Interactive Simplifier Tracing and Debugging in Isabelle

The Isabelle proof assistant comes equipped with a very powerful tactic for term simplification. While tremendously useful, the results of simplifying a term do not always match the user's expectation: sometimes, the resulting term is not in the form the user expected, or the simplifier fails to apply a rule. We describe a new, interactive tracing facility which offers insight into the hierarchical structure of the simplification with user-defined filtering, memoization and search. The new simplifier trace is integrated into the Isabelle/jEdit Prover IDE.Comment: Conferences on Intelligent Computer Mathematics, 201

The Significance of Nasal Carriage of Staphylococcus Aureus and the Incidence of Postoperative Wound Infection

Staphylococcus aureus infections are associated with considerable morbidity and, in certain situations, mortality. The association between the nasal carriage of S. aureus and subsequent infection has been comprehensively established in a variety of clinical settings, in particular, patients undergoing haemodialysis and continuous ambulatory peritoneal dialysis (CAPD), and in patients undergoing surgery. Postoperative wound infections are associated with a high degree of morbidity and represent an important medical issue. Until recently, eradication of S. aureus nasal carriage by various topical and systemic agents had proved unsuccessful. Mupirocin is a novel topical antibiotic with excellent antibacterial activity against staphylococci. Recent studies have demonstrated that intranasal administration of mupirocin is effective in eradicating the nasal carriage of S. aureus and in reducing the incidence of S. aureus infections in haemodialysis and CAPD patients. It has been suggested that sufficient evidence now exists to test the hypothesis that eradication of the carrier state in surgical patients preoperatively may reduce the incidence of S. aureus postoperative wound infections

From LCF to Isabelle/HOL

Interactive theorem provers have developed dramatically over the past four decades, from primitive beginnings to today's powerful systems. Here, we focus on Isabelle/HOL and its distinctive strengths. They include automatic proof search, borrowing techniques from the world of first order theorem proving, but also the automatic search for counterexamples. They include a highly readable structured language of proofs and a unique interactive development environment for editing live proof documents. Everything rests on the foundation conceived by Robin Milner for Edinburgh LCF: a proof kernel, using abstract types to ensure soundness and eliminate the need to store proofs. Compared with the research prototypes of the 1970s, Isabelle is a practical and versatile tool. It is used by system designers, mathematicians and many others

Capturing Hiproofs in HOL Light

Hierarchical proof trees (hiproofs for short) add structure to ordinary proof trees, by allowing portions of trees to be hierarchically nested. The additional structure can be used to abstract away from details, or to label particular portions to explain their purpose. In this paper we present two complementary methods for capturing hiproofs in HOL Light, along with a tool to produce web-based visualisations. The first method uses tactic recording, by modifying tactics to record their arguments and construct a hierarchical tree; this allows a tactic proof script to be modified. The second method uses proof recording, which extends the HOL Light kernel to record hierachical proof trees alongside theorems. This method is less invasive, but requires care to manage the size of the recorded objects. We have implemented both methods, resulting in two systems: Tactician and HipCam

Monte Carlo study of the critical properties of the three-dimensional 120-degree model

We report on large scale finite-temperature Monte Carlo simulations of the classical $120^\circ$ or $e_g$ orbital-only model on the simple cubic lattice in three dimensions with a focus towards its critical properties. This model displays a continuous phase transition to an orbitally ordered phase. While the correlation length exponent $\nu\approx0.665$ is close to the 3D XY value, the exponent $\eta \approx 0.15$ differs substantially from O(N) values. We also introduce a discrete variant of the $e_g$ model, called $e_g$-clock model, which is found to display the same set of exponents. Further, an emergent U(1) symmetry is found at the critical point $T_c$, which persists for $T<T_c$ below a crossover length scaling as $\Lambda \sim \xi^a$, with an unusually small $a\approx1.3$.Comment: 13 pages, 6 figure

Emergence of chaotic scattering in ultracold Er and Dy

We show that for ultracold magnetic lanthanide atoms chaotic scattering emerges due to a combination of anisotropic interaction potentials and Zeeman coupling under an external magnetic field. This scattering is studied in a collaborative experimental and theoretical effort for both dysprosium and erbium. We present extensive atom-loss measurements of their dense magnetic Feshbach resonance spectra, analyze their statistical properties, and compare to predictions from a random-matrix-theory inspired model. Furthermore, theoretical coupled-channels simulations of the anisotropic molecular Hamiltonian at zero magnetic field show that weakly-bound, near threshold diatomic levels form overlapping, uncoupled chaotic series that when combined are randomly distributed. The Zeeman interaction shifts and couples these levels, leading to a Feshbach spectrum of zero-energy bound states with nearest-neighbor spacings that changes from randomly to chaotically distributed for increasing magnetic field. Finally, we show that the extreme temperature sensitivity of a small, but sizeable fraction of the resonances in the Dy and Er atom-loss spectra is due to resonant non-zero partial-wave collisions. Our threshold analysis for these resonances indicates a large collision-energy dependence of the three-body recombination rate