doc-src/Codegen/Thy/document/Codegen.tex

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-\begin{isabellebody}%
-\def\isabellecontext{Codegen}%
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-{\isafoldtheory}%
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-\isadelimML
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-\endisadelimML
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-\isatagML
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-\endisatagML
-{\isafoldML}%
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-\isadelimML
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-\endisadelimML
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-\isamarkupchapter{Code generation from Isabelle theories%
-}
-\isamarkuptrue%
-%
-\isamarkupsection{Introduction%
-}
-\isamarkuptrue%
-%
-\isamarkupsubsection{Motivation%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Executing formal specifications as programs is a well-established
-  topic in the theorem proving community.  With increasing
-  application of theorem proving systems in the area of
-  software development and verification, its relevance manifests
-  for running test cases and rapid prototyping.  In logical
-  calculi like constructive type theory,
-  a notion of executability is implicit due to the nature
-  of the calculus.  In contrast, specifications in Isabelle
-  can be highly non-executable.  In order to bridge
-  the gap between logic and executable specifications,
-  an explicit non-trivial transformation has to be applied:
-  code generation.
-
-  This tutorial introduces a generic code generator for the
-  Isabelle system \cite{isa-tutorial}.
-  Generic in the sense that the
-  \qn{target language} for which code shall ultimately be
-  generated is not fixed but may be an arbitrary state-of-the-art
-  functional programming language (currently, the implementation
-  supports SML \cite{SML}, OCaml \cite{OCaml} and Haskell
-  \cite{haskell-revised-report}).
-  We aim to provide a
-  versatile environment
-  suitable for software development and verification,
-  structuring the process
-  of code generation into a small set of orthogonal principles
-  while achieving a big coverage of application areas
-  with maximum flexibility.
-
-  Conceptually the code generator framework is part
-  of Isabelle's \isa{Pure} meta logic; the object logic
-  \isa{HOL} which is an extension of \isa{Pure}
-  already comes with a reasonable framework setup and thus provides
-  a good working horse for raising code-generation-driven
-  applications.  So, we assume some familiarity and experience
-  with the ingredients of the \isa{HOL} \emph{Main} theory
-  (see also \cite{isa-tutorial}).%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Overview%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The code generator aims to be usable with no further ado
-  in most cases while allowing for detailed customization.
-  This manifests in the structure of this tutorial:
-  we start with a generic example \secref{sec:example}
-  and introduce code generation concepts \secref{sec:concept}.
-  Section
-  \secref{sec:basics} explains how to use the framework naively,
-  presuming a reasonable default setup.  Then, section
-  \secref{sec:advanced} deals with advanced topics,
-  introducing further aspects of the code generator framework
-  in a motivation-driven manner.  Last, section \secref{sec:ml}
-  introduces the framework's internal programming interfaces.
-
-  \begin{warn}
-    Ultimately, the code generator which this tutorial deals with
-    is supposed to replace the already established code generator
-    by Stefan Berghofer \cite{Berghofer-Nipkow:2002}.
-    So, for the moment, there are two distinct code generators
-    in Isabelle.
-    Also note that while the framework itself is
-    object-logic independent, only \isa{HOL} provides a reasonable
-    framework setup.    
-  \end{warn}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{An example: a simple theory of search trees \label{sec:example}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-When writing executable specifications using \isa{HOL},
-  it is convenient to use
-  three existing packages: the datatype package for defining
-  datatypes, the function package for (recursive) functions,
-  and the class package for overloaded definitions.
-
-  We develope a small theory of search trees; trees are represented
-  as a datatype with key type \isa{{\isacharprime}a} and value type \isa{{\isacharprime}b}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{datatype}\isamarkupfalse%
-\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree\ {\isacharequal}\ Leaf\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}linorder{\isachardoublequoteclose}\ {\isacharprime}b\isanewline
-\ \ {\isacharbar}\ Branch\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharprime}a{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent Note that we have constrained the type of keys
-  to the class of total orders, \isa{linorder}.
