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% This file was modified by the DOF LaTeX converter, version 0.0.3
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%
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\begin{isabellebody}%
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\setisabellecontext{IsaDofApplications}%
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%
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\isadelimtheory
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%
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\endisadelimtheory
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%
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\isatagtheory
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%
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\endisatagtheory
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{\isafoldtheory}%
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%
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\isadelimtheory
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\ \isanewline
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\endisadelimtheory
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%
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\isaDofTitle%
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%
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[label={tit}, type={title}]%
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{Using The Isabelle Ontology Framework}%
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%
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\isaDofSubtitle%
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%
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[label={stit}, type={subtitle}]%
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{Linking the Formal with the Informal}%
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%
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\isaDofTextAuthor%
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%
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[label={adb}, type={author}, email={a.brucker{\isacharat}sheffield.ac.uk}, orcid={0000-0002-6355-1200},
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affiliation={University of Sheffield, Sheffield, UK}]%
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{Achim D. Brucker}%
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%
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\isaDofTextAuthor%
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%
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[label={idir}, type={author}, email={idir.aitsadoune{\isacharat}centralesupelec.fr},
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affiliation = {CentraleSupelec, Paris, France}]%
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{Idir Ait-Sadoune}%
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%
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\isaDofTextAuthor%
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%
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[label={paolo}, type={author},email={paolo.crisafulli{\isacharat}irt-systemx.fr},
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affiliation = {IRT-SystemX, Paris, France}]%
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{Paolo Crisafulli}%
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%
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\isaDofTextAuthor%
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%
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[label={bu}, type={author}, email={wolff{\isacharat}lri.fr},
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affiliation={Universit\'e Paris-Sud, Paris, France}]%
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{Burkhart Wolff}%
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%
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\isaDofTextAbstract%
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%
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[label={abs}, type={abstract}, keywordlist={Ontology,Ontological Modeling,Isabelle/DOF}]%
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{
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While Isabelle is mostly known as part of Isabelle/HOL (an interactive
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theorem prover), it actually provides a framework for developing a wide
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spectrum of applications. A particular strength
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of the Isabelle framework is the combination of text editing, formal verification,
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and code generation.
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Up to now, Isabelle's document preparation system lacks a mechanism
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for ensuring the structure of different document types (as, e.g.,
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required in certification processes) in general and, in particular,
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mechanism for linking informal and formal parts of a document.
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In this paper, we present \isadof, a novel Document Ontology Framework
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on top of Isabelle. \isadof allows for conventional typesetting
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\emph{as well} as formal development. We show how to model document
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ontologies inside \isadof, how to use the resulting meta-information
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for enforcing a certain document structure, and discuss ontology-specific IDE support.}%
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%
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\isaDofSectionIntroduction%
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%
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[label={intro}, type={introduction}]%
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{Introduction}%
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%
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\isaDofTextIntroduction%
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%
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[label={introtext}, type={introduction}]%
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{
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The linking of the \emph{formal} to the \emph{informal} is perhaps the
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most pervasive challenge in the digitization of knowledge and its
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propagation. This challenge incites numerous research efforts
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summarized under the labels {\isacharbackquote}{\isacharbackquote}semantic web'', {\isacharbackquote}{\isacharbackquote}data mining'', or any
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form of advanced {\isacharbackquote}{\isacharbackquote}semantic'' text processing. A key role in
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structuring this linking play \emph{document ontologies} (also called
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\emph{vocabulary} in the semantic web
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community~\cite{w3c:ontologies:2015}), \ie, a machine-readable form of
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the structure of documents as well as the document discourse.
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Such ontologies can be used for the scientific discourse within scholarly
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articles, mathematical libraries, and in the engineering discourse
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of standardized software certification documents\cite{boulanger:cenelec-50128:2015,cc:cc-part3:2006}.
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Further applications are the domain-specific discourse in juridical texts or medical reports.
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In general, an ontology is a formal explicit description of \emph{concepts}
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in a domain of discourse (called \emph{classes}), properties of each concept
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describing \emph{attributes} of the concept, as well as \emph{links} between
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them. A particular link between concepts is the \emph{is-a} relation declaring
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the instances of a subclass to be instances of the super-class.
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The main objective of this paper is to present \isadof, a novel
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framework to \emph{model} typed ontologies and to \emph{enforce} them during
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document evolution. Based on Isabelle infrastructures, ontologies may refer to
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types, terms, proven theorems, code, or established assertions.
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Based on a novel adaption of the Isabelle IDE, a document is checked to be
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\emph{conform} to a particular ontology---\isadof is
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designed to give fast user-feedback \emph{during the capture of
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content}. This is particularly valuable in case of document changes,
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where the \emph{coherence} between the formal and the informal parts of the
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content can be mechanically checked.
