major ingredients of SED fitting, with a special emphasis on describing the interplay between the quality of the available data, the quality of the available models, and the best fitting technique to use in order to obtain a realistic measurement as well as realistic uncertainties. We conclude that SED fitting can be used effectively to derive a range of physical properties of galaxies, such as redshift, stellar masses, star formation rates, dust masses, and metallicities, with care taken not to over-interpret the available data. Yet there still exist many issues such as estimating the age of the oldest stars in a galaxy, finer details ofdust properties and dust-star geometry, and the influences of poorly understood, luminous stellar types and phases. The challenge for the coming years will be to improve both the models and the observational data sets to resolve these uncertainties. The present review will be made available on an interactive, moderated web page (sedfitting.org), where the community can access and change the text. The intention is to expand the text and keep it up to date over the coming years.Comment: 54 pages, 26 figures, Accepted for publication in Astrophysics & Space Scienc

Observations of the High Redshift Universe

(Abridged) In these lectures aimed for non-specialists, I review progress in understanding how galaxies form and evolve. Both the star formation history and assembly of stellar mass can be empirically traced from redshifts z~6 to the present, but how the various distant populations inter-relate and how stellar assembly is regulated by feedback and environmental processes remains unclear. I also discuss how these studies are being extended to locate and characterize the earlier sources beyond z~6. Did early star-forming galaxies contribute significantly to the reionization process and over what period did this occur? Neither theory nor observations are well-developed in this frontier topic but the first results presented here provide important guidance on how we will use more powerful future facilities.Comment: To appear in `First Light in Universe', Saas-Fee Advanced Course 36, Swiss Soc. Astrophys. Astron. in press. 115 pages, 64 figures (see http://www.astro.caltech.edu/~rse/saas-fee.pdf for hi-res figs.) For lecture ppt files see http://obswww.unige.ch/saas-fee/preannouncement/course_pres/overview_f.htm

Automated Synthesis of Induction Axioms for Programs with Second-Order Recursion

In order to support the verification of programs, verification tools such as ACL2 or Isabelle try to extract suitable induction axioms from the definitions of terminating, recursively defined procedures. How-ever, these extraction techniques have difficulties with procedures that are defined by second-order recursion: There a first-order procedure f passes itself as an argument to a second-order procedure like map, every, foldl, etc., which leads to indirect recursive calls. For instance, second-order recursion is commonly used in algorithms on data structures such as terms (variadic trees). We present a method to automatically extract induction axioms from such procedures. Furthermore, we describe how the induction axioms can be optimized (i. e., generalized and simplified). An implementation of our methods demonstrates that the approach facilitates straightforward inductive proofs in a verification tool

Kernwaffen und das Atlantische Buendnis. Kernwaffen und die Erhaltung des Friedens - eine deutsche Erwiderung

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