-
-  We define \isa{find} and \isa{update} functions:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{primrec}\isamarkupfalse%
-\isanewline
-\ \ find\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharprime}a{\isasymColon}linorder{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ option{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}find\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\ it\ {\isacharequal}\ {\isacharparenleft}if\ it\ {\isacharequal}\ key\ then\ Some\ val\ else\ None{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}find\ {\isacharparenleft}Branch\ t{\isadigit{1}}\ key\ t{\isadigit{2}}{\isacharparenright}\ it\ {\isacharequal}\ {\isacharparenleft}if\ it\ {\isasymle}\ key\ then\ find\ t{\isadigit{1}}\ it\ else\ find\ t{\isadigit{2}}\ it{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{fun}\isamarkupfalse%
-\isanewline
-\ \ update\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}linorder\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a{\isacharcomma}\ {\isacharprime}b{\isacharparenright}\ searchtree{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}\isanewline
-\ \ \ \ if\ it\ {\isacharequal}\ key\ then\ Leaf\ key\ entry\isanewline
-\ \ \ \ \ \ else\ if\ it\ {\isasymle}\ key\isanewline
-\ \ \ \ \ \ then\ Branch\ {\isacharparenleft}Leaf\ it\ entry{\isacharparenright}\ it\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\isanewline
-\ \ \ \ \ \ else\ Branch\ {\isacharparenleft}Leaf\ key\ val{\isacharparenright}\ it\ {\isacharparenleft}Leaf\ it\ entry{\isacharparenright}\isanewline
-\ \ \ {\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ {\isacharparenleft}Branch\ t{\isadigit{1}}\ key\ t{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}\isanewline
-\ \ \ \ if\ it\ {\isasymle}\ key\isanewline
-\ \ \ \ \ \ then\ {\isacharparenleft}Branch\ {\isacharparenleft}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ t{\isadigit{1}}{\isacharparenright}\ key\ t{\isadigit{2}}{\isacharparenright}\isanewline
-\ \ \ \ \ \ else\ {\isacharparenleft}Branch\ t{\isadigit{1}}\ key\ {\isacharparenleft}update\ {\isacharparenleft}it{\isacharcomma}\ entry{\isacharparenright}\ t{\isadigit{2}}{\isacharparenright}{\isacharparenright}\isanewline
-\ \ \ {\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent For testing purpose, we define a small example
-  using natural numbers \isa{nat} (which are a \isa{linorder})
-  as keys and list of nats as values:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ example\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}nat{\isacharcomma}\ nat\ list{\isacharparenright}\ searchtree{\isachardoublequoteclose}\isanewline
-\isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}example\ {\isacharequal}\ update\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharcomma}\ {\isacharbrackleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharbrackright}{\isacharparenright}\ {\isacharparenleft}update\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isacharcomma}\ {\isacharbrackleft}Suc\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharparenright}{\isacharbrackright}{\isacharparenright}\isanewline
-\ \ \ \ {\isacharparenleft}update\ {\isacharparenleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ {\isacharbrackleft}Suc\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharbrackright}{\isacharparenright}\ {\isacharparenleft}Leaf\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}\ {\isacharbrackleft}{\isacharbrackright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent Then we generate code%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ example\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}tree{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent which looks like:
-  \lstsml{Thy/examples/tree.ML}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Code generation concepts and process \label{sec:concept}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-\begin{figure}[h]
-  \centering
-  \includegraphics[width=0.7\textwidth]{codegen_process}
-  \caption{code generator -- processing overview}
-  \label{fig:process}
-  \end{figure}
-
-  The code generator employs a notion of executability
-  for three foundational executable ingredients known
-  from functional programming:
-  \emph{defining equations}, \emph{datatypes}, and
-  \emph{type classes}. A defining equation as a first approximation
-  is a theorem of the form \isa{f\ t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}\ {\isasymdots}\ t\isactrlisub n\ {\isasymequiv}\ t}
-  (an equation headed by a constant \isa{f} with arguments
-  \isa{t\isactrlisub {\isadigit{1}}\ t\isactrlisub {\isadigit{2}}\ {\isasymdots}\ t\isactrlisub n} and right hand side \isa{t}).
-  Code generation aims to turn defining equations
-  into a functional program by running through
-  a process (see figure \ref{fig:process}):
-
-  \begin{itemize}
-
-    \item Out of the vast collection of theorems proven in a
-      \qn{theory}, a reasonable subset modeling
-      defining equations is \qn{selected}.
-
-    \item On those selected theorems, certain
-      transformations are carried out
-      (\qn{preprocessing}).  Their purpose is to turn theorems
-      representing non- or badly executable
-      specifications into equivalent but executable counterparts.
-      The result is a structured collection of \qn{code theorems}.
-
-    \item These \qn{code theorems} then are \qn{translated}
-      into an Haskell-like intermediate
-      language.
-
-    \item Finally, out of the intermediate language the final
-      code in the desired \qn{target language} is \qn{serialized}.
-
-  \end{itemize}
-
-  From these steps, only the two last are carried out
-  outside the logic; by keeping this layer as
-  thin as possible, the amount of code to trust is
-  kept to a minimum.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Basics \label{sec:basics}%
-}
-\isamarkuptrue%
-%
-\isamarkupsubsection{Invoking the code generator%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Thanks to a reasonable setup of the \isa{HOL} theories, in
-  most cases code generation proceeds without further ado:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{primrec}\isamarkupfalse%
-\isanewline
-\ \ fac\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}fac\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}fac\ {\isacharparenleft}Suc\ n{\isacharparenright}\ {\isacharequal}\ Suc\ n\ {\isacharasterisk}\ fac\ n{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent This executable specification is now turned to SML code:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ fac\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}fac{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent  The \isa{{\isasymEXPORTCODE}} command takes a space-separated list of
-  constants together with \qn{serialization directives}
-  These start with a \qn{target language}
-  identifier, followed by a file specification
-  where to write the generated code to.