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To avoid any misunderstanding: \isadof is \emph{not a theory in HOL}
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on ontologies and operations to track and trace links in texts,
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it is an \emph{environment to write structured text} which \emph{may contain}
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Isabelle/HOL definitions and proofs like mathematical articles, tech-reports and
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scientific papers---as the present one, which is written in \isadof
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itself. \isadof is a plugin into the Isabelle/Isar
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framework in the style of~\cite{wenzel.ea:building:2007}.}%
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%
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\isaDofDeclareReferenceTextSection%
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%
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[label={bgrnd}, type={text_section}]%
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%
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%
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\isaDofDeclareReferenceTextSection%
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%
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[label={isadof}, type={text_section}]%
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%
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%
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\isaDofDeclareReferenceTextSection%
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%
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[label={ontomod}, type={text_section}]%
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%
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%
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\isaDofDeclareReferenceTextSection%
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%
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[label={ontopide}, type={text_section}]%
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%
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%
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\isaDofDeclareReferenceTextSection%
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%
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[label={conclusion}, type={text_section}]%
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%
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\begin{isamarkuptext}%
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The plan of the paper is follows: we start by introducing the underlying
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Isabelel sytem (\autoref{bgrnd}) followed by presenting the
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essentials of \isadof and its ontology language (\autoref{isadof}).
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It follows \autoref{ontomod}, where we present three application
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scenarios from the point of view of the ontology modeling. In \autoref{ontopide}
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we discuss the user-interaction generated from the ontological definitions. Finally, we draw
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conclusions and discuss related work in \autoref{conclusion}.%
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\end{isamarkuptext}\isamarkuptrue%
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%
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%
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\isaDofSectionTextSection%
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%
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[label={bgrnd}, type={text_section},
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text_section.main_author={Some({\isacharat}{docitem adb}::author)}]%
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{Background: The Isabelle System}%
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%
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\begin{isamarkuptext}%
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While Isabelle is widely perceived as an interactive theorem prover
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for HOL (Higher-order Logic)~\cite{nipkow.ea:isabelle:2002}, we
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would like to emphasize the view that Isabelle is far more than that:
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it is the \emph{Eclipse of Formal Methods Tools}. This refers to the
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``\textsl{generic system framework of Isabelle/Isar underlying recent
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versions of Isabelle. Among other things, Isar provides an
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infrastructure for Isabelle plug-ins, comprising extensible state
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components and extensible syntax that can be bound to ML
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programs. Thus, the Isabelle/Isar architecture may be understood as
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an extension and refinement of the traditional `LCF approach', with
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explicit infrastructure for building derivative
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\emph{systems}.}''~\cite{wenzel.ea:building:2007}
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The current system framework offers moreover the following features:
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\begin{compactitem}
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\item a build management grouping components into to pre-compiled sessions,
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\item a prover IDE (PIDE) framework~\cite{wenzel:asynchronous:2014} with
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various front-ends
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\item documentation - and code generators,
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\item an extensible front-end language Isabelle/Isar, and,
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\item last but not least, an LCF style, generic theorem prover kernel as
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the most prominent and deeply integrated system component.
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\end{compactitem}%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\isaDofFigure%
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%
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[label={architecture}, type={figure},relative_width={100},
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src={figures/isabelle-architecture}]%
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{The system architecture of Isabelle (left-hand side) and the
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asynchronous communication between the Isabelle system and
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the IDE (right-hand side).}%
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%
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\begin{isamarkuptext}%
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The Isabelle system architecture shown in \autoref{architecture}
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comes with many layers, with Standard ML (SML) at the bottom layer as implementation
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language. The architecture actually foresees a \emph{Nano-Kernel} (our terminology) which
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resides in the SML structure \texttt{Context}. This structure provides a kind of container called
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\emph{context} providing an identity, an ancestor-list as well as typed, user-defined state
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for components (plugins) such as \isadof. On top of the latter, the LCF-Kernel, tactics,
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automated proof procedures as well as specific support for higher specification constructs
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were built.%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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We would like to detail the documentation generation of the architecture,
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which is based on literate specification commands such as \inlineisar+section+ \ldots,
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\inlineisar+subsection+ \ldots, \inlineisar+text+ \ldots, etc.
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Thus, a user can add a simple text:
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\begin{isar}
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text\<Open>This is a description.\<Close>
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\end{isar}
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These text-commands can be arbitrarily mixed with other commands stating definitions, proofs, code, etc.,
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and will result in the corresponding output in generated \LaTeX{} or HTML documents.
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Now, \emph{inside} the textual content, it is possible to embed a \emph{text-antiquotation}:
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\begin{isar}
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text\<Open>According to the reflexivity axiom @{thm refl}, we obtain in \<Gamma>
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for @{term "fac 5"} the result @{value "fac 5"}.\<Close>
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\end{isar}
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which is represented in the generated output by:
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\begin{out}
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According to the reflexivity axiom $x = x$, we obtain in $\Gamma$ for $\operatorname{fac} 5$
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the result $120$.
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\end{out}
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where \inlineisar+refl+ is actually the reference to the axiom of reflexivity in HOL.
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For the antiquotation \inlineisar+@{value "fac 5"}+ we assume the usual definition for
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\inlineisar+fac+ in HOL.%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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Thus, antiquotations can refer to formal content, can be type-checked before being
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displayed and can be used for calculations before actually being typeset. When editing,
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Isabelle's PIDE offers auto-completion and error-messages while typing the above
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\emph{semi-formal} content.%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\isaDofSectionTextSection%
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%
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[label={isadof}, type={text_section},
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text_section.main_author={Some({\isacharat}{docitem adb}::author)}]%
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{\isadof}%
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%
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\begin{isamarkuptext}%
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An \isadof document consists of three components:
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\begin{compactitem}
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\item the \emph{ontology definition} (which is an Isabelle theory file with definitions
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for document-classes and all auxiliary datatypes.
