(*************************************************************************
 * Copyright (C) 
 *               2019      The University of Exeter 
 *               2018-2019 The University of Paris-Saclay
 *               2018      The University of Sheffield
 *
 * License:
 *   This program can be redistributed and/or modified under the terms
 *   of the 2-clause BSD-style license.
 *
 *   SPDX-License-Identifier: BSD-2-Clause
 *************************************************************************)

(*<*)
theory "02_Background"
  imports "01_Introduction"
begin
(*>*)

chapter*[background::text_section]\<open> Background\<close>
section*[bgrnd1::introduction]\<open>The Isabelle System Architecture\<close>

figure*[architecture::figure,relative_width="95",src="''figures/isabelle-architecture''"]\<open> 
     The system architecture of Isabelle (left-hand side) and the 
     asynchronous communication between the Isabelle system and 
     the IDE (right-hand side). \<close>

text*[bg::introduction]\<open>
While Isabelle @{cite "nipkow.ea:isabelle:2002"} is widely perceived as an interactive theorem 
prover for HOL (Higher-order Logic)~@{cite "nipkow.ea:isabelle:2002"}, we would like to emphasize
the view that Isabelle is far more than that: it is the \<^emph>\<open>Eclipse of Formal Methods Tools\<close>.  This 
refers to the ``\<^emph>\<open>generic system framework of Isabelle/Isar underlying recent versions of Isabelle.  
Among other things, Isar provides an infrastructure for Isabelle plug-ins, comprising extensible 
state components and extensible syntax that can be bound to ML programs. Thus, the Isabelle/Isar 
architecture may be understood as an extension and refinement of the traditional `LCF approach', 
with explicit infrastructure for building derivative systems.\<close>''~@{cite "wenzel.ea:building:2007"} 

The current system framework offers moreover the following features:
\<^item> a build management grouping components into to pre-compiled sessions,
\<^item> a prover IDE (PIDE) framework~@{cite "wenzel:asynchronous:2014"} with various front-ends 
\<^item> documentation-generation,
\<^item> code generators for various target languages,
\<^item> an extensible front-end language Isabelle/Isar, and,
\<^item> last but not least, an LCF style, generic theorem prover kernel as 
  the most prominent and deeply integrated system component.


The Isabelle system architecture shown in @{docitem \<open>architecture\<close>} comes with many layers, 
with Standard ML (SML) at the bottom layer as implementation  language. The architecture actually 
foresees a \<^emph>\<open>Nano-Kernel\<close> (our terminology) which resides in the SML structure \inlinesml{Context}. 
This structure provides a kind of container called \<^emph>\<open>context\<close> providing an identity, an 
ancestor-list as well as typed, user-defined state for components (plugins) such as \isadof. 
On top of the latter, the LCF-Kernel, tactics,  automated proof procedures as well as specific 
support for higher specification constructs were built.\<close>

section*[dof::introduction]\<open>The Document Model Required by \dof\<close>
text\<open>
  In this section, we explain the assumed document model underlying our Document Ontology Framework 
  (\dof) in general. In particular we discuss the concepts \<^emph>\<open>integrated document\<close>, \<^emph>\<open>sub-document\<close>, 
  \<^emph>\<open>text-element\<close> and \<^emph>\<open>semantic macros\<close> occurring inside text-elements. Furthermore, we assume two 
  different levels of parsers (for \<^emph>\<open>outer\<close> and \<^emph>\<open>inner syntax\<close>) where the inner-syntax is basically 
  a typed \inlineisar|\<lambda>|-calculus and some Higher-order Logic (HOL).
\<close>

(*<*)
declare_reference*["fig:dependency"::text_section]
(*>*)


text\<open>
  We assume a hierarchical document model\index{document model}, \ie, an \<^emph>\<open>integrated\<close> document 
  consist of a hierarchy \<^emph>\<open>sub-documents\<close>  (files) that can depend acyclically on each other. 
  Sub-documents can have different document types in order to capture documentations consisting of 
  documentation, models, proofs, code of various forms and other technical artifacts.  We call the 
  main sub-document type, for historical reasons, \<^emph>\<open>theory\<close>-files.  A theory file\bindex{theory!file}
  consists of a \<^emph>\<open>header\<close>\bindex{header}, a \<^emph>\<open>context definition\<close>\index{context}, and a body 
  consisting of a sequence of \<^emph>\<open>command\<close>s (see @{figure (unchecked) "fig:dependency"}). Even the header consists 
  of a sequence of commands used for introductory text elements not depending on any context.  
  The context-definition contains an \inlineisar{import} and a 
  \inlineisar{keyword} section, for example:
\begin{isar}
"  theory Example         (* Name of the 'theory'                     *)
"    imports              (* Declaration of 'theory' dependencies     *)
"      Main               (* Imports a library called 'Main'          *)
"    keywords             (* Registration of keywords defined locally *)
"      requirement        (* A command for describing requirements    *)
\end{isar}
  where \inlineisar{Example} is the abstract name of the text-file,
  \inlineisar{Main} refers to an imported theory (recall that the import
  relation must be acyclic) and \inlineisar{keywords} are used to
  separate commands from each other.

