The design of modern proof assistants is faced with several sometimes conflicting goals, including scalability, extensibility, and soundness of proof checking. In this paper, we propose a new design for proof assistants, in an attempt to address some of these difficulties. The new design is characterized by a pervasive use of macros in representing and checking proofs, and a foundational format for theory files based on JSON. We realize these ideas in a prototype proof assistant called holpy, implemented in Python. We also demonstrate how proof automation can be extended using Python under this framework. Finally, we present a case study about a simple imperative language.
Languages for defining proof automation is an active area of research. Lean's metaprogramming language @cite_3 allows users to define automation in Lean itself. Another research direction is to add typing to tactic languages @cite_13 @cite_18 . Recent efforts to implement proof assistants in imperative languages include Lean (implemented in C++), and Platzer's work on Orbital @cite_14 and KeYmaera KeYmaera X @cite_7 @cite_9 for reasoning about hybrid systems (implemented in Java Scala).
@cite_18 @cite_14 @cite_7 @cite_9 @cite_3 @cite_13
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We describe the metaprogramming framework currently used in Lean, an interactive theorem prover based on dependent type theory. This framework extends Lean's object language with an API to some of Lean's internal structures and procedures, and provides ways of reflecting object-level expressions into the met alanguage. We provide evidence to show that our implementation is performant, and that it provides a convenient and flexible way of writing not only small-scale interactive tactics, but also more substantial kinds of automation. Scholars are increasingly citing electronic “web references” which are not preserved in libraries or full text archives. WebCite is a new standard for citing web references. To “webcite” a document involves archiving the cited Web page through www.webcitation.org and citing the WebCite permalink instead of (or in addition to) the unstable live Web page. This journal has amended its “instructions for authors” accordingly, asking authors to archive cited Web pages before submitting a manuscript. Almost 200 other journals are already using the system. We discuss the rationale for WebCite, its technology, and how scholars, editors, and publishers can benefit from the service. Citing scholars initiate an archiving process of all cited Web references, ideally before they submit a manuscript. Authors of online documents and websites which are expected to be cited by others can ensure that their work is permanently available by creating an archived copy using WebCite and providing the citation information including the WebCite link on their Web document(s). Editors should ask their authors to cache all cited Web addresses (Uniform Resource Locators, or URLs) “prospectively” before submitting their manuscripts to their journal. Editors and publishers should also instruct their copyeditors to cache cited Web material if the author has not done so already. Finally, WebCite can process publisher submitted “citing articles” (submitted for example as eXtensible Markup Language [XML] documents) to automatically archive all cited Web pages shortly before or on publication. Finally, WebCite can act as a focussed crawler, caching retrospectively references of already published articles. Copyright issues are addressed by honouring respective Internet standards (robot exclusion files, no-cache and no-archive tags). Long-term preservation is ensured by agreements with libraries and digital preservation organizations. The resulting WebCite Index may also have applications for research assessment exercises, being able to measure the impact of Web services and published Web documents through access and Web citation metrics. @PARASPLIT [J Med Internet Res 2005;7(5):e60] A citing sentence is one that appears in a scientific article and cites previous work. Citing sentences have been studied and used in many applications. For example, they have been used in scientific paper summarization, automatic survey generation, paraphrase identification, and citation function classification. Citing sentences that cite multiple papers are common in scientific writing. This observation should be taken into consideration when using citing sentences in applications. For instance, when a citing sentence is used in a summary of a scientific paper, only the fragments of the sentence that are relevant to the summarized paper should be included in the summary. In this paper, we present and compare three different approaches for identifying the fragments of a citing sentence that are related to a given target reference. Our methods are: word classification, sequence labeling, and segment classification. Our experiments show that segment classification achieves the best results. KeYmaera X is a theorem prover for differential dynamic logic ( Open image in new window ), a logic for specifying and verifying properties of hybrid systems. Reasoning about complicated hybrid systems models requires support for sophisticated proof techniques, efficient computation, and a user interface that crystallizes salient properties of the system. KeYmaera X allows users to specify custom proof search techniques as tactics, execute these tactics in parallel, and interface with partial proofs via an extensible user interface. A new form of document coupling called co-citation is