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\item the \emph{core} of the document itself which is an Isabelle theory
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importing the ontology definition. \isadof provides an own family of text-element
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commands such as \inlineisar+title*+, \inlineisar+section*+, \inlineisar+text*+, etc.,
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which can be annotated with meta-information defined in the underlying ontology definition.
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\item the \emph{layout definition} for the given ontology exploiting this meta-information.
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\end{compactitem}
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\isadof is a novel Isabelle system component providing specific support for all these three parts.
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Note that the document core \emph{may}, but \emph{must} not
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use Isabelle definitions or proofs for checking the formal content---the
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present paper is actually an example of a document not containing any proof.
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The document generation process of \isadof is currently restricted to \LaTeX, which means
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that the layout is defined by a set of \LaTeX{} style files. Several layout
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definitions for one ontology are possible and pave the way that different \emph{views} for
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the same central document were generated, addressing the needs of different purposes and/or target
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readers.
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While the ontology and the layout definition will have to be developed by an expert
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with knowledge over Isabelle and \isadof and the back end technology depending on the layout
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definition, the core is intended to require only minimal knowledge of these two. Document core
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authors \emph{can} use \LaTeX{} commands in their source, but this limits the possibility
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of using different representation technologies, \eg, HTML, and increases the risk of arcane
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error-messages in generated \LaTeX{}.
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The \isadof ontology specification language consists basically on a notation for
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document classes, where the attributes were typed with HOL-types and can be instantiated
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by terms HOL-terms, \ie, the actual parsers and type-checkers of the Isabelle system were reused.
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This has the particular advantage that \isadof commands can be arbitrarily mixed with
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Isabelle/HOL commands providing the machinery for type declarations and term specifications such
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as enumerations. In particular, document class definitions provide:
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\begin{compactitem}
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\item a HOL-type for each document class as well as inheritance,
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\item support for attributes with HOL-types and optional default values,
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\item support for overriding of attribute defaults but not overloading, and
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\item text-elements annotated with document classes; they are mutable
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instances of document classes.
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\end{compactitem}
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Attributes referring to other ontological concepts are called \emph{links}.
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The HOL-types inside the document specification language support built-in types for Isabelle/HOL \inlineisar+typ+'s,
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\inlineisar+term+'s, and \inlineisar+thm+'s reflecting internal Isabelle's internal types
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for these entities; when denoted in HOL-terms to instantiate an attribute, for example, there is a
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specific syntax (called \emph{inner syntax antiquotations}) that is checked by \isadof
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for consistency.
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Document classes can have a \inlineisar+where+ clause containing a regular
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expression over class names. Classes with such a \inlineisar+where+ were called \emph{monitor classes}.
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While document classes and their inheritance relation structure meta-data of text-elements
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in an object-oriented manner, monitor classes enforce structural organization
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of documents via the language specified by the regular expression
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enforcing a sequence of text-elements that must belong to the corresponding classes.
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To start using \isadof, one creates an Isabelle project (with the name
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\inlinebash{IsaDofApplications}):
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\begin{bash}
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isabelle DOF_mkroot -o scholarly_paper -t lncs -d IsaDofApplications
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\end{bash}
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where the \inlinebash{-o scholarly_paper} specifies the ontology for writing scientific articles and
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\inlinebash{-t lncs} specifies the use of Springer's \LaTeX-configuration for the Lecture Notes in Computer Science series. The project
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can be formally checked, including the generation of the article in PDF using the
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following command:
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\begin{bash}
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isabelle build -d . IsaDofApplications
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\end{bash}%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\isaDofSectionTechnical%
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%
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[label={ontomod}, type={technical}]%
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{Modeling Ontologies in \isadof}%
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%
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\begin{isamarkuptext}%
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In this section, we will use the \isadof document ontology language
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for three different application scenarios: for scholarly papers, for mathematical
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exam sheets as well as standardization documents where the concepts of the
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standard are captured in the ontology. For space reasons, we will concentrate in all three
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cases on aspects of the modeling due to space limitations.%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\isaDofSubsectionExample%
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%
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[label={scholar_onto}, type={example}]%
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{The Scholar Paper Scenario: Eating One's Own Dog Food.}%
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%
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\begin{isamarkuptext}%
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The following ontology is a simple ontology modeling scientific papers. In this
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\isadof application scenario, we deliberately refrain from integrating references to
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(Isabelle) formal content in order demonstrate that \isadof is not a framework from
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Isabelle users to Isabelle users only.
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Of course, such references can be added easily and represent a particular strength
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of \isadof.
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\begin{figure}
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\begin{isar}
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doc_class title =
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short_title :: "string option" <= None
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doc_class subtitle =
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abbrev :: "string option" <= None
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doc_class author =
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affiliation :: "string"
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doc_class abstract =
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keyword_list :: "string list" <= None
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doc_class text_section =
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main_author :: "author option" <= None
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todo_list :: "string list" <= "[]"
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\end{isar}
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\caption{The core of the ontology definition for writing scholarly papers.}
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\label{fig:paper-onto-core}
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\end{figure}
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The first part of the ontology \inlineisar+scholarly_paper+ (see \autoref{fig:paper-onto-core})
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contains the document class definitions
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with the usual text-elements of a scientific paper. The attributes \inlineisar+short_title+,
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\inlineisar+abbrev+ etc are introduced with their types as well as their default values.
