186 lines
12 KiB
Plaintext
Executable File
186 lines
12 KiB
Plaintext
Executable File
(*************************************************************************
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* Copyright (C)
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* 2019-2021 The University of Exeter
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* 2018-2021 The University of Paris-Saclay
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* 2018 The University of Sheffield
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*
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* License:
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* This program can be redistributed and/or modified under the terms
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* of the 2-clause BSD-style license.
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*
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* SPDX-License-Identifier: BSD-2-Clause
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*************************************************************************)
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(*<*)
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theory "02_Background"
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imports "01_Introduction"
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begin
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(*>*)
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chapter*[background::text_section]\<open> Background\<close>
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section*[bgrnd1::introduction]\<open>The Isabelle System Architecture\<close>
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figure*[architecture::figure,relative_width="95",src="''figures/isabelle-architecture''"]\<open>
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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). \<close>
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text*[bg::introduction]\<open>
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While Isabelle @{cite "nipkow.ea:isabelle:2002"} is widely perceived as an interactive theorem
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prover for HOL (Higher-order Logic)~@{cite "nipkow.ea:isabelle:2002"}, we would like to emphasize
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the view that Isabelle is far more than that: it is the \<^emph>\<open>Eclipse of Formal Methods Tools\<close>. This
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refers to the ``\<^emph>\<open>generic system framework of Isabelle/Isar underlying recent versions of Isabelle.
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Among other things, Isar provides an infrastructure for Isabelle plug-ins, comprising extensible
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state components and extensible syntax that can be bound to ML programs. Thus, the Isabelle/Isar
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architecture may be understood as an extension and refinement of the traditional `LCF approach',
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with explicit infrastructure for building derivative systems.\<close>''~@{cite "wenzel.ea:building:2007"}
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The current system framework offers moreover the following features:
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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 various front-ends
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\<^item> documentation-generation,
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\<^item> code generators for various target languages,
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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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The Isabelle system architecture shown in @{docitem \<open>architecture\<close>} comes with many layers,
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with Standard ML (SML) at the bottom layer as implementation language. The architecture actually
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foresees a \<^emph>\<open>Nano-Kernel\<close> (our terminology) which resides in the SML structure\<^boxed_sml>\<open>Context\<close>.
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This structure provides a kind of container called \<^emph>\<open>context\<close> providing an identity, an
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ancestor-list as well as typed, user-defined state for components (plugins) such as \<^isadof>.
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On top of the latter, the LCF-Kernel, tactics, automated proof procedures as well as specific
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support for higher specification constructs were built.\<close>
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section*[dof::introduction]\<open>The Document Model Required by \<^dof>\<close>
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text\<open>
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In this section, we explain the assumed document model underlying our Document Ontology Framework
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(\<^dof>) in general. In particular we discuss the concepts
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\<^emph>\<open>integrated document\<close>\<^bindex>\<open>integrated document\<close>, \<^emph>\<open>sub-document\<close>\<^bindex>\<open>sub-document\<close>,
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\<^emph>\<open>text-element\<close>\<^bindex>\<open>text-element\<close>, and \<^emph>\<open>semantic macros\<close>\<^bindex>\<open>semantic macros\<close> occurring
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inside text-elements. Furthermore, we assume two different levels of parsers
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(for \<^emph>\<open>outer\<close> and \<^emph>\<open>inner syntax\<close>) where the inner-syntax is basically a typed \<open>\<lambda>\<close>-calculus
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and some Higher-order Logic (HOL)\<^bindex>\<open>HOL\<close>.
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\<close>
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(*<*)
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declare_reference*["fig:dependency"::text_section]
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(*>*)
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text\<open>
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We assume a hierarchical document model\<^index>\<open>document model\<close>, \<^ie>, an \<^emph>\<open>integrated\<close> document
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consist of a hierarchy \<^emph>\<open>sub-documents\<close> (files) that can depend acyclically on each other.