defined as the frequency with which two documents are cited together. The co-citation frequency of two scientific papers can be determined by comparing lists of citing documents in the Science Citation Index and counting identical entries. Networks of co-cited papers can be generated for specific scientific specialties, and an example is drawn from the literature of particle physics. Co-citation patterns are found to differ significantly from bibliographic coupling patterns, but to agree generally with patterns of direct citation. Clusters of co-cited papers provide a new way to study the specialty structure of science. They may provide a new approach to indexing and to the creation of SDI profiles. In recent years scholars have built maps of science by connecting the academic fields that cite each other, are cited together, or that cite a similar literature. But since scholars cannot always publish in the fields they cite, or that cite them, these science maps are only rough proxies for the potential of a scholar, organization, or country, to enter a new academic field. Here we use a large dataset of scholarly publications disambiguated at the individual level to create a map of science-or research space-where links connect pairs of fields based on the probability that an individual has published in both of them. We find that the research space is a significantly more accurate predictor of the fields that individuals and organizations will enter in the future than citation based science maps. At the country level, however, the research space and citations based science maps are equally accurate. These findings show that data on career trajectories-the set of fields that individuals have previously published in-provide more accurate predictors of future research output for more focalized units-such as individuals or organizations-than citation based science maps. In a document network such as a citation network of scientific documents, web-logs, etc., the content produced by authors exhibits their interest in certain topics. In addition some authors influence other authors' interests. In this work, we propose to model the influence of cited authors along with the interests of citing authors. Moreover, we hypothesize that apart from the citations present in documents, the context surrounding the citation mention provides extra topical information about the cited authors. However, associating terms in the context to the cited authors remains an open problem. We propose novel document generation schemes that incorporate the context while simultaneously modeling the interests of citing authors and influence of the cited authors. Our experiments show significant improvements over baseline models for various evaluation criteria such as link prediction between document and cited author, and quantitatively explaining unseen text. Abstract Documents in computer-readable form can be used to provide information about other documents, i.e. those they cite. To do this efficiently requires procedures for computer recognition of citing statements. This is not easy, especially for multi-sentence citing statements. Computer recognition procedures have been developed which are accurate to the following extent: 73 of the words in statements selected by computer procedures as being citing statements are words which are correctly attributable to the corresponding documents. The retrieval effectiveness of computer-recognized citing statements was tested in the following way. First, for eight retrieval requests in inorganiic chemistry, average recall by search of Chemical Abstracts Service indexing and Chemical Abstracts abstract text words was found to be 50 . Words from citing statements referring to the papers to be retrieved were then added to the index terms and abstract words as additional access points, and searching was repeated. Average recall increased to 70 . Only words from citing statements published within a year of the cited papers were used. The retrieval effect of citing statement words alone (published within a year) without index or abstract terms was the following: average recall was 40 . When just the words of the titles of the cited papers were added to those citing statement words, average recall increased to 50 . For more than three and one-half decades, beginning in the early 1960s, a heavy emphasis on proof finding has been a key component of the Argonne paradigm, whose use has directly led to significant advances in automated reasoning and important contributions to mathematics and logic. The theorems studied range from the trivial to the deep, even including some that corresponded to open questions. Often the paradigm asks for a theorem whose proof is in hand but that cannot be obtained in a fully automated manner by the program in use. The theorem whose hypothesis consists solely of the Meredith single axiom for two-valued sentential (or propositional) calculus and whose conclusion is the Lukasiewicz three-axiom system for that area of formal logic was just such a theorem. Featured in this article is the methodology that enabled the program OTTER to find the first fully automated proof of the cited theorem, a proof with the intriguing property that none of its steps contains a term of the form i>n(i>n(i>t)) for any term i>t. As evidence of the power of the new methodology, the article also discusses OTTER's success in obtaining the first known proof of a theorem concerning a single axiom of Lukasiewicz. Historically, papers have been physically bound to the journal in which they were published; but