Experience Implementing a Performant Category-Theory Library in Coq

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to cope with large categorical constructions without slowing proof script processing unacceptably. In this paper, we share the lessons we have learned about how to represent very abstract mathematical objects and arguments in Coq and how future proof assistants might be designed to better support such reasoning. One particular encoding trick to which we draw attention allows category-theoretic arguments involving duality to be internalized in Coq's logic with definitional equality. Ours may be the largest Coq development to date that uses the relatively new Coq version developed by homotopy type theorists, and we reflect on which new features were especially helpful.Comment: The final publication will be available at link.springer.com. This version includes a full bibliography which does not fit in the Springer version; other than the more complete references, this is the version submitted as a final copy to ITP 201

Termination Casts: A Flexible Approach to Termination with General Recursion

This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The central idea is to include a primitive type-form "Terminates t", expressing that term t is terminating; and then allow terms t to be coerced from possibly diverging to total, using a proof of Terminates t. We call such coercions termination casts, and show how to implement terminating recursion using them. For the meta-theory of the system, we describe a translation from Teqt to a logical theory of termination for general recursive, simply typed functions. Every typing judgment of Teqt is translated to a theorem expressing the appropriate termination property of the computational part of the Teqt term.Comment: In Proceedings PAR 2010, arXiv:1012.455

Strategies used as spectroscopy of financial markets reveal new stylized facts

We propose a new set of stylized facts quantifying the structure of financial markets. The key idea is to study the combined structure of both investment strategies and prices in order to open a qualitatively new level of understanding of financial and economic markets. We study the detailed order flow on the Shenzhen Stock Exchange of China for the whole year of 2003. This enormous dataset allows us to compare (i) a closed national market (A-shares) with an international market (B-shares), (ii) individuals and institutions and (iii) real investors to random strategies with respect to timing that share otherwise all other characteristics. We find that more trading results in smaller net return due to trading frictions. We unveiled quantitative power laws with non-trivial exponents, that quantify the deterioration of performance with frequency and with holding period of the strategies used by investors. Random strategies are found to perform much better than real ones, both for winners and losers. Surprising large arbitrage opportunities exist, especially when using zero-intelligence strategies. This is a diagnostic of possible inefficiencies of these financial markets.Comment: 13 pages including 5 figures and 1 tabl

A consistent foundation for Isabelle/HOL

The interactive theorem prover Isabelle/HOL is based on well understood Higher-Order Logic (HOL), which is widely believed to be consistent (and provably consistent in set theory by a standard semantic argument). However, Isabelle/HOL brings its own personal touch to HOL: overloaded constant definitions, used to achieve Haskell-like type classes in the user space. These features are a delight for the users, but unfortunately are not easy to get right as an extension of HOL—they have a history of inconsistent behavior. It has been an open question under which criteria overloaded constant definitions and type definitions can be combined together while still guaranteeing consistency. This paper presents a solution to this problem: non-overlapping definitions and termination of the definition-dependency relation (tracked not only through constants but also through types) ensures relative consistency of Isabelle/HOL

Molecular profiling of signet ring cell colorectal cancer provides a strong rationale for genomic targeted and immune checkpoint inhibitor therapies

We would like to thank all patients whose samples were used in this study. We are also thankful to the Northern Ireland Biobank and Grampian Biorepository for providing us with tissue blocks and patient data; and Dr HG Coleman (Queen’s University Belfast) for her advice on statistical analyses. This work has been carried out with financial support from Cancer Research UK (grant: C11512/A18067), Experimental Cancer Medicine Centre Network (grant: C36697/A15590 from Cancer Research UK and the NI Health and Social Care Research and Development Division), the Sean Crummey Memorial Fund and the Tom Simms Memorial Fund. The Northern Ireland Biobank is funded by HSC Research and Development Division of the Public Health Agency in Northern Ireland and Cancer Research UK through the Belfast CRUK Centre and the Northern Ireland Experimental Cancer Medicine Centre; additional support was received from Friends of the Cancer Centre. The Northern Ireland Molecular Pathology Laboratory which is responsible for creating resources for the Northern Ireland Biobank has received funding from Cancer Research UK, Friends of the Cancer Centre and Sean Crummey Foundation.Peer reviewedPublisher PD

Comprehending Isabelle/HOL's consistency

The proof assistant Isabelle/HOL is based on an extension of Higher-Order Logic (HOL) with ad hoc overloading of constants. It turns out that the interaction between the standard HOL type definitions and the Isabelle-specific ad hoc overloading is problematic for the logical consistency. In previous work, we have argued that standard HOL semantics is no longer appropriate for capturing this interaction, and have proved consistency using a nonstandard semantics. The use of an exotic semantics makes that proof hard to digest by the community. In this paper, we prove consistency by proof-theoretic means—following the healthy intuition of definitions as abbreviations, realized in HOLC, a logic that augments HOL with comprehension types. We hope that our new proof settles the Isabelle/HOL consistency problem once and for all. In addition, HOLC offers a framework for justifying the consistency of new deduction schemas that address practical user needs