-
-  Internally, the defining equations for all selected
-  constants are taken, including any transitively required
-  constants, datatypes and classes, resulting in the following
-  code:
-
-  \lstsml{Thy/examples/fac.ML}
-
-  The code generator will complain when a required
-  ingredient does not provide a executable counterpart,
-  e.g.~generating code
-  for constants not yielding
-  a defining equation (e.g.~the Hilbert choice
-  operation \isa{SOME}):%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimML
-%
-\endisadelimML
-%
-\isatagML
-%
-\endisatagML
-{\isafoldML}%
-%
-\isadelimML
-%
-\endisadelimML
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ pick{\isacharunderscore}some\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}pick{\isacharunderscore}some\ xs\ {\isacharequal}\ {\isacharparenleft}SOME\ x{\isachardot}\ x\ {\isasymin}\ set\ xs{\isacharparenright}{\isachardoublequoteclose}%
-\isadelimML
-%
-\endisadelimML
-%
-\isatagML
-%
-\endisatagML
-{\isafoldML}%
-%
-\isadelimML
-%
-\endisadelimML
-\isanewline
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ pick{\isacharunderscore}some\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}fail{\isacharunderscore}const{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent will fail.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Theorem selection%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The list of all defining equations in a theory may be inspected
-  using the \isa{{\isasymPRINTCODESETUP}} command:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{print{\isacharunderscore}codesetup}\isamarkupfalse%
-%
-\begin{isamarkuptext}%
-\noindent which displays a table of constant with corresponding
-  defining equations (the additional stuff displayed
-  shall not bother us for the moment).
-
-  The typical \isa{HOL} tools are already set up in a way that
-  function definitions introduced by \isa{{\isasymDEFINITION}},
-  \isa{{\isasymPRIMREC}}, \isa{{\isasymFUN}},
-  \isa{{\isasymFUNCTION}}, \isa{{\isasymCONSTDEFS}},
-  \isa{{\isasymRECDEF}} are implicitly propagated
-  to this defining equation table. Specific theorems may be
-  selected using an attribute: \emph{code func}. As example,
-  a weight selector function:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{primrec}\isamarkupfalse%
-\isanewline
-\ \ pick\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharparenleft}nat\ {\isasymtimes}\ {\isacharprime}a{\isacharparenright}\ list\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}pick\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}\ n\ {\isacharequal}\ {\isacharparenleft}let\ {\isacharparenleft}k{\isacharcomma}\ v{\isacharparenright}\ {\isacharequal}\ x\ in\isanewline
-\ \ \ \ if\ n\ {\isacharless}\ k\ then\ v\ else\ pick\ xs\ {\isacharparenleft}n\ {\isacharminus}\ k{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent We want to eliminate the explicit destruction
-  of \isa{x} to \isa{{\isacharparenleft}k{\isacharcomma}\ v{\isacharparenright}}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}pick\ {\isacharparenleft}{\isacharparenleft}k{\isacharcomma}\ v{\isacharparenright}{\isacharhash}xs{\isacharparenright}\ n\ {\isacharequal}\ {\isacharparenleft}if\ n\ {\isacharless}\ k\ then\ v\ else\ pick\ xs\ {\isacharparenleft}n\ {\isacharminus}\ k{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-\isanewline
-%
-\endisadelimproof
-\isanewline
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ pick\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}pick{\isadigit{1}}{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent This theorem now is used for generating code:
-
-  \lstsml{Thy/examples/pick1.ML}
-
-  \noindent The policy is that \emph{default equations} stemming from
-  \isa{{\isasymDEFINITION}},
-  \isa{{\isasymPRIMREC}}, \isa{{\isasymFUN}},
-  \isa{{\isasymFUNCTION}}, \isa{{\isasymCONSTDEFS}},
-  \isa{{\isasymRECDEF}} statements are discarded as soon as an
-  equation is explicitly selected by means of \emph{code func}.
-  Further applications of \emph{code func} add theorems incrementally,
-  but syntactic redundancies are implicitly dropped.  For example,
-  using a modified version of the \isa{fac} function
-  as defining equation, the then redundant (since
-  syntactically subsumed) original defining equations
-  are dropped.
-
-  \begin{warn}
-    The attributes \emph{code} and \emph{code del}
-    associated with the existing code generator also apply to
-    the new one: \emph{code} implies \emph{code func},
-    and \emph{code del} implies \emph{code func del}.