in the digital age papers are available individually, no longer tied to their respective journals. Hence, papers now can be read and cited based on their own merits, independently of the journal's physical availability, reputation, or impact factor (IF). We compare the strength of the relationship between journals' IFs and the actual citations received by their respective papers from 1902 to 2009. Throughout most of the 20th century, papers' citation rates were increasingly linked to their respective journals' IFs. However, since 1990, the advent of the digital age, the relation between IFs and paper citations has been weakening. This began first in physics, a field that was quick to make the transition into the electronic domain. Furthermore, since 1990 the overall proportion of highly cited papers coming from highly cited journals has been decreasing and, of these highly cited papers, the proportion not coming from highly cited journals has been increasing. Should this pattern continue, it might bring an end to the use of the IF as a way to evaluate the quality of journals, papers, and researchers. © 2012 Wiley Periodicals, Inc. Lean is a new open source theorem prover being developed at Microsoft Research and Carnegie Mellon University, with a small trusted kernel based on dependent type theory. It aims to bridge the gap between interactive and automated theorem proving, by situating automated tools and methods in a framework that supports user interaction and the construction of fully specified axiomatic proofs. Lean is an ongoing and long-term effort, but it already provides many useful components, integrated development environments, and a rich API which can be used to embed it into other systems. It is currently being used to formalize category theory, homotopy type theory, and abstract algebra. We describe the project goals, system architecture, and main features, and we discuss applications and continuing work. KeYmaera is a hybrid verification tool for hybrid systems that combines deductive, real algebraic, and computer algebraic prover technologies. It is an automated and interactive theorem prover for a natural specification and verification logic for hybrid systems. KeYmaera supports differential dynamic logic, which is a real-valued first-order dynamic logic for hybrid programs, a program notation for hybrid automata. For automating the verification process, KeYmaera implements a generalized free-variable sequent calculus and automatic proof strategies that decompose the hybrid system specification symbolically. To overcome the complexity of real arithmetic, we integrate real quantifier elimination following an iterative background closure strategy. Our tool is particularly suitable for verifying parametric hybrid systems and has been used successfully for verifying collision avoidance in case studies from train control and air traffic management. Citation relationship between scientific publications has been successfully used for scholarly bibliometrics, information retrieval and data mining tasks, and citation-based recommendation algorithms are well documented. While previous studies investigated citation relations from various viewpoints, most of them share the same assumption that, if paper1 cites paper2 (or author1 cites author2), they are connected, regardless of citation importance, sentiment, reason, topic, or motivation. However, this assumption is oversimplified. In this study, we employ an innovative "context-rich heterogeneous network" approach, which paves a new way for citation recommendation task. In the network, we characterize 1) the importance of citation relationships between citing and cited papers, and 2) the topical citation motivation. Unlike earlier studies, the citation information, in this paper, is characterized by citation textual contexts extracted from the full-text citing paper. We also propose algorithm to cope with the situation when large portion of full-text missing information exists in the bibliographic repository. Evaluation results show that, context-rich heterogeneous network can significantly enhance the citation recommendation performance. Part I. Tutorial: 1. Introduction to ML 2. The HOL logic 3. Introduction to proof with HOL 4. Goal-oriented proof: tactics and tacticals 5. Example: a simple parity checker 6. How to program a proof tool 7. Example: the binomial theorem Part II. The Meta-Language ML: 8. The history of ML 9. Introduction and examples 10. Syntax of ML 11. Semantics of ML 12. ML types 13. Primitive ML identifier bindings 14. General purpose and list processing functions 15. ML system functions Part III. The Hol Logic: 16. Syntax and semantics 17. Theories Part IV. The Hol System: 18. The HOL logic in ML Part V. Theorem-Proving With HOL: 19. Derived inference rules 20. Conversions 21. Goal-directed proof: tactics and tacticals Appendices. MSRLM is the release of our internal language modeling tool chain used in Microsoft Research. It was used in our submission for NIST MT 2006. The main difference with other freely available tools is that it was designed to scale to large amounts of data. We successfully built a language model on high end hardware on 40 billion words of web data within 8 hours. It only supports a minimal set of features. Large gigaword language models may be consumed in a first pass machine translation decoding without further processing. This document describes the implementation and usage of the tools summarily. It is our stated goal and hope that this release will be useful to the scientific community. The