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Sub-documents can have different document types in order to capture documentations consisting of
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documentation, models, proofs, code of various forms and other technical artifacts. We call the
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main sub-document type, for historical reasons, \<^emph>\<open>theory\<close>-files. A theory file\<^bindex>\<open>theory!file\<close>
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consists of a \<^emph>\<open>header\<close>\<^bindex>\<open>header\<close>, a \<^emph>\<open>context definition\<close>\<^index>\<open>context\<close>, and a body
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consisting of a sequence of \<^emph>\<open>command\<close>s (see @{figure (unchecked) "fig:dependency"}). Even
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the header consists of a sequence of commands used for introductory text elements not depending on
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any context. The context-definition contains an \<^boxed_theory_text>\<open>import\<close> and a
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\<^boxed_theory_text>\<open>keyword\<close> section, for example:
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@{boxed_theory_text [display]\<open>
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theory Example \<comment>\<open>Name of the 'theory'\<close>
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imports \<comment>\<open>Declaration of 'theory' dependencies\<close>
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Main \<comment>\<open>Imports a library called 'Main'\<close>
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keywords \<comment>\<open>Registration of keywords defined locally\<close>
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requirement \<comment>\<open>A command for describing requirements\<close> \<close>}
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where \<^boxed_theory_text>\<open>Example\<close> is the abstract name of the text-file, \<^boxed_theory_text>\<open>Main\<close>
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refers to an imported theory (recall that the import relation must be acyclic) and
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\<^boxed_theory_text>\<open>keywords\<close> are used to separate commands from each other.
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\<close>
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text\<open> A text-element \<^index>\<open>text-element\<close> may look like this:
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@{boxed_theory_text [display]\<open>
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text\<open> According to the \<^emph>\<open>reflexivity\<close> axiom @{thm refl},
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we obtain in \<Gamma> for @{term "fac 5"} the result @{value "fac 5"}.\<close>\<close>}
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so it is a command \<^theory_text>\<open>text\<close> followed by an argument (here in \<open>\<open> ... \<close>\<close> paranthesis) which
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contains characters and and a special notation for semantic macros \<^bindex>\<open>semantic macros\<close>
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(here \<^theory_text>\<open>@{term "fac 5"}).\<close>
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\<close>
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text\<open>
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We distinguish fundamentally two different syntactic levels:
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\<^item> the \<^emph>\<open>outer-syntax\<close>\<^bindex>\<open>syntax!outer\<close>\<^index>\<open>outer syntax|see {syntax, outer}\<close> (\<^ie>, the
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syntax for commands) is processed by a lexer-library and parser combinators built on top, and
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\<^item> the \<^emph>\<open>inner-syntax\<close>\<^bindex>\<open>syntax!inner\<close>\<^index>\<open>inner syntax|see {syntax, inner}\<close> (\<^ie>, the
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syntax for \<open>\<lambda>\<close>-terms in HOL) with its own parametric polymorphism type checking.
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On the semantic level, we assume a validation process for an integrated document, where the
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semantics of a command is a transformation \<open>\<theta> \<rightarrow> \<theta>\<close> for some system state \<open>\<theta>\<close>.
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This document model can be instantiated with outer-syntax commands for common
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text elements, \<^eg>, \<^theory_text>\<open>section\<open>...\<close>\<close> or \<^theory_text>\<open>text\<open>...\<close>\<close>.
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Thus, users can add informal text to a sub-document using a text command:
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@{boxed_theory_text [display] \<open>text\<open>This is a description.\<close>\<close> }
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This will type-set the corresponding text in, for example, a PDF document. However, this
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translation is not necessarily one-to-one: text elements can be enriched by formal, \<^ie>,
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machine-checked content via \<^emph>\<open>semantic macros\<close>, called antiquotations\<^bindex>\<open>antiquotation\<close>:
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@{boxed_theory_text [display]
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\<open>text\<open> According to the \<^emph>\<open>reflexivity\<close> axiom @{thm refl}, we obtain in \<Gamma>
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for @{term "fac 5"} the result @{value "fac 5"}.\<close>\<close>
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}
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which is represented in the final document (\<^eg>, a PDF) by:
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@{boxed_pdf [display]
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\<open>According to the $\emph{reflexivity}$ axiom $\mathrm{x = x}$, we obtain in $\Gamma$
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for $\operatorname{fac} \text{\textrm{5}}$ the result $\text{\textrm{120}}$.\<close>
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}
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Semantic macros are partial functions of type \<open>\<theta> \<rightarrow> text\<close>; since they can use the
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system state, they can perform all sorts of specific checks or evaluations (type-checks,
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executions of code-elements, references to text-elements or proven theorems such as
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\<open>refl\<close>, which is the reference to the axiom of reflexivity).