-  \end{warn}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Type classes%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Type classes enter the game via the Isar class package.
-  For a short introduction how to use it, see \cite{isabelle-classes};
-  here we just illustrate its impact on code generation.
-
-  In a target language, type classes may be represented
-  natively (as in the case of Haskell).  For languages
-  like SML, they are implemented using \emph{dictionaries}.
-  Our following example specifies a class \qt{null},
-  assigning to each of its inhabitants a \qt{null} value:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{class}\isamarkupfalse%
-\ null\ {\isacharequal}\ type\ {\isacharplus}\isanewline
-\ \ \isakeyword{fixes}\ null\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\isanewline
-\isanewline
-\isacommand{primrec}\isamarkupfalse%
-\isanewline
-\ \ head\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a{\isasymColon}null\ list\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}head\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ null{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}head\ {\isacharparenleft}x{\isacharhash}xs{\isacharparenright}\ {\isacharequal}\ x{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent  We provide some instances for our \isa{null}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{instantiation}\isamarkupfalse%
-\ option\ \isakeyword{and}\ list\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}type{\isacharparenright}\ null\isanewline
-\isakeyword{begin}\isanewline
-\isanewline
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ {\isachardoublequoteopen}null\ {\isacharequal}\ None{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ {\isachardoublequoteopen}null\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{instance}\isamarkupfalse%
-%
-\isadelimproof
-\ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-\isanewline
-\isanewline
-\isacommand{end}\isamarkupfalse%
-%
-\begin{isamarkuptext}%
-\noindent Constructing a dummy example:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ {\isachardoublequoteopen}dummy\ {\isacharequal}\ head\ {\isacharbrackleft}Some\ {\isacharparenleft}Suc\ {\isadigit{0}}{\isacharparenright}{\isacharcomma}\ None{\isacharbrackright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-Type classes offer a suitable occasion to introduce
-  the Haskell serializer.  Its usage is almost the same
-  as SML, but, in accordance with conventions
-  some Haskell systems enforce, each module ends
-  up in a single file. The module hierarchy is reflected in
-  the file system, with root directory given as file specification.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ dummy\ \isakeyword{in}\ Haskell\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lsthaskell{Thy/examples/Codegen.hs}
-  \noindent (we have left out all other modules).
-
-  \medskip
-
-  The whole code in SML with explicit dictionary passing:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ dummy\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}class{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/class.ML}
-
-  \medskip
-
-  \noindent or in OCaml:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ dummy\ \isakeyword{in}\ OCaml\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}class{\isachardot}ocaml{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/class.ocaml}
-
-  \medskip The explicit association of constants
-  to classes can be inspected using the \isa{{\isasymPRINTCLASSES}}
-  command.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{Recipes and advanced topics \label{sec:advanced}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-In this tutorial, we do not attempt to give an exhaustive
-  description of the code generator framework; instead,
-  we cast a light on advanced topics by introducing
-  them together with practically motivated examples.  Concerning
-  further reading, see
-
-  \begin{itemize}
-
-  \item the Isabelle/Isar Reference Manual \cite{isabelle-isar-ref}
-    for exhaustive syntax diagrams.
-  \item or \cite{Haftmann-Nipkow:2007:codegen} which deals with foundational issues
-    of the code generator framework.
-
-  \end{itemize}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Library theories \label{sec:library}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The \isa{HOL} \isa{Main} theory already provides a code
-  generator setup
-  which should be suitable for most applications. Common extensions
-  and modifications are available by certain theories of the \isa{HOL}
-  library; beside being useful in applications, they may serve
-  as a tutorial for customizing the code generator setup.
-
-  \begin{description}
-
-    \item[\isa{Code{\isacharunderscore}Integer}] represents \isa{HOL} integers by big
-       integer literals in target languages.
-    \item[\isa{Code{\isacharunderscore}Char}] represents \isa{HOL} characters by 
-       character literals in target languages.
-    \item[\isa{Code{\isacharunderscore}Char{\isacharunderscore}chr}] like \isa{Code{\isacharunderscore}Char},
-       but also offers treatment of character codes; includes
-       \isa{Code{\isacharunderscore}Integer}.
-    \item[\isa{Efficient{\isacharunderscore}Nat}] \label{eff_nat} implements natural numbers by integers,
-       which in general will result in higher efficency; pattern
-       matching with \isa{{\isadigit{0}}} / \isa{Suc}
-       is eliminated;  includes \isa{Code{\isacharunderscore}Integer}.
-    \item[\isa{Code{\isacharunderscore}Index}] provides an additional datatype
-       \isa{index} which is mapped to target-language built-in integers.
-       Useful for code setups which involve e.g. indexing of
-       target-language arrays.