Black Vulture Conflict and Management in the United States: Damage Trends, Management Overview, and Research Needs

Contrary to rapid declines of many vulture (Accipitridae, Cathartidea) species worldwide, black vulture (Coragyps atratus) populations are increasing and expanding their range in North America. Vultures exhibit complex behaviors and can adapt to any human-dominated landscape or land use. These traits, combined with population growth and range expansion, have contributed to increased human–vulture conflicts. Our goal was to summarize the current status and trends in human–black vulture conflicts (hereafter human–vulture conflicts), review available management strategies, identify knowledge gaps, and provide recommendations to enhance management and understanding of this species and the associated conflicts. We found human–vulture conflicts are increasing in agriculture (livestock), private and public property (both personal and infrastructure-based), and threats to human health and safety. The greatest increases in conflicts were reported in agriculture and private and public property damage. Regarding livestock depredation, good progress has been made toward assessing producer perceptions of the conflicts, including estimates of economic damage and mitigation strategies, but a basic understanding of the underlying mechanism driving the conflict and advancing strategies to mitigate damage is lacking. For damaged property, little information is available regarding economic losses and perceptions of stakeholders who are experiencing the damage, and most of the tools recommended for mitigating this damage have not been rigorously evaluated. Regarding human health and safety, recent research quantifying flight behavior of black vultures has direct implications for reducing aircraft collision risks. However, it is unclear what factors influence roost site selection and the most effective means to leverage the sensory ecology of the species to mitigate risks. We identify additional knowledge gaps and research needs that if addressed could increase managers’ understanding of black vulture ecology and facilitate enhanced management of this species while simultaneously allowing for the species to provide valuable ecosystem services

Isabelle/DOF: Design and Implementation

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record17th International Conference, SEFM 2019 Oslo, Norway, September 18–20, 2019DOF is a novel framework for defining ontologies and enforcing them during document development and evolution. A major goal of DOF is the integrated development of formal certification documents (e. g., for Common Criteria or CENELEC 50128) that require consistency across both formal and informal arguments. To support a consistent development of formal and informal parts of a document, we provide Isabelle/DOF, an implementation of DOF on top of the formal methods framework Isabelle/HOL. A particular emphasis is put on a deep integration into Isabelleâs IDE, which allows for smooth ontology development as well as immediate ontological feedback during the editing of a document. In this paper, we give an in-depth presentation of the design concepts of DOFâs Ontology Definition Language (ODL) and key aspects of the technology of its implementation. Isabelle/DOF is the first ontology language supporting machine-checked links between the formal and informal parts in an LCF-style interactive theorem proving environment. Sufficiently annotated, large documents can easily be developed collabo- ratively, while ensuring their consistency, and the impact of changes (in the formal and the semi-formal content) is tracked automatically.IRT SystemX, Paris-Saclay, Franc

Food Additives as Inhibitors of Intestinal Drug Transporter OATP2B1

Food additives are compounds that are added to food and beverage to improve the taste, color, preservation, or composition. Generally, food additives are considered safe for human use due to safety evaluations conducted by food safety authorities and high safety margins applied to permitted usage levels. However, the interaction potential of food additives with simultaneously administered medication has not received much attention. Even though many food additives are poorly absorbed into systemic circulation, high concentrations could exist in the intestinal lumen, making intestinal drug transporters, such as the uptake transporter organic anion transporting polypeptide 2B1 (OATP2B1), a possible site of food additive-drug interactions. In the present work, we aimed to characterize the interaction of a selection of 25 food additives including colorants, preservatives, and sweeteners with OATP2B1 in vitro. In human embryonic kidney 293 (HEK293) cells transiently overexpressing OATP2B1 or control, uptake of dibromofluorescein was studied with and without 50 mu M food additive at pH 7.4. As OATP2B1 displays substrate- and pH-dependent transport functions and the intraluminal pH varies along the gastrointestinal tract, we performed the studies also at pH 5.5 using estrone sulfate as an OATP2B1 substrate. Food additives that inhibited OATP2B1-mediated substrate transport by >= 50% were subjected to dose-response studies. Six colorants were identified and validated as OATP2B1 inhibitors at pH 5.5, but only three of these were categorized as inhibitors at pH 7.4. One sweetener was validated as an inhibitor under both assay conditions, whereas none of the preservatives exhibited >= 50% inhibition of OATP2B1-mediated transport. Extrapolation of computed inhibitory constants (K-i values) to estimations of intestinal food additive concentrations implies that selected colorants could inhibit intestinal OATP2B1 also in vivo. These results suggest that food additives, especially colorants, could alter the pharmacokinetics of orally administered OATP2B1 substrate drugs, although further in vivo studies are warranted to understand the overall clinical consequences of the findings.Peer reviewe