Smart matching

One of the most annoying aspects in the formalization of mathematics is the need of transforming notions to match a given, existing result. This kind of transformations, often based on a conspicuous background knowledge in the given scientific domain (mostly expressed in the form of equalities or isomorphisms), are usually implicit in the mathematical discourse, and it would be highly desirable to obtain a similar behavior in interactive provers. The paper describes the superposition-based implementation of this feature inside the Matita interactive theorem prover, focusing in particular on the so called smart application tactic, supporting smart matching between a goal and a given result.Comment: To appear in The 9th International Conference on Mathematical Knowledge Management: MKM 201

Asynchronous processing of Coq documents: from the kernel up to the user interface

The work described in this paper improves the reactivity of the Coq system by completely redesigning the way it processes a formal document. By subdividing such work into independent tasks the system can give precedence to the ones of immediate interest for the user and postpones the others. On the user side, a modern interface based on the PIDE middleware aggregates and present in a consistent way the output of the prover. Finally postponed tasks are processed exploiting modern, parallel, hardware to offer better scalability.Comment: in Proceedings of ITP, Aug 2015, Nanjing, Chin

Deriving Proved Equality Tests in Coq-Elpi: Stronger Induction Principles for Containers in Coq

We describe a procedure to derive equality tests and their correctness proofs from inductive type declarations in Coq. Programs and proofs are derived compositionally, reusing code and proofs derived previously. The key steps are two. First, we design appropriate induction principles for data types defined using parametric containers. Second, we develop a technique to work around the modularity limitations imposed by the purely syntactic termination check Coq performs on recursive proofs. The unary parametricity translation of inductive data types turns out to be the key to both steps. Last but not least, we provide an implementation of the procedure for the Coq proof assistant based on the Elpi [Dunchev et al., 2015] extension language

Event Indexing Systems for Efficient Selection and Analysis of HERA Data

The design and implementation of two software systems introduced to improve the efficiency of offline analysis of event data taken with the ZEUS Detector at the HERA electron-proton collider at DESY are presented. Two different approaches were made, one using a set of event directories and the other using a tag database based on a commercial object-oriented database management system. These are described and compared. Both systems provide quick direct access to individual collision events in a sequential data store of several terabytes, and they both considerably improve the event analysis efficiency. In particular the tag database provides a very flexible selection mechanism and can dramatically reduce the computing time needed to extract small subsamples from the total event sample. Gains as large as a factor 20 have been obtained.Comment: Accepted for publication in Computer Physics Communication

Isoenzyme A and Urinary N-Acetyl-β-D-Glucosaminidase Activity in Normal Pregnancy

Urinary N-acetyl-β-d-glucosaminidase (NAG) activity has been found to increase during normal uncomplicated pregnancy and such behavior could limit the diagnostic value of this enzyme for detection of subclinical tubular injury. The aim of this study was to evaluate urinary NAG activity and isoenzyme A in normal pregnant women at 30th week of pregnancy and in healthy women, to discriminate between physiological and lesional enzymuria.Enzyme activities in first morning fasting urine samples from 20 nonpregnant control and 20 normal pregnant women at 30th gestational week were evaluated by fluorometric methods.Both total and isoenzyme A activity was significantly higher ( p0.01) in urines of normal pregnant women compared with control urines, whereas ratio between these two parameters was significantly lower ( p0.001).The increase of urinary NAG activity during normal uncomplicated pregnancy appears to be characterized by a prevalent increase in isoenzyme A form, a finding associated with functional (not lesional) enzymuria. The fluorometric assays may represent a simple and rapid method to evaluate whether increase in urinary NAG activity represents a renal physiological adaptation during pregnancy

Elpi: an extension language for Coq (Metaprogramming Coq in the Elpi λProlog dialect)

Elpi is dialect of λProlog that can be used as an extension language for Coq. It lets one define commands and tactics in a high level programming language tailored to the manipulation of syntax trees containing binders and existentially quantified meta variables

Locking of Commensurate Phases in the Planar Model in an External Magnetic Field

Commensurate configuration locking is known in models like the anisotropic next-nearest-neighbor Ising model and the Frenkel-Kontorova model. We find an analogous scenario in the planar model with competing interactions when an external magnetic field is applied in the plane in which the spins lie. This model falls in the same symmetry class of the Heisenberg model with planar anisotropy. We performed a low-field, low-temperature expansion for the free energy of the model and we find phase locking energy for states with wave vectors of the form G/p where p is an integer and G is a reciprocal-lattice vector. The helix characterized by p=3 is peculiar because the commensuration energy vanishes at zero temperature. The helix corresponding to p=4 is not stable against the switching of a magnetic field that forces the spins into an up-up-down-down configuration analogous to the spin-flop phase of an antiferromagnet. For a generic commensurate value of p\u3e4, we expect locking both at zero and finite temperature as we have verified for p=5 and 6. The consequences of our results are examined for the 3N model (a tetragonal spin lattice with in-plane competitive interactions up to third-nearest neighbors)

Phase Locking in Heisenberg Helimagnets

We consider a Heisenberg model with ferromagnetic nearest‐neighbor and competing further‐neighbor exchange interactions in a small applied magnetic field at low temperature T. As a function of the exchange constants, the modulation vector is shown to have devil’s staircase behavior. We consider the effects of nonzero temperature and quantum effects. We find a special modulation wave vector at which the incommensurability energy vanishes for the classical system at T=0