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Semantic macros establish \<^emph>\<open>formal content\<close> inside informal content; they can be
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type-checked before being displayed and can be used for calculations before being
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typeset. They represent the device for linking the formal with the informal.
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\<close>
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figure*["fig:dependency"::figure,relative_width="70",src="''figures/document-hierarchy''"]
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\<open>A Theory-Graph in the Document Model. \<close>
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section*[bgrnd21::introduction]\<open>Implementability of the Required Document Model\<close>
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text\<open>
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Batch-mode checkers for \<^dof> can be implemented in all systems of the LCF-style prover family,
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\<^ie>, systems with a type-checked \<open>term\<close>, and abstract \<open>thm\<close>-type for theorems
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(protected by a kernel). This includes, \<^eg>, ProofPower, HOL4, HOL-light, Isabelle, or Coq
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and its derivatives. \<^dof> is, however, designed for fast interaction in an IDE. If a user wants
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to benefit from this experience, only Isabelle and Coq have the necessary infrastructure of
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asynchronous proof-processing and support by a PIDE~@{cite "wenzel:asynchronous:2014" and
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"wenzel:system:2014" and "barras.ea:pervasive:2013" and "faithfull.ea:coqoon:2018"} which
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in many features over-accomplishes the required features of \<^dof>. For example, current Isabelle
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versions offer cascade-syntaxes (different syntaxes and even parser-technologies which can be
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nested along the \<open>\<open>...\<close>\<close> barriers), while \<^dof> actually only requires a two-level syntax model.
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\<close>
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figure*["fig:dof-ide"::figure,relative_width="95",src="''figures/cicm2018-combined''"]\<open>
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The \<^isadof> IDE (left) and the corresponding PDF (right), showing the first page
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of~@{cite "brucker.ea:isabelle-ontologies:2018"}.\<close>
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text\<open>
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We call the present implementation of \<^dof> on the Isabelle platform \<^isadof> .
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@{docitem "fig:dof-ide"} shows a screen-shot of an introductory paper on
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\<^isadof>~@{cite "brucker.ea:isabelle-ontologies:2018"}: the \<^isadof> PIDE can be seen on the left,
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while the generated presentation in PDF is shown on the right.
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Isabelle provides, beyond the features required for \<^dof>, a lot of additional benefits.
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Besides UTF8-support for characters used in text-elements, Isabelle offers built-in already a
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mechanism user-programmable antiquotations \<^index>\<open>antiquotations\<close> which we use to implement
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semantic macros \<^index>\<open>semantic macros\<close> in \<^isadof> (We will actually use these two terms
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as synonym in the context of \<^isadof>). Moreover, \<^isadof> allows for the asynchronous
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evaluation and checking of the document content~@{cite "wenzel:asynchronous:2014" and
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"wenzel:system:2014" and "barras.ea:pervasive:2013"} and is dynamically extensible. Its PIDE
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provides a \<^emph>\<open>continuous build, continuous check\<close> functionality, syntax highlighting, and
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auto-completion. It also provides infrastructure for displaying meta-information (\<^eg>, binding
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and type annotation) as pop-ups, while hovering over sub-expressions. A fine-grained dependency
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analysis allows the processing of individual parts of theory files asynchronously, allowing
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Isabelle to interactively process large (hundreds of theory files) documents. Isabelle can group
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sub-documents into sessions, \<^ie>, sub-graphs of the document-structure that can be ``pre-compiled''
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and loaded instantaneously, \<^ie>, without re-processing, which is an important means to scale up. \<close>
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(*<*)
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end
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(*>*)
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