-    \item[\isa{Code{\isacharunderscore}Message}] provides an additional datatype
-       \isa{message{\isacharunderscore}string} which is isomorphic to strings;
-       \isa{message{\isacharunderscore}string}s are mapped to target-language strings.
-       Useful for code setups which involve e.g. printing (error) messages.
-
-  \end{description}
-
-  \begin{warn}
-    When importing any of these theories, they should form the last
-    items in an import list.  Since these theories adapt the
-    code generator setup in a non-conservative fashion,
-    strange effects may occur otherwise.
-  \end{warn}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Preprocessing%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Before selected function theorems are turned into abstract
-  code, a chain of definitional transformation steps is carried
-  out: \emph{preprocessing}.  In essence, the preprocessor
-  consists of two components: a \emph{simpset} and \emph{function transformers}.
-
-  The \emph{simpset} allows to employ the full generality of the Isabelle
-  simplifier.  Due to the interpretation of theorems
-  as defining equations, rewrites are applied to the right
-  hand side and the arguments of the left hand side of an
-  equation, but never to the constant heading the left hand side.
-  An important special case are \emph{inline theorems} which may be
-  declared an undeclared using the
-  \emph{code inline} or \emph{code inline del} attribute respectively.
-  Some common applications:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\begin{itemize}
-%
-\begin{isamarkuptext}%
-\item replacing non-executable constructs by executable ones:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\ \ \isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ inline{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}x\ {\isasymin}\ set\ xs\ {\isasymlongleftrightarrow}\ x\ mem\ xs{\isachardoublequoteclose}%
-\isadelimproof
-\ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\item eliminating superfluous constants:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\ \ \isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ inline{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharequal}\ Suc\ {\isadigit{0}}{\isachardoublequoteclose}%
-\isadelimproof
-\ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\item replacing executable but inconvenient constructs:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\ \ \isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ inline{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ \ \ {\isachardoublequoteopen}xs\ {\isacharequal}\ {\isacharbrackleft}{\isacharbrackright}\ {\isasymlongleftrightarrow}\ List{\isachardot}null\ xs{\isachardoublequoteclose}%
-\isadelimproof
-\ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\end{itemize}
-%
-\begin{isamarkuptext}%
-\emph{Function transformers} provide a very general interface,
-  transforming a list of function theorems to another
-  list of function theorems, provided that neither the heading
-  constant nor its type change.  The \isa{{\isadigit{0}}} / \isa{Suc}
-  pattern elimination implemented in
-  theory \isa{Efficient{\isacharunderscore}Nat} (see \secref{eff_nat}) uses this
-  interface.
-
-  \noindent The current setup of the preprocessor may be inspected using
-  the \isa{{\isasymPRINTCODESETUP}} command.
-
-  \begin{warn}
-    The attribute \emph{code unfold}
-    associated with the existing code generator also applies to
-    the new one: \emph{code unfold} implies \emph{code inline}.
-  \end{warn}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Concerning operational equality%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Surely you have already noticed how equality is treated
-  by the code generator:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{primrec}\isamarkupfalse%
-\isanewline
-\ \ collect{\isacharunderscore}duplicates\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}a\ list{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ \ \ {\isachardoublequoteopen}collect{\isacharunderscore}duplicates\ xs\ ys\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ xs{\isachardoublequoteclose}\isanewline
-\ \ {\isacharbar}\ {\isachardoublequoteopen}collect{\isacharunderscore}duplicates\ xs\ ys\ {\isacharparenleft}z{\isacharhash}zs{\isacharparenright}\ {\isacharequal}\ {\isacharparenleft}if\ z\ {\isasymin}\ set\ xs\isanewline
-\ \ \ \ \ \ then\ if\ z\ {\isasymin}\ set\ ys\isanewline
-\ \ \ \ \ \ \ \ then\ collect{\isacharunderscore}duplicates\ xs\ ys\ zs\isanewline
-\ \ \ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ xs\ {\isacharparenleft}z{\isacharhash}ys{\isacharparenright}\ zs\isanewline
-\ \ \ \ \ \ else\ collect{\isacharunderscore}duplicates\ {\isacharparenleft}z{\isacharhash}xs{\isacharparenright}\ {\isacharparenleft}z{\isacharhash}ys{\isacharparenright}\ zs{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-The membership test during preprocessing is rewritten,
-  resulting in \isa{op\ mem}, which itself
-  performs an explicit equality check.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ collect{\isacharunderscore}duplicates\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}collect{\isacharunderscore}duplicates{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/collect_duplicates.ML}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Obviously, polymorphic equality is implemented the Haskell
-  way using a type class.  How is this achieved?  HOL introduces
-  an explicit class \isa{eq} with a corresponding operation
-  \isa{eq{\isacharunderscore}class{\isachardot}eq} such that \isa{eq{\isacharunderscore}class{\isachardot}eq\ x\ y\ {\isacharequal}\ {\isacharparenleft}x\ {\isacharequal}\ y{\isacharparenright}}.
