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

A Vernacular for Coherent Logic

We propose a simple, yet expressive proof representation from which proofs for different proof assistants can easily be generated. The representation uses only a few inference rules and is based on a frag- ment of first-order logic called coherent logic. Coherent logic has been recognized by a number of researchers as a suitable logic for many ev- eryday mathematical developments. The proposed proof representation is accompanied by a corresponding XML format and by a suite of XSL transformations for generating formal proofs for Isabelle/Isar and Coq, as well as proofs expressed in a natural language form (formatted in LATEX or in HTML). Also, our automated theorem prover for coherent logic exports proofs in the proposed XML format. All tools are publicly available, along with a set of sample theorems.Comment: CICM 2014 - Conferences on Intelligent Computer Mathematics (2014

ENIGMA: Efficient Learning-based Inference Guiding Machine

ENIGMA is a learning-based method for guiding given clause selection in saturation-based theorem provers. Clauses from many proof searches are classified as positive and negative based on their participation in the proofs. An efficient classification model is trained on this data, using fast feature-based characterization of the clauses . The learned model is then tightly linked with the core prover and used as a basis of a new parameterized evaluation heuristic that provides fast ranking of all generated clauses. The approach is evaluated on the E prover and the CASC 2016 AIM benchmark, showing a large increase of E's performance.Comment: Submitted to LPAR 201

Environmental pollutants from the Scott and Shackleton expeditions during the ‘Heroic Age’ of Antarctic exploration

Early explorers to Antarctica built wooden huts and brought huge quantities of supplies and equipment to support their geographical and scientific studies for several years. When the expeditions ended and relief ships arrived, a rapid exodus frequently allowed only essential items to be taken north. The huts and thousands of items were left behind. Fuel depots with unused containers of petroleum products, asbestos materials, and diverse chemicals were also left at the huts. This investigation found high concentrations of polyaromatic hydrocarbons in soils under and around the historic fuel depots, including anthracene, benzo[b]fluoranthene, benzo[k]fluoranthene, chrysene, fluorene, and pyrene, as well as benzo[a]anthracene, benzo[a]pyrene, and fluoranthene, which are recognized carcinogens. Asbestos materials within the huts have been identified and extensive amounts of fragmented asbestos were found littering the ground around the Cape Evans hut. These materials are continually abraded and fragmented as tourists walk over them and the coarse scoria breaks and grinds down the materials. A chemical spill, within the Cape Evans hut, apparently from caustic substances from one of the scientific experiments, has caused an unusual deterioration and defibration on affected woods. Although these areas are important historic sites protected by international treaties, the hazardous waste materials left by the early explorers should be removed and remedial action taken to restore the site to as pristine a condition as possible. Recommendations are discussed for international efforts to study and clean up these areas, where the earliest environmental pollution in Antarctica was produced

PhyloCSF: a comparative genomics method to distinguish protein-coding and non-coding regions

As high-throughput transcriptome sequencing provides evidence for novel transcripts in many species, there is a renewed need for accurate methods to classify small genomic regions as protein-coding or non-coding. We present PhyloCSF, a novel comparative genomics method that analyzes a multi-species nucleotide sequence alignment to determine whether it is likely to represent a conserved protein-coding region, based on a formal statistical comparison of phylogenetic codon models. We show that PhyloCSF's classification performance in 12-species _Drosophila_ genome alignments exceeds all other methods we compared in a previous study, and we provide a software implementation for use by the community. We anticipate that this method will be widely applicable as the transcriptomes of many additional species, tissues, and subcellular compartments are sequenced, particularly in the context of ENCODE and modENCODE

A Proof Strategy Language and Proof Script Generation for Isabelle/HOL

We introduce a language, PSL, designed to capture high level proof strategies in Isabelle/HOL. Given a strategy and a proof obligation, PSL's runtime system generates and combines various tactics to explore a large search space with low memory usage. Upon success, PSL generates an efficient proof script, which bypasses a large part of the proof search. We also present PSL's monadic interpreter to show that the underlying idea of PSL is transferable to other ITPs.Comment: This paper has been submitted to CADE2

Screening fungi isolated from historic Discovery Hut on Ross Island, Antarctica for cellulose degradation

To survive in Antarctica, early explorers of Antarctica's Heroic Age erected wooden buildings and brought in large quantities of supplies. The introduction of wood and other organic materials may have provided new nutrient sources for fungi that were indigenous to Antarctica or were brought in with the materials. From 30 samples taken from Discovery Hut, 156 filamentous fungi were isolated on selective media. Of these, 108 were screened for hydrolytic activity on carboxymethyl cellulose, of which 29 demonstrated activities. Endo-1, 4-β-glucanase activity was confirmed in the extracellular supernatant from seven isolates when grown at 4°C, and also when they were grown at 15°C. Cladosporium oxysporum and Geomyces sp. were shown to grow on a variety of synthetic cellulose substrates and to use cellulose as a nutrient source at temperate and cold temperatures. The research findings from the present study demonstrate that Antarctic filamentous fungi isolated from a variety of substrates (wood, straw, and food stuffs) are capable of cellulose degradation and can grow well at low temperatures

A formalized general theory of syntax with bindings

We present the formalization of a theory of syntax with bindings that has been developed and refined over the last decade to support several large formalization efforts. Terms are defined for an arbitrary number of constructors of varying numbers of inputs, quotiented to alpha-equivalence and sorted according to a binding signature. The theory includes a rich collection of properties of the standard operators on terms, such as substitution and freshness. It also includes induction and recursion principles and support for semantic interpretation, all tailored for smooth interaction with the bindings and the standard operators

Hidden breakpoints in genome alignments

During the course of evolution, an organism's genome can undergo changes that affect the large-scale structure of the genome. These changes include gene gain, loss, duplication, chromosome fusion, fission, and rearrangement. When gene gain and loss occurs in addition to other types of rearrangement, breakpoints of rearrangement can exist that are only detectable by comparison of three or more genomes. An arbitrarily large number of these "hidden" breakpoints can exist among genomes that exhibit no rearrangements in pairwise comparisons. We present an extension of the multichromosomal breakpoint median problem to genomes that have undergone gene gain and loss. We then demonstrate that the median distance among three genomes can be used to calculate a lower bound on the number of hidden breakpoints present. We provide an implementation of this calculation including the median distance, along with some practical improvements on the time complexity of the underlying algorithm. We apply our approach to measure the abundance of hidden breakpoints in simulated data sets under a wide range of evolutionary scenarios. We demonstrate that in simulations the hidden breakpoint counts depend strongly on relative rates of inversion and gene gain/loss. Finally we apply current multiple genome aligners to the simulated genomes, and show that all aligners introduce a high degree of error in hidden breakpoint counts, and that this error grows with evolutionary distance in the simulation. Our results suggest that hidden breakpoint error may be pervasive in genome alignments.Comment: 13 pages, 4 figure