  We distinguish fundamentally two different syntactic levels:
  \<^item> the \emph{outer-syntax}\bindex{syntax!outer}\index{outer syntax|see {syntax, outer}} (\ie, the 
    syntax for commands) is processed by a lexer-library and parser combinators built on top, and
  \<^item> the \emph{inner-syntax}\bindex{syntax!inner}\index{inner syntax|see {syntax, inner}} (\ie, the 
    syntax for \inlineisar|\<lambda>|-terms in HOL) with its own parametric polymorphism type 
    checking.


  On the semantic level, we assume a validation process for an integrated document, where the 
  semantics of a command is a transformation \inlineisar+\<theta> \<rightarrow> \<theta>+ for some system state 
  \inlineisar+\<theta>+. This document model can be instantiated with outer-syntax commands for common 
  text elements, \eg, \inlineisar+section{*...*}+ or \inlineisar+text{*...*}+.  Thus, users can add 
  informal text to a sub-document using a text command:
  \begin{isar}
    text\<Open>This is a description.\<Close>
  \end{isar}
  This will type-set the corresponding text in, for example, a PDF document.  However, this 
  translation is not necessarily one-to-one: text elements can be enriched by formal, \ie, 
  machine-checked content via \emph{semantic macros}, called antiquotations\bindex{antiquotation}:
\begin{isar}
text\<Open>According to the reflexivity axiom <@>{thm refl}, we obtain in \<Gamma> 
      for <@>{term "fac 5"} the result <@>{value "fac 5"}.\<Close>
\end{isar}
which is represented in the final document (\eg, a PDF) by:
\begin{out}
According to the reflexivity axiom $\mathrm{x = x}$, we obtain in $\Gamma$ for $\operatorname{fac} \text{\textrm{5}}$ the result $\text{\textrm{120}}$.
\end{out}
  Semantic macros are partial functions of type \inlineisar+\<theta> \<rightarrow> text+; since they can use the
  system state, they can perform all sorts of specific checks or evaluations (type-checks, 
  executions of code-elements, references to text-elements or proven theorems such as 
  \inlineisar+refl+, which is the reference to the axiom of reflexivity).

  Semantic macros establish \<^emph>\<open>formal content\<close> inside informal content; they can be 
  type-checked before being displayed and can be used for calculations before being 
  typeset. They represent the device for linking the formal with the informal. 
\<close>

figure*["fig:dependency"::figure,relative_width="70",src="''figures/document-hierarchy''"]
       \<open>A Theory-Graph in the Document Model. \<close>

section*[bgrnd21::introduction]\<open>Implementability of the Required Document Model.\<close>
text\<open> 
  Batch-mode checkers for \dof can be implemented in all systems of the LCF-style prover family, 
  \ie, systems with a type-checked \inlinesml{term}, and abstract \inlinesml{thm}-type for
  theorems (protected by a kernel).  This includes, \eg, ProofPower, HOL4, HOL-light, Isabelle, or 
  Coq and its derivatives. \dof is, however, designed for fast interaction in an IDE. If a user wants
  to benefit from this experience, only Isabelle and Coq have the necessary infrastructure of 
  asynchronous proof-processing and support by a PIDE~@{cite "wenzel:asynchronous:2014" and 
  "wenzel:system:2014" and "barras.ea:pervasive:2013"
  and "faithfull.ea:coqoon:2018"} which in many features over-accomplishes the required 
  features of \dof. For example, current Isabelle versions offer cascade-syntaxes (different 
  syntaxes and even parser-technologies which can be nested along the 
  \inlineisar+\<Open> ... \<Close> + barriers, while \dof actually only requires a two-level 
  syntax model.
\<close>

figure*["fig:dof-ide"::figure,relative_width="95",src="''figures/cicm2018-combined''"]\<open> 
     The \isadof IDE (left) and the corresponding PDF (right), showing the first page
      of~\cite{brucker.ea:isabelle-ontologies:2018}.\<close>

text\<open> 
  We call the present implementation of \dof on the Isabelle platform  \isadof. 
  @{docitem "fig:dof-ide"} shows  a screen-shot of an introductory paper on 
  \isadof~@{cite "brucker.ea:isabelle-ontologies:2018"}: the \isadof PIDE can be seen on the left, 
  while the generated presentation in PDF is shown on the right.

  Isabelle provides, beyond the features required for \dof, a lot of additional benefits. For 
  example, it also allows the asynchronous evaluation and checking of the document 
  content~@{cite "wenzel:asynchronous:2014" and "wenzel:system:2014" and
  "barras.ea:pervasive:2013"} and is dynamically extensible. Its PIDE provides a 
  \<^emph>\<open>continuous build, continuous check\<close>  functionality, syntax highlighting, and auto-completion. 
  It also provides infrastructure for displaying meta-information (\eg, binding and type annotation)
  as pop-ups, while hovering over sub-expressions.  A fine-grained dependency analysis allows the 
  processing of individual parts of theory files asynchronously, allowing Isabelle to interactively
  process large (hundreds of theory files) documents.  Isabelle can group sub-documents into sessions,
  \ie, sub-graphs of the document-structure that can be ``pre-compiled'' and loaded
  instantaneously, \ie, without re-processing. \<close>

(*<*) 
end
(*>*)