-  The preprocessing framework does the rest.
-  For datatypes, instances of \isa{eq} are implicitly derived
-  when possible.  For other types, you may instantiate \isa{eq}
-  manually like any other type class.
-
-  Though this \isa{eq} class is designed to get rarely in
-  the way, a subtlety
-  enters the stage when definitions of overloaded constants
-  are dependent on operational equality.  For example, let
-  us define a lexicographic ordering on tuples:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{instantiation}\isamarkupfalse%
-\ {\isacharasterisk}\ {\isacharcolon}{\isacharcolon}\ {\isacharparenleft}ord{\isacharcomma}\ ord{\isacharparenright}\ ord\isanewline
-\isakeyword{begin}\isanewline
-\isanewline
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ {\isacharbrackleft}code\ func\ del{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}p{\isadigit{1}}\ {\isacharless}\ p{\isadigit{2}}\ {\isasymlongleftrightarrow}\ {\isacharparenleft}let\ {\isacharparenleft}x{\isadigit{1}}{\isacharcomma}\ y{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ p{\isadigit{1}}{\isacharsemicolon}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ p{\isadigit{2}}\ in\isanewline
-\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isacharless}\ y{\isadigit{2}}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{definition}\isamarkupfalse%
-\isanewline
-\ \ {\isacharbrackleft}code\ func\ del{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}p{\isadigit{1}}\ {\isasymle}\ p{\isadigit{2}}\ {\isasymlongleftrightarrow}\ {\isacharparenleft}let\ {\isacharparenleft}x{\isadigit{1}}{\isacharcomma}\ y{\isadigit{1}}{\isacharparenright}\ {\isacharequal}\ p{\isadigit{1}}{\isacharsemicolon}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isacharequal}\ p{\isadigit{2}}\ in\isanewline
-\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isasymle}\ y{\isadigit{2}}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{instance}\isamarkupfalse%
-%
-\isadelimproof
-\ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{{\isachardot}{\isachardot}}\isamarkupfalse%
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-\isanewline
-\isanewline
-\isacommand{end}\isamarkupfalse%
-\isanewline
-\isanewline
-\isacommand{lemma}\isamarkupfalse%
-\ ord{\isacharunderscore}prod\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}ord{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isacharless}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}ord{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isasymle}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isasymle}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{unfolding}\isamarkupfalse%
-\ less{\isacharunderscore}prod{\isacharunderscore}def\ less{\isacharunderscore}eq{\isacharunderscore}prod{\isacharunderscore}def\ \isacommand{by}\isamarkupfalse%
-\ simp{\isacharunderscore}all%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-Then code generation will fail.  Why?  The definition
-  of \isa{op\ {\isasymle}} depends on equality on both arguments,
-  which are polymorphic and impose an additional \isa{eq}
-  class constraint, thus violating the type discipline
-  for class operations.
-
-  The solution is to add \isa{eq} explicitly to the first sort arguments in the
-  code theorems:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ ord{\isacharunderscore}prod{\isacharunderscore}code\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}{\isacharbraceleft}ord{\isacharcomma}\ eq{\isacharbraceright}{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isacharless}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\isanewline
-\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isacharless}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}{\isacharparenleft}x{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}{\isacharbraceleft}ord{\isacharcomma}\ eq{\isacharbraceright}{\isacharcomma}\ y{\isadigit{1}}\ {\isasymColon}\ {\isacharprime}b{\isasymColon}ord{\isacharparenright}\ {\isasymle}\ {\isacharparenleft}x{\isadigit{2}}{\isacharcomma}\ y{\isadigit{2}}{\isacharparenright}\ {\isasymlongleftrightarrow}\isanewline
-\ \ \ \ x{\isadigit{1}}\ {\isacharless}\ x{\isadigit{2}}\ {\isasymor}\ {\isacharparenleft}x{\isadigit{1}}\ {\isacharequal}\ x{\isadigit{2}}\ {\isasymand}\ y{\isadigit{1}}\ {\isasymle}\ y{\isadigit{2}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{unfolding}\isamarkupfalse%
-\ ord{\isacharunderscore}prod\ \isacommand{by}\isamarkupfalse%
-\ rule{\isacharplus}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent Then code generation succeeds:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ {\isasymle}\ {\isasymColon}\ {\isacharprime}a{\isasymColon}{\isacharbraceleft}eq{\isacharcomma}\ ord{\isacharbraceright}\ {\isasymtimes}\ {\isacharprime}b{\isasymColon}ord\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymtimes}\ {\isacharprime}b\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}lexicographic{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/lexicographic.ML}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-In general, code theorems for overloaded constants may have more
-  restrictive sort constraints than the underlying instance relation
-  between class and type constructor as long as the whole system of
-  constraints is coregular; code theorems violating coregularity
-  are rejected immediately.  Consequently, it might be necessary
-  to delete disturbing theorems in the code theorem table,
-  as we have done here with the original definitions \isa{less{\isacharunderscore}prod{\isacharunderscore}def}
-  and \isa{less{\isacharunderscore}eq{\isacharunderscore}prod{\isacharunderscore}def}.