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Our model prescribes an optional \inlineisar+main_author+ and a todo-list attached to an arbitrary
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text section; since instances of this class are mutable (meta)-objects of text-elements, they
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can be modified arbitrarily through subsequent text and of course globally during text evolution.
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Since \inlineisar+author+ is a HOL-type internally generated by \isadof framework and can therefore
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appear in the \inlineisar+main_author+ attribute of the \inlineisar+text_section+ class;
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semantic links between concepts can be modeled this way.
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The translation of its content to, \eg, Springer's \LaTeX{} setup for the Lecture Notes in Computer
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Science Series, as required by many scientific conferences, is mostly straight-forward.%
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\end{isamarkuptext}\isamarkuptrue%
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%
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\isaDofFigure%
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%
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[label={fig1}, type={figure}, spawn_columns=False,relative_width={95},
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src={figures/Dogfood-Intro}]%
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{Ouroboros I: This paper from inside \ldots}%
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%
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\begin{isamarkuptext}%
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\autoref{fig1} shows the corresponding view in the Isabelle/PIDE of the present paper.
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Note that the text uses \isadof's own text-commands containing the meta-information provided by
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the underlying ontology.
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We proceed by a definition of \inlineisar+introduction+'s, which we define as the extension of
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\inlineisar+text_section+ which is intended to capture common infrastructure:
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\begin{isar}
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doc_class introduction = text_section +
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comment :: string
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\end{isar}
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As a consequence of the definition as extension, the \inlineisar+introduction+ class
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inherits the attributes \inlineisar+main_author+ and \inlineisar+todo_list+ together with
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the corresponding default values.
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As a variant of the introduction, we could add here an attribute that contains the formal
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claims of the article --- either here, or, for example, in the keyword list of the abstract.
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As type, one could use either the built-in type \inlineisar+term+ (for syntactically correct,
|
||||
but not necessarily proven entity) or \inlineisar+thm+ (for formally proven entities). It suffices
|
||||
to add the line:
|
||||
\begin{isar}
|
||||
claims :: "thm list"
|
||||
\end{isar}
|
||||
and to extent the \LaTeX-style accordingly to handle the additional field.
|
||||
Note that \inlineisar+term+ and \inlineisar+thm+ are types reflecting the core-types of the
|
||||
Isabelle kernel. In a corresponding conclusion section, one could model analogously an
|
||||
achievement section; by programming a specific compliance check in SML, the implementation
|
||||
of automated forms of validation check for specific categories of papers is envisageable.
|
||||
Since this requires deeper knowledge in Isabelle programming, however, we consider this out
|
||||
of the scope of this paper.
|
||||
|
||||
|
||||
We proceed more or less conventionally by the subsequent sections (\autoref{fig:paper-onto-sections})
|
||||
\begin{figure}
|
||||
\begin{isar}
|
||||
doc_class technical = text_section +
|
||||
definition_list :: "string list" <= "[]"
|
||||
|
||||
doc_class example = text_section +
|
||||
comment :: string
|
||||
|
||||
doc_class conclusion = text_section +
|
||||
main_author :: "author option" <= None
|
||||
|
||||
doc_class related_work = conclusion +
|
||||
main_author :: "author option" <= None
|
||||
|
||||
doc_class bibliography =
|
||||
style :: "string option" <= "''LNCS''"
|
||||
\end{isar}
|
||||
\caption{Various types of sections of a scholarly papers.}
|
||||
\label{fig:paper-onto-sections}
|
||||
\end{figure}
|
||||
and finish with a monitor class definition that enforces a textual ordering
|
||||
in the document core by a regular expression (\autoref{fig:paper-onto-monitor}).
|
||||
\begin{figure}
|
||||
\begin{isar}
|
||||
doc_class article =
|
||||
trace :: "(title + subtitle + author+ abstract +
|
||||
introduction + technical + example +
|
||||
conclusion + bibliography) list"
|
||||
where "(title ~~ \<lbrakk>subtitle\<rbrakk> ~~ \<lbrace>author\<rbrace>$^+$+ ~~ abstract ~~
|
||||
introduction ~~ \<lbrace>technical || example\<rbrace>$^+$ ~~ conclusion ~~
|
||||
bibliography)"
|
||||
\end{isar}
|
||||
\caption{A monitor for the scholarly paper ontology.}
|
||||
\label{fig:paper-onto-monitor}
|
||||
\end{figure}%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
We might wish to add a component into our ontology that models figures to be included into
|
||||
the document. This boils down to the exercise of modeling structured data in the style of a
|
||||
functional programming language in HOL and to reuse the implicit HOL-type inside a suitable document
|
||||
class \inlineisar+figure+:
|
||||
\begin{isar}
|
||||
datatype placement = h | t | b | ht | hb
|
||||
doc_class figure = text_section +
|
||||
relative_width :: "string" (* percent of textwidth *)
|
||||
src :: "string"
|
||||
placement :: placement
|
||||
spawn_columns :: bool <= True
|
||||
\end{isar}%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
Alternatively, by including the HOL-libraries for rationals, it is possible to
|
||||
use fractions or even mathematical reals. This must be counterbalanced by syntactic
|
||||
and semantic convenience. Choosing the mathematical reals, \eg, would have the drawback that
|
||||
attribute evaluation could be substantially more complicated.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofFigure%
|
||||
%
|
||||
[label={fig_figures}, type={figure}, spawn_columns=False,relative_width={85},
|
||||
src={figures/Dogfood-figures}]%
|
||||
{Ouroboros II: figures \ldots}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
The document class \inlineisar+figure+ --- supported by the \isadof text command
|
||||
\inlineisar+figure*+ --- makes it possible to express the pictures and diagrams in this paper
|
||||
such as \autoref{fig_figures}.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofSubsectionExample%
|
||||
%
|
||||
[label={mathex_onto}, type={example}]%
|
||||
{The Math-Exam Scenario}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
The Math-Exam Scenario is an application with mixed formal and
|
||||
semi-formal content. It addresses applications where the author of the exam is not present
|
||||
during the exam and the preparation requires a very rigorous process, as the french
|
||||
\emph{baccaleaureat} and exams at The University of Sheffield.