tool may not be used in a commercial product, or to build models used in a commercial product, or in for any commercial purpose. In addition, we require that you kindly cite this technical report when publishing results derived with this language model tool chain. This describes the LM tool which is available as: http: research.microsoft.com research downloads details 78e26f9c-fc9a-44bb-80a769324c62df8c details.aspx Purpose – The purpose of this paper is to suggest an alternative to the widely used Times Cited criterion for analysing citation networks. The approach involves taking account of the natures of the papers that cite a given paper, so as to differentiate between papers that attract the same number of citations.Design methodology approach – ArticleRank is an algorithm that has been derived from Google's PageRank algorithm to measure the influence of journal articles. ArticleRank is applied to two datasets – a citation network based on an early paper on webometrics, and a self‐citation network based on the 19 most cited papers in the Journal of Documentation – using citation data taken from the Web of Knowledge database.Findings – ArticleRank values provide a different ranking of a set of papers from that provided by the corresponding Times Cited values, and overcomes the inability of the latter to differentiate between papers with the same numbers of citations. The difference in rankings between Times Cited ... The Internet gives individuals more choice in political news and information sources and more tools to filter out disagreeable information. Citing the preference described by selective exposure theory — people prefer information that supports their beliefs and avoid counter-attitudinal information — observers warn that people may use these tools to access only agreeable information and thus live in ideological echo chambers. We report on a field deployment of a browser extension that showed users feedback about the political lean of their weekly and all time reading behaviors. Compared to a control group, showing feedback led to a modest move toward balanced exposure, corresponding to 1-2 visits per week to ideologically opposing sites or 5-10 additional visits per week to centrist sites. In this work, we study the use of Twitter by House, Senate and gubernatorial candidates during the midterm (2010) elections in the U.S. Our data includes almost 700 candidates and over 690k documents that they produced and cited in the 3.5 years leading to the elections. We utilize graph and text mining techniques to analyze differences between Democrats, Republicans and Tea Party candidates, and suggest a novel use of language modeling for estimating content cohesiveness. Our findings show significant differences in the usage patterns of social media, and suggest conservative candidates used this medium more effectively, conveying a coherent message and maintaining a dense graph of connections. Despite the lack of party leadership, we find Tea Party members display both structural and language-based cohesiveness. Finally, we investigate the relation between network structure, content and election results by creating a proof-of-concept model that predicts candidate victory with an accuracy of 88.0 . Classical papers are of great help for beginners to get familiar with a new research area. However, digging them out is a difficult problem. This paper proposes Claper, a novel academic recommendation system based on two proven principles: the Principle of Download Persistence and the Principle of Citation Approaching (we prove them based on real-world datasets). The principle of download persistence indicates that classical papers have few decreasing download frequencies since they were published. The principle of citation approaching indicates that a paper which cites a classical paper is likely to cite citations of that classical paper. Our experimental results based on large-scale real-world datasets illustrate Claper can effectively recommend classical papers of high quality to beginners and thus help them enter their research areas. Modern proof assistants such as Coq and Isabelle provide high degrees of expressiveness and assurance because they support formal reasoning in higher-order logic and supply explicit machine-checkable proof objects. Unfortunately, large scale proof development in these proof assistants is still an extremely difficult and time-consuming task. One major weakness of these proof assistants is the lack of a single language where users can develop complex tactics and decision procedures using a rich programming model and in a typeful manner. This limits the scalability of the proof development process, as users avoid developing domain-specific tactics and decision procedures. In this paper, we present VeriML - a novel language design that couples a type-safe effectful computational language with first-class support for manipulating logical terms such as propositions and proofs. The main idea behind our design is to integrate a rich logical framework - similar to the one supported by Coq - inside a computational language inspired by ML. The language design is such that the added features are orthogonal to the rest of the computational language, and also do not require significant additions to the logic language, so soundness is guaranteed. We have built a prototype implementation of VeriML including both its type-checker and an interpreter. We demonstrate the effectiveness of our design by showing a number of type-safe tactics and decision procedures written in VeriML.