-
-  In some cases, the automatically derived defining equations
-  for equality on a particular type may not be appropriate.
-  As example, watch the following datatype representing
-  monomorphic parametric types (where type constructors
-  are referred to by natural numbers):%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{datatype}\isamarkupfalse%
-\ monotype\ {\isacharequal}\ Mono\ nat\ {\isachardoublequoteopen}monotype\ list{\isachardoublequoteclose}%
-\isadelimproof
-%
-\endisadelimproof
-%
-\isatagproof
-%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-Then code generation for SML would fail with a message
-  that the generated code conains illegal mutual dependencies:
-  the theorem \isa{Mono\ tyco{\isadigit{1}}\ typargs{\isadigit{1}}\ {\isacharequal}\ Mono\ tyco{\isadigit{2}}\ typargs{\isadigit{2}}\ {\isasymequiv}\ tyco{\isadigit{1}}\ {\isacharequal}\ tyco{\isadigit{2}}\ {\isasymand}\ typargs{\isadigit{1}}\ {\isacharequal}\ typargs{\isadigit{2}}} already requires the
-  instance \isa{monotype\ {\isasymColon}\ eq}, which itself requires
-  \isa{Mono\ tyco{\isadigit{1}}\ typargs{\isadigit{1}}\ {\isacharequal}\ Mono\ tyco{\isadigit{2}}\ typargs{\isadigit{2}}\ {\isasymequiv}\ tyco{\isadigit{1}}\ {\isacharequal}\ tyco{\isadigit{2}}\ {\isasymand}\ typargs{\isadigit{1}}\ {\isacharequal}\ typargs{\isadigit{2}}};  Haskell has no problem with mutually
-  recursive \isa{instance} and \isa{function} definitions,
-  but the SML serializer does not support this.
-
-  In such cases, you have to provide you own equality equations
-  involving auxiliary constants.  In our case,
-  \isa{list{\isacharunderscore}all{\isadigit{2}}} can do the job:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ monotype{\isacharunderscore}eq{\isacharunderscore}list{\isacharunderscore}all{\isadigit{2}}\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}Mono\ tyco{\isadigit{1}}\ typargs{\isadigit{1}}\ {\isacharequal}\ Mono\ tyco{\isadigit{2}}\ typargs{\isadigit{2}}\ {\isasymlongleftrightarrow}\isanewline
-\ \ \ \ \ tyco{\isadigit{1}}\ {\isacharequal}\ tyco{\isadigit{2}}\ {\isasymand}\ list{\isacharunderscore}all{\isadigit{2}}\ {\isacharparenleft}op\ {\isacharequal}{\isacharparenright}\ typargs{\isadigit{1}}\ typargs{\isadigit{2}}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ list{\isacharunderscore}all{\isadigit{2}}{\isacharunderscore}eq\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharparenright}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-does not depend on instance \isa{monotype\ {\isasymColon}\ eq}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ {\isacharequal}\ {\isacharcolon}{\isacharcolon}\ monotype\ {\isasymRightarrow}\ monotype\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\isanewline
-\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}monotype{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/monotype.ML}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Programs as sets of theorems%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-As told in \secref{sec:concept}, code generation is based
-  on a structured collection of code theorems.
-  For explorative purpose, this collection
-  may be inspected using the \isa{{\isasymCODETHMS}} command:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{code{\isacharunderscore}thms}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ mod\ {\isacharcolon}{\isacharcolon}\ nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent prints a table with \emph{all} defining equations
-  for \isa{op\ mod}, including
-  \emph{all} defining equations those equations depend
-  on recursivly.  \isa{{\isasymCODETHMS}} provides a convenient
-  mechanism to inspect the impact of a preprocessor setup
-  on defining equations.
-  
-  Similarly, the \isa{{\isasymCODEDEPS}} command shows a graph
-  visualizing dependencies between defining equations.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Constructor sets for datatypes%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Conceptually, any datatype is spanned by a set of
-  \emph{constructors} of type \isa{{\isasymtau}\ {\isacharequal}\ {\isasymdots}\ {\isasymRightarrow}\ {\isasymkappa}\ {\isasymalpha}\isactrlisub {\isadigit{1}}\ {\isasymdots}\ {\isasymalpha}\isactrlisub n}
-  where \isa{{\isacharbraceleft}{\isasymalpha}\isactrlisub {\isadigit{1}}{\isacharcomma}\ {\isasymdots}{\isacharcomma}\ {\isasymalpha}\isactrlisub n{\isacharbraceright}} is excactly the set of \emph{all}
-  type variables in \isa{{\isasymtau}}.  The HOL datatype package
-  by default registers any new datatype in the table
-  of datatypes, which may be inspected using
-  the \isa{{\isasymPRINTCODESETUP}} command.