|
||||
|
||||
We assume that the content has four different types of addressees, which have a different
|
||||
\emph{view} on the integrated document
|
||||
\begin{compactitem}
|
||||
\item the \emph{setter}, \ie, the author of the exam,
|
||||
\item the \emph{checker}, \ie, an internal person that checks the exam for feasibility
|
||||
and non-ambiguity,
|
||||
\item the \emph{external examiner}, \ie, an external person that checks the exam for
|
||||
feasibility and non-ambiguity, and
|
||||
\item the \emph{student}, \ie, the addressee of the exam.
|
||||
\end{compactitem}
|
||||
The latter quality assurance mechanism is used in many universities,
|
||||
where for organizational reasons the execution of an exam takes place in facilities
|
||||
where the author of the exam is not expected to be physically present.
|
||||
Furthermore, we assume a simple grade system (thus, some calculation is required).
|
||||
|
||||
\begin{figure}
|
||||
\begin{isar}
|
||||
doc_class Author = ...
|
||||
datatype Subject = algebra | geometry | statistical
|
||||
datatype Grade = A1 | A2 | A3
|
||||
|
||||
doc_class Header = examTitle :: string
|
||||
examSubject :: Subject
|
||||
date :: string
|
||||
timeAllowed :: int -- minutes
|
||||
|
||||
datatype ContentClass = setter
|
||||
| checker
|
||||
| external_examiner
|
||||
| student
|
||||
|
||||
doc_class Exam_item =
|
||||
concerns :: "ContentClass set"
|
||||
|
||||
doc_class Exam_item =
|
||||
concerns :: "ContentClass set"
|
||||
|
||||
type_synonym SubQuestion = string
|
||||
\end{isar}
|
||||
\caption{The core of the ontology modeling math exams.}
|
||||
\label{fig:onto-exam}
|
||||
\end{figure}
|
||||
The heart of this ontology (see \autoref{fig:onto-exam}) is an alternation of questions and answers,
|
||||
where the answers can consist of simple yes-no answers (QCM style check-boxes) or lists of formulas.
|
||||
Since we do not
|
||||
assume familiarity of the students with Isabelle (\inlineisar+term+ would assume that this is a
|
||||
parse-able and type-checkable entity), we basically model a derivation as a sequence of strings
|
||||
(see \autoref{fig:onto-questions}).
|
||||
\begin{figure}
|
||||
\begin{isar}
|
||||
doc_class Answer_Formal_Step = Exam_item +
|
||||
justification :: string
|
||||
"term" :: "string"
|
||||
|
||||
doc_class Answer_YesNo = Exam_item +
|
||||
step_label :: string
|
||||
yes_no :: bool -- \isa{for\ checkboxes}
|
||||
|
||||
datatype Question_Type =
|
||||
formal | informal | mixed
|
||||
|
||||
doc_class Task = Exam_item +
|
||||
level :: Level
|
||||
type :: Question_Type
|
||||
subitems :: "(SubQuestion *
|
||||
(Answer_Formal_Step list + Answer_YesNo) list) list"
|
||||
concerns :: "ContentClass set" <= "UNIV"
|
||||
mark :: int
|
||||
doc_class Exercise = Exam_item +
|
||||
type :: Question_Type
|
||||
content :: "(Task) list"
|
||||
concerns :: "ContentClass set" <= "UNIV"
|
||||
mark :: int
|
||||
\end{isar}
|
||||
\caption{An exam can contain different types of questions.}
|
||||
\label{fig:onto-questions}
|
||||
\end{figure}
|
||||
|
||||
In many institutions, it makes sense to have a rigorous process of validation
|
||||
for exam subjects: is the initial question correct? Is a proof in the sense of the
|
||||
question possible? We model the possibility that the \isa{examiner} validates a
|
||||
question by a sample proof validated by Isabelle (see \autoref{fig:onto-exam-monitor}). In our scenario this sample proofs
|
||||
are completely \emph{intern}, \ie, not exposed to the students but just additional
|
||||
material for the internal review process of the exam.
