24,406 research outputs found
Productive Corecursion in Logic Programming
Logic Programming is a Turing complete language. As a consequence, designing
algorithms that decide termination and non-termination of programs or decide
inductive/coinductive soundness of formulae is a challenging task. For example,
the existing state-of-the-art algorithms can only semi-decide coinductive
soundness of queries in logic programming for regular formulae. Another, less
famous, but equally fundamental and important undecidable property is
productivity. If a derivation is infinite and coinductively sound, we may ask
whether the computed answer it determines actually computes an infinite
formula. If it does, the infinite computation is productive. This intuition was
first expressed under the name of computations at infinity in the 80s. In
modern days of the Internet and stream processing, its importance lies in
connection to infinite data structure processing.
Recently, an algorithm was presented that semi-decides a weaker property --
of productivity of logic programs. A logic program is productive if it can give
rise to productive derivations. In this paper we strengthen these recent
results. We propose a method that semi-decides productivity of individual
derivations for regular formulae. Thus we at last give an algorithmic
counterpart to the notion of productivity of derivations in logic programming.
This is the first algorithmic solution to the problem since it was raised more
than 30 years ago. We also present an implementation of this algorithm.Comment: Paper presented at the 33nd International Conference on Logic
Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1, 2017
16 pages, LaTeX, no figure
Beating the Productivity Checker Using Embedded Languages
Some total languages, like Agda and Coq, allow the use of guarded corecursion
to construct infinite values and proofs. Guarded corecursion is a form of
recursion in which arbitrary recursive calls are allowed, as long as they are
guarded by a coinductive constructor. Guardedness ensures that programs are
productive, i.e. that every finite prefix of an infinite value can be computed
in finite time. However, many productive programs are not guarded, and it can
be nontrivial to put them in guarded form.
This paper gives a method for turning a productive program into a guarded
program. The method amounts to defining a problem-specific language as a data
type, writing the program in the problem-specific language, and writing a
guarded interpreter for this language.Comment: In Proceedings PAR 2010, arXiv:1012.455
Teaching and learning trigonometry with technology
Modern school classrooms have access to a range of potential technologies, ranging from calculators to computers to the Internet. This paper explores some of the potential for such technologies to affect the curriculum and teaching of trigonometry in the secondary school. We identify some of the ways in which the teaching of trigonometry might be supported by the availability of various forms of technology. We consider circular measures, graphs of functions, trigonometric identities, equations and statistical modeling and focus on activities that are not possible without the use of technology. Modern technology provides an excellent means of exploring many of the concepts associated with trigonometry, both trigonometric and circular functions. Many of these opportunities for learning were not available before technology development and access within schools we enjoy today. This paper suggests some of the avenues for exploration
Colliding Winds in Low-Mass Binary Star Systems: wind interactions and implications for habitable planets
Context. In binary star systems, the winds from the two components impact
each other, leading to strong shocks and regions of enhanced density and
temperature. Potentially habitable circumbinary planets must continually be
exposed to these interactions regions.
Aims. We study, for the first time, the interactions between winds from
low-mass stars in a binary system, to show the wind conditions seen by
potentially habitable circumbinary planets.
Methods. We use the advanced 3D numerical hydrodynamic code Nurgush to model
the wind interactions of two identical winds from two solar mass stars with
circular orbits and a binary separation of 0.5 AU. As input into this model, we
use a 1D hydrodynamic simulation of the solar wind, run using the Versatile
Advection Code. We derive the locations of stable and habitable orbits in this
system to explore what wind conditions potentially habitable planets will be
exposed to during their orbits.
Results. Our wind interaction simulations result in the formation of two
strong shock waves separated by a region of enhanced density and temperature.
The wind-wind interaction region has a spiral shape due to Coriolis forces
generated by the orbital motions of the two stars. The stable and habitable
zone in this system extends from approximately 1.4 AU to 2.4 AU. (TRUNCATED)Comment: 15 pages, 11 figures, to be published in A&
Assessing Ontological Arguments
Part I argues that ontological arguments, like other classical proofs of the existence of God, are parts of larger arguments in which they are embedded. These larger arguments include reasons supporting the proofs’ premises and responses to them, and to the proofs’ claims to validity and non-circularity, since, in the final analysis, our assessment of the proofs will express our best judgment of the cumulative force of all the considerations bearing on their overall adequacy. Part II illustrates these points by examining contemporary defences of, and attacks on, one of the ontological argument’s central premises, namely, that God’s existence is logically possible
Artifacts in incomplete data tomography - with applications to photoacoustic tomography and sonar
We develop a paradigm using microlocal analysis that allows one to
characterize the visible and added singularities in a broad range of incomplete
data tomography problems. We give precise characterizations for photo- and
thermoacoustic tomography and Sonar, and provide artifact reduction strategies.
In particular, our theorems show that it is better to arrange Sonar detectors
so that the boundary of the set of detectors does not have corners and is
smooth. To illustrate our results, we provide reconstructions from synthetic
spherical mean data as well as from experimental photoacoustic data
Towards the Integration of an Intuitionistic First-Order Prover into Coq
An efficient intuitionistic first-order prover integrated into Coq is useful
to replay proofs found by external automated theorem provers. We propose a
two-phase approach: An intuitionistic prover generates a certificate based on
the matrix characterization of intuitionistic first-order logic; the
certificate is then translated into a sequent-style proof.Comment: In Proceedings HaTT 2016, arXiv:1606.0542
ALMA data suggest the presence of a spiral structure in the inner wind of CW Leo
(abbreviated) We aim to study the inner wind of the well-known AGB star CW
Leo. Different diagnostics probing different geometrical scales have pointed
toward a non-homogeneous mass-loss process: dust clumps are observed at
milli-arcsec scale, a bipolar structure is seen at arcsecond-scale and
multi-concentric shells are detected beyond 1". We present the first ALMA Cycle
0 band 9 data around 650 GHz. The full-resolution data have a spatial
resolution of 0".42x0".24, allowing us to study the morpho-kinematical
structure within ~6". Results: We have detected 25 molecular lines. The
emission of all but one line is spatially resolved. The dust and molecular
lines are centered around the continuum peak position. The dust emission has an
asymmetric distribution with a central peak flux density of ~2 Jy. The
molecular emission lines trace different regions in the wind acceleration
region and suggest that the wind velocity increases rapidly from about 5 R*
almost reaching the terminal velocity at ~11 R*. The channel maps for the
brighter lines show a complex structure; specifically for the 13CO J=6-5 line
different arcs are detected within the first few arcseconds. The curved
structure present in the PV map of the 13CO J=6-5 line can be explained by a
spiral structure in the inner wind, probably induced by a binary companion.
From modeling the ALMA data, we deduce that the potential orbital axis for the
binary system lies at a position angle of ~10-20 deg to the North-East and that
the spiral structure is seen almost edge-on. We infer an orbital period of 55
yr and a binary separation of 25 au (or ~8.2 R*). We tentatively estimate that
the companion is an unevolved low-mass main-sequence star. The ALMA data hence
provide us for the first time with the crucial kinematical link between the
dust clumps seen at milli-arcsecond scale and the almost concentric arcs seen
at arcsecond scale.Comment: 22 pages, 18 Figures, Astronomy & Astrophysic
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