Strong normalisation for applied lambda calculi

We consider the untyped lambda calculus with constructors and recursively defined constants. We construct a domain-theoretic model such that any term not denoting bottom is strongly normalising provided all its `stratified approximations' are. From this we derive a general normalisation theorem for applied typed lambda-calculi: If all constants have a total value, then all typeable terms are strongly normalising. We apply this result to extensions of G\"odel's system T and system F extended by various forms of bar recursion for which strong normalisation was hitherto unknown.Comment: 14 pages, paper acceptet at electronic journal LMC

Practical Subtyping for System F with Sized (Co-)Induction

We present a rich type system with subtyping for an extension of System F. Our type constructors include sum and product types, universal and existential quantifiers, inductive and coinductive types. The latter two size annotations allowing the preservation of size invariants. For example it is possible to derive the termination of the quicksort by showing that partitioning a list does not increase its size. The system deals with complex programs involving mixed induction and coinduction, or even mixed (co-)induction and polymorphism (as for Scott-encoded datatypes). One of the key ideas is to completely separate the induction on sizes from the notion of recursive programs. We use the size change principle to check that the proof is well-founded, not that the program terminates. Termination is obtained by a strong normalization proof. Another key idea is the use symbolic witnesses to handle quantifiers of all sorts. To demonstrate the practicality of our system, we provide an implementation that accepts all the examples discussed in the paper and much more

A Theory of Explicit Substitutions with Safe and Full Composition

Many different systems with explicit substitutions have been proposed to implement a large class of higher-order languages. Motivations and challenges that guided the development of such calculi in functional frameworks are surveyed in the first part of this paper. Then, very simple technology in named variable-style notation is used to establish a theory of explicit substitutions for the lambda-calculus which enjoys a whole set of useful properties such as full composition, simulation of one-step beta-reduction, preservation of beta-strong normalisation, strong normalisation of typed terms and confluence on metaterms. Normalisation of related calculi is also discussed.Comment: 29 pages Special Issue: Selected Papers of the Conference "International Colloquium on Automata, Languages and Programming 2008" edited by Giuseppe Castagna and Igor Walukiewic

Multi-frequency study of a new Fe-rich supernova remnant in the Large Magellanic Cloud, MCSNR J0508-6902

We present a detailed radio, X-ray and optical study of a newly discovered Large Magellanic Cloud (LMC) supernova remnant (SNR) which we denote MCSNR J0508-6902. Observations from the Australian Telescope Compact Array (ATCA) and the $\textit{XMM-Newton}$ X-ray observatory are complemented by deep H$\alpha$ images and Anglo Australian Telescope AAOmega spectroscopic data to study the SNR shell and its shock-ionisation. Archival data at other wavelengths are also examined. The remnant follows a filled-in shell type morphology in the radio-continuum and has a size of $\sim$74 pc $\times$ 57 pc at the LMC distance. The X-ray emission exhibits a faint soft shell morphology with Fe-rich gas in its interior $-$ indicative of a Type Ia origin. The remnant appears to be mostly dissipated at higher radio-continuum frequencies leaving only the south-eastern limb fully detectable while in the optical it is the western side of the SNR shell that is clearly detected. The best-fit temperature to the shell X-ray emission ($kT = 0.41^{+0.05}_{-0.06}$ keV) is consistent with other large LMC SNRs. We determined an O/Fe ratio of $<21$ and an Fe mass of 0.5-1.8$~M_{\odot}$ in the interior of the remnant, both of which are consistent with the Type Ia scenario. We find an equipartition magnetic field for the remnant of $\sim$28 $\mu$G, a value typical of older SNRs and consistent with other analyses which also infer an older remnant

XMM-Newton observations of three poor clusters: Similarity in dark matter and entropy profiles down to low mass

(Abridged) We present an analysis of the mass and entropy profiles of three poor clusters (A1991, A2717 and MKW9) observed with XMM-Newton. The clusters have similar temperatures (kT=2.65, 2.53 and 2.58 keV), and similar redshifts (0.04 < z < 0.06). We trace the surface brightness, temperature, entropy and integrated mass profiles up to 0.5 (0.35 for MKW9) of the virial radius (r_200). The integrated mass profiles are very similar in physical units and are reasonably well fitted with the NFW mass model with concentration parameters of c_200=4-6 and M_200=1.2-1.6 X 10^14 h_70^-1 \msun. The entropy profiles are similar at large scale, but there is some scatter in the central region (r<50 kpc). None of the clusters has an isentropic core. Including XMM data on A1983 (kT=2.2 keV), and A1413 (kT = 6.5 keV), we discuss the structural and scaling properties of cluster mass and entropy profiles. The scaled mass profiles display <20% dispersion in the 0.05 - 0.5 r_200 radial range. The c_200 parameters of these clusters, and other values from the literature, are fully consistent with the c_200 - M_200 relation derived from simulations. The dispersion in scaled entropy profiles is small, implying self-similarity down to low mass (kT ~2 keV), and is reduced by 30-40% (to ~20%) if we use the empirical relation S \propto T^0.65 instead of the standard self-similar relation, S \propto T. The mean scaled profile is well fitted by a power law for 0.05 < r_200 < 0.5, with a slope slightly lower than expected from pure shock heating (\alpha = 0.94+/-0.14), and a normalisation at 0.1 r_200 consistent with previous studies. The gas history thus likely depends both on gravitational processes and the interplay between cooling and various galaxy feedback mechanisms.Comment: Final refereed version to appear in A&A. Minor changes. 15 pages, 12 figures (Figs 1 & 3 low res