|
||||
\begin{figure}
|
||||
\begin{isar}
|
||||
doc_class Validation =
|
||||
tests :: "term list" <="[]"
|
||||
proofs :: "thm list" <="[]"
|
||||
|
||||
doc_class Solution = Exam_item +
|
||||
content :: "Exercise list"
|
||||
valids :: "Validation list"
|
||||
concerns :: "ContentClass set" <= "{setter,checker,external_examiner}"
|
||||
|
||||
doc_class MathExam=
|
||||
content :: "(Header + Author + Exercise) list"
|
||||
global_grade :: Grade
|
||||
where "\<lbrace>Author\<rbrace>$^+$ ~~ Header ~~ \<lbrace>Exercise ~~ Solution\<rbrace>$^+$ "
|
||||
\end{isar}
|
||||
\caption{Validating exams.}
|
||||
\label{fig:onto-exam-monitor}
|
||||
\end{figure}%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofDeclareReferenceFigure%
|
||||
%
|
||||
[label={{fig_qcm}}, type={figure}]%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
Using the \LaTeX{} package hyperref, it is possible to conceive an interactive
|
||||
exam-sheets with multiple-choice and/or free-response elements
|
||||
(see \autoref{fig_qcm}). With the
|
||||
help of the latter, it is possible that students write in a browser a formal mathematical
|
||||
derivation---as part of an algebra exercise, for example---which is submitted to the examiners
|
||||
electronically.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
%
|
||||
\isaDofFigure%
|
||||
%
|
||||
[label={fig_qcm}, type={figure}, spawn_columns=False,relative_width={90},
|
||||
src={figures/InteractiveMathSheet}]%
|
||||
{A Generated QCM Fragment \ldots}%
|
||||
%
|
||||
\isaDofSubsectionExample%
|
||||
%
|
||||
[label={cenelec_onto}, type={example}]%
|
||||
{The Certification Scenario following CENELEC}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
Documents to be provided in formal certifications (such as CENELEC
|
||||
50126/50128, the DO-178B/C, or Common Criteria) can much profit from the control of ontological consistency:
|
||||
a lot of an evaluators work consists in tracing down the links from requirements over
|
||||
assumptions down to elements of evidence, be it in the models, the code, or the tests.
|
||||
In a certification process, traceability becomes a major concern; and providing
|
||||
mechanisms to ensure complete traceability already at the development of the
|
||||
global document will clearly increase speed and reduce risk and cost of a
|
||||
certification process. Making the link-structure machine-checkable, be it between requirements,
|
||||
assumptions, their implementation and their discharge by evidence (be it tests, proofs, or
|
||||
authoritative arguments), is therefore natural and has the potential to decrease the cost
|
||||
of developments targeting certifications. Continuously checking the links between the formal
|
||||
and the semi-formal parts of such documents is particularly valuable during the (usually
|
||||
collaborative) development effort.
|
||||
|
||||
As in many other cases, formal certification documents come with an own terminology and
|
||||
pragmatics of what has to be demonstrated and where, and how the trace-ability of requirements through
|
||||
design-models over code to system environment assumptions has to be assured.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
In the sequel, we present a simplified version of an ontological model used in a
|
||||
case-study~\cite{bezzecchi.ea:making:2018}. We start with an introduction of the concept of requirement
|
||||
(see \autoref{fig:conceptual}).
|
||||
\begin{figure}
|
||||
\begin{isar}
|
||||
doc_class requirement = long_name :: "string option"
|
||||
|
||||
doc_class requirement_analysis = no :: "nat"
|
||||
where "requirement_item +"
|
||||
|
||||
doc_class hypothesis = requirement +
|
||||
hyp_type :: hyp_type <= physical (* default *)
|
||||
|
||||
datatype ass_kind = informal | semiformal | formal
|
||||
|
||||
doc_class assumption = requirement +
|
||||
assumption_kind :: ass_kind <= informal
|
||||
\end{isar}
|
||||
\caption{Modeling requirements.}
|
||||
\label{fig:conceptual}
|
||||
\end{figure}
|
||||
Such ontologies can be enriched by larger explanations and examples, which may help
|
||||
the team of engineers substantially when developing the central document for a certification,
|
||||
like an explication what is precisely the difference between an \emph{hypothesis} and an
|
||||
\emph{assumption} in the context of the evaluation standard. Since the PIDE makes for each
|
||||
document class its definition available by a simple mouse-click, this kind on meta-knowledge
|
||||
can be made far more accessible during the document evolution.
|
||||
|
||||
For example, the term of category \emph{assumption} is used for domain-specific assumptions.
|
||||
It has formal, semi-formal and informal sub-categories. They have to be
|
||||
tracked and discharged by appropriate validation procedures within a
|
||||
certification process, by it by test or proof. It is different from a hypothesis, which is
|
||||
globally assumed and accepted.
