Towards Parameterized Regular Type Inference Using Set Constraints

We propose a method for inferring \emph{parameterized regular types} for logic programs as solutions for systems of constraints over sets of finite ground Herbrand terms (set constraint systems). Such parameterized regular types generalize \emph{parametric} regular types by extending the scope of the parameters in the type definitions so that such parameters can relate the types of different predicates. We propose a number of enhancements to the procedure for solving the constraint systems that improve the precision of the type descriptions inferred. The resulting algorithm, together with a procedure to establish a set constraint system from a logic program, yields a program analysis that infers tighter safe approximations of the success types of the program than previous comparable work, offering a new and useful efficiency vs. precision trade-off. This is supported by experimental results, which show the feasibility of our analysis

Scattering Polarization of the Ca II IR Triplet for Probing the Quiet Solar Chromosphere

The chromosphere of the quiet Sun is an important stellar atmospheric region whose thermal and magnetic structure we need to decipher for unlocking new discoveries in solar and stellar physics. To this end, we must identify and exploit observables sensitive to weak magnetic fields (B<100 G) and to the presence of cool and hot gas in the bulk of the solar chromosphere. Here we report on an investigation of the Hanle effect in two semi-empirical models of the quiet solar atmosphere with different chromospheric thermal structures. Our study reveals that scattering polarization in the Ca II IR triplet has thermal and magnetic sensitivities potentially of great diagnostic value. The linear polarization in the 8498 A line shows a strong sensitivity to inclined magnetic fields with strengths between 0.001 and 10 G, while the emergent linear polarization in the 8542 A and 8662 A lines is mainly sensitive to magnetic fields with strengths between 0.001 and 0.1 G. The reason for this is that the scattering polarization of the 8542 A and 8662 A lines, unlike the 8498 A line, is controlled mainly by the Hanle effect in their (metastable) lower levels. Therefore, in regions with magnetic strengths sensibly larger than 1 G, their Stokes Q and U profiles are sensitive only to the orientation of the magnetic field vector. We also find that for given magnetic field configurations the sign of the Q/I and U/I profiles of the 8542 A and 8662 A lines is the same in both atmospheric models, while the sign of the linear polarization profile of the 8498 A line turns out to be very sensitive to the thermal structure of the lower chromosphere. We suggest that spectropolarimetric observations providing information on the relative scattering polarization amplitudes of the Ca II IR triplet will be very useful to improve our empirical understanding of the thermal and magnetic structure of the quiet chromosphere.Comment: 27 pages, 16 figures, to appear in Ap