|
||||
|
||||
In the sequel, the category \emph{exported constraint} (or \emph{ec} for short)
|
||||
is used for formal assumptions, that arise during the analysis,
|
||||
design or implementation and have to be tracked till the final
|
||||
evaluation target, and discharged by appropriate validation procedures
|
||||
within the certification process, by it by test or proof. A particular class of interest
|
||||
is the category \emph{safety related application condition} (or \emph{srac}
|
||||
for short) which is used for \emph{ec}'s that establish safety properties
|
||||
of the evaluation target. Their track-ability throughout the certification
|
||||
is therefore particularly critical. This is naturally modeled as follows:
|
||||
\begin{isar}
|
||||
doc_class ec = assumption +
|
||||
assumption_kind :: ass_kind <= (*default *) formal
|
||||
|
||||
doc_class srac = ec +
|
||||
assumption_kind :: ass_kind <= (*default *) formal
|
||||
\end{isar}%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofSectionTechnical%
|
||||
%
|
||||
[label={ontopide}, type={technical}]%
|
||||
{Ontology-based IDE support}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
We present a selection of interaction scenarios \autoref{scholar_onto}
|
||||
and \autoref{cenelec_onto} with Isabelle/PIDE instrumented by \isadof.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofSubsectionExample%
|
||||
%
|
||||
[label={scholar_pide}, type={example}]%
|
||||
{A Scholarly Paper}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
In \autoref{fig-Dogfood-II-bgnd1} and \autoref{fig-bgnd-text_section} we show how
|
||||
hovering over links permits to explore its meta-information.
|
||||
Clicking on a document class identifier permits to hyperlink into the corresponding
|
||||
class definition (\autoref{fig:Dogfood-IV-jumpInDocCLass}); hovering over an attribute-definition
|
||||
(which is qualified in order to disambiguate; \autoref{fig:Dogfood-V-attribute}).%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofSideBySideFigure%
|
||||
%
|
||||
[label={{text-elements}}, type={side_by_side_figure},anchor={fig-Dogfood-II-bgnd1}
|
||||
,caption={Exploring a Reference of a Text-Element.}
|
||||
,relative_width={48}
|
||||
,src={figures/Dogfood-II-bgnd1}
|
||||
,anchor2={fig-bgnd-text_section}
|
||||
,caption2={Exploring the class of a text element.}
|
||||
,relative_width2={47}
|
||||
,src2={figures/Dogfood-III-bgnd-text_section}
|
||||
]%
|
||||
{Exploring text elements.}%
|
||||
%
|
||||
\isaDofSideBySideFigure%
|
||||
%
|
||||
[label={{hyperlinks}}, type={side_by_side_figure},anchor={fig:Dogfood-IV-jumpInDocCLass}
|
||||
,caption={Hyperlink to Class-Definition.}
|
||||
,relative_width={48}
|
||||
,src={figures/Dogfood-IV-jumpInDocCLass}
|
||||
,anchor2={fig:Dogfood-V-attribute}
|
||||
,caption2={Exploring an attribute.}
|
||||
,relative_width2={47}
|
||||
,src2={figures/Dogfood-III-bgnd-text_section}
|
||||
]%
|
||||
{Hyperlinks.}%
|
||||
%
|
||||
\isaDofDeclareReferenceFigure%
|
||||
%
|
||||
[label={{figDogfoodVIlinkappl}}, type={figure}]%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
An ontological reference application in
|
||||
\autoref{figDogfoodVIlinkappl}: the
|
||||
ontology-dependant antiquotation \inlineisar|@ {example ...}| refers to the corresponding
|
||||
text-elements. Hovering allows for inspection, clicking for jumping to the definition.
|
||||
If the link does not exist or has a non-compatible type, the text is not validated.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
%
|
||||
\isaDofFigure%
|
||||
%
|
||||
[label={figDogfoodVIlinkappl}, type={figure},relative_width={80},
|
||||
src={figures/Dogfood-V-attribute}]%
|
||||
{Exploring an attribute (hyperlinked to the class).}%
|
||||
%
|
||||
\isaDofSubsectionExample%
|
||||
%
|
||||
[label={cenelec_pide}, type={example}]%
|
||||
{CENELEC}%
|
||||
%
|
||||
\isaDofDeclareReferenceFigure%
|
||||
%
|
||||
[label={figfig3}, type={figure}]%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
The corresponding view in \autoref{figfig3} shows core part of a document,
|
||||
coherent to the \autoref{cenelec_onto}. The first sample shows standard Isabelle antiquotations
|
||||
\cite{wenzel:isabelle-isar:2017} into formal entities of a theory. This way, the informal parts
|
||||
of a document get ``formal content'' and become more robust under change.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
%
|
||||
\isaDofFigure%
|
||||
%
|
||||
[label={figfig3}, type={figure},relative_width={80},
|
||||
src={figures/antiquotations-PIDE}]%
|
||||
{Standard antiquotations referring to theory elements.}%
|
||||
%
|
||||
\isaDofDeclareReferenceFigure%
|
||||
%
|
||||
[label={figfig5}, type={figure}]%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
The subsequent sample in \autoref{figfig5} shows the definition of an
|
||||
\emph{safety-related application condition}, a side-condition of a theorem which
|
||||
has the consequence that a certain calculation must be executed sufficiently fast on an embedded
|
||||
device. This condition can not be established inside the formal theory but has to be
|
||||
checked by system integration tests.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
%
|
||||
\isaDofFigure%
|
||||
%
|
||||
[label={figfig5}, type={figure},relative_width={80},
|
||||
src={figures/srac-definition}]%
|
||||
{Defining a SRAC reference \ldots}%
|
||||
%
|
||||
\isaDofFigure%
|
||||
%
|
||||
[label={figfig7}, type={figure},relative_width={80},
|
||||
src={figures/srac-as-es-application}]%
|
||||
{Using a SRAC as EC document reference.}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
Now we reference in \autoref{figfig7} this safety-related condition;
|
||||
however, this happens in a context where general \emph{exported constraints} are listed.
|
||||
\isadof's checks establish that this is legal in the given ontology.
|
||||
|
||||
This example shows that ontological modeling is indeed adequate for large technical,
|
||||
collaboratively developed documentations, where modifications can lead easily to incoherence.
|
||||
The current checks help to systematically avoid this type of incoherence between formal and
|
||||
informal parts.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isaDofSectionConclusion%
|
||||
%
|
||||
[label={conclusion}, type={conclusion}]%
|
||||
{Conclusion and Related Work}%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
We have demonstrated the use of \isadof, a novel ontology modeling and enforcement
|
||||
IDE deeply integrated into the Isabelle/Isar Framework. The two most distinguishing features are
|
||||
\begin{compactitem}
|
||||
\item \isadof and its ontology language are a strongly typed language that allows
|
||||
for referring (albeit not reasoning) to entities of Isabelle/HOL, most notably types, terms,
|
||||
and (formally proven) theorems, and
|
||||
\item \isadof is supported by the Isabelle/PIDE framework; thus, the advantages of an IDE for
|
||||
text-exploration (which is the type of this link? To which text element does this link refer?
|
||||
Which are the syntactic alternatives here?) were available during editing
|
||||
instead of a post-hoc validation process.
|
||||
\end{compactitem}%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
Of course, a conventional batch-process also exists which can be used
|
||||
for the validation of large document bases in a conventional continuous build process.
|
||||
This combination of formal and semi-informal elements, as well as a systematic enforcement
|
||||
of the coherence to a document ontology of the latter, is, as we believe, novel and offers
|
||||
a unique potential for the semantic treatment of scientific texts and technical documentations.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
To our knowledge, this is the first ontology-driven framework for
|
||||
editing mathematical and technical documents that focuses particularly
|
||||
on documents mixing formal and informal content---a type of documents
|
||||
that is very common in technical certification processes. We see
|
||||
mainly one area of related works: IDEs and text editors that support
|
||||
editing and checking of documents based on an ontology. There is a
|
||||
large group of ontology editors (\eg, Prot{\'e}g{\'e}~\cite{protege},
|
||||
Fluent Editor~\cite{cognitum}, NeOn~\cite{neon}, or
|
||||
OWLGrEd~\cite{owlgred}). With them, we share the support for defining
|
||||
ontologies as well as auto-completion when editing documents based on
|
||||
an ontology. While our ontology definitions are currently based on a
|
||||
textual definition, widely used ontology editors (\eg,
|
||||
OWLGrEd~\cite{owlgred}) also support graphical notations. This could
|
||||
be added to \isadof in the future. A unique feature of \isadof is the
|
||||
deep integration of formal and informal text parts. The only other
|
||||
work in this area wea are aware of is rOntorium~\cite{rontorium}, a plugin
|
||||
for Prot{\'e}g{\'e} that integrates R~\cite{adler:r:2010} into an
|
||||
ontology environment. Here, the main motivation behind this
|
||||
integration is to allow for statistically analyze ontological
|
||||
documents. Thus, this is complementary to our work.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
\isadof in its present form has a number of technical short-comings as well
|
||||
as potentials not yet explored. On the long list of the short-comings is the
|
||||
fact that strings inside HOL-terms do not support, for example, Unicode.
|
||||
For the moment, \isadof is conceived as an
|
||||
add-on for Isabelle/HOL; a much deeper integration of \isadof into Isabelle
|
||||
could increase both performance and uniformity. Finally, different target
|
||||
presentation (such as HTML) would be highly desirable in particular for the
|
||||
math exam scenarios. And last but not least, it would be desirable that PIDE
|
||||
itself is ``ontology-aware'' and can, for example, use meta-information
|
||||
to control read- and write accesses of \emph{parts} of documents.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isamarkupparagraph{Availability.%
|
||||
}
|
||||
\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
The implementation of the framework, the discussed ontology definitions,
|
||||
and examples are available at
|
||||
\url{https://git.logicalhacking.com/HOL-OCL/Isabelle_DOF/}.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isamarkupparagraph{Acknowledgement.%
|
||||
}
|
||||
\isamarkuptrue%
|
||||
%
|
||||
\begin{isamarkuptext}%
|
||||
This work was partly supported by the framework of IRT SystemX, Paris-Saclay, France,
|
||||
and therefore granted with public funds within the scope of the
|
||||
Program ``Investissements d’Avenir''.%
|
||||
\end{isamarkuptext}\isamarkuptrue%
|
||||
%
|
||||
\isadelimtheory
|
||||
%
|
||||
\endisadelimtheory
|
||||
%
|
||||
\isatagtheory
|
||||
%
|
||||
\endisatagtheory
|
||||
{\isafoldtheory}%
|
||||
%
|
||||
\isadelimtheory
|
||||
%
|
||||
\endisadelimtheory
|
||||
%
|
||||
\end{isabellebody}%
|
||||
%%% Local Variables:
|
||||
%%% mode: latex
|
||||
%%% TeX-master: "root"
|
||||
%%% End:
|
Loading…
Reference in New Issue