-
-  In some cases, it may be convenient to alter or
-  extend this table;  as an example, we will develope an alternative
-  representation of natural numbers as binary digits, whose
-  size does increase logarithmically with its value, not linear
-  \footnote{Indeed, the \isa{Efficient{\isacharunderscore}Nat} theory (see \ref{eff_nat})
-    does something similar}.  First, the digit representation:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{definition}\isamarkupfalse%
-\ Dig{\isadigit{0}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{0}}\ n\ {\isacharequal}\ {\isadigit{2}}\ {\isacharasterisk}\ n{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{definition}\isamarkupfalse%
-\ Dig{\isadigit{1}}\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{1}}\ n\ {\isacharequal}\ Suc\ {\isacharparenleft}{\isadigit{2}}\ {\isacharasterisk}\ n{\isacharparenright}{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\noindent We will use these two ">digits"< to represent natural numbers
-  in binary digits, e.g.:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ {\isadigit{4}}{\isadigit{2}}{\isacharcolon}\ {\isachardoublequoteopen}{\isadigit{4}}{\isadigit{2}}\ {\isacharequal}\ Dig{\isadigit{0}}\ {\isacharparenleft}Dig{\isadigit{1}}\ {\isacharparenleft}Dig{\isadigit{0}}\ {\isacharparenleft}Dig{\isadigit{1}}\ {\isacharparenleft}Dig{\isadigit{0}}\ {\isadigit{1}}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp\ add{\isacharcolon}\ Dig{\isadigit{0}}{\isacharunderscore}def\ Dig{\isadigit{1}}{\isacharunderscore}def{\isacharparenright}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent Of course we also have to provide proper code equations for
-  the operations, e.g. \isa{op\ {\isacharplus}}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ plus{\isacharunderscore}Dig\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}{\isadigit{0}}\ {\isacharplus}\ n\ {\isacharequal}\ n{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}m\ {\isacharplus}\ {\isadigit{0}}\ {\isacharequal}\ m{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharplus}\ Dig{\isadigit{0}}\ n\ {\isacharequal}\ Dig{\isadigit{1}}\ n{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{0}}\ m\ {\isacharplus}\ {\isadigit{1}}\ {\isacharequal}\ Dig{\isadigit{1}}\ m{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}{\isadigit{1}}\ {\isacharplus}\ Dig{\isadigit{1}}\ n\ {\isacharequal}\ Dig{\isadigit{0}}\ {\isacharparenleft}n\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{1}}\ m\ {\isacharplus}\ {\isadigit{1}}\ {\isacharequal}\ Dig{\isadigit{0}}\ {\isacharparenleft}m\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{0}}\ m\ {\isacharplus}\ Dig{\isadigit{0}}\ n\ {\isacharequal}\ Dig{\isadigit{0}}\ {\isacharparenleft}m\ {\isacharplus}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{0}}\ m\ {\isacharplus}\ Dig{\isadigit{1}}\ n\ {\isacharequal}\ Dig{\isadigit{1}}\ {\isacharparenleft}m\ {\isacharplus}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{1}}\ m\ {\isacharplus}\ Dig{\isadigit{0}}\ n\ {\isacharequal}\ Dig{\isadigit{1}}\ {\isacharparenleft}m\ {\isacharplus}\ n{\isacharparenright}{\isachardoublequoteclose}\isanewline
-\ \ {\isachardoublequoteopen}Dig{\isadigit{1}}\ m\ {\isacharplus}\ Dig{\isadigit{1}}\ n\ {\isacharequal}\ Dig{\isadigit{0}}\ {\isacharparenleft}m\ {\isacharplus}\ n\ {\isacharplus}\ {\isadigit{1}}{\isacharparenright}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ Dig{\isadigit{0}}{\isacharunderscore}def\ Dig{\isadigit{1}}{\isacharunderscore}def{\isacharparenright}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-%
-\begin{isamarkuptext}%
-\noindent We then instruct the code generator to view \isa{{\isadigit{0}}},
-  \isa{{\isadigit{1}}}, \isa{Dig{\isadigit{0}}} and \isa{Dig{\isadigit{1}}} as
-  datatype constructors:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{code{\isacharunderscore}datatype}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{0}}{\isasymColon}nat{\isachardoublequoteclose}\ {\isachardoublequoteopen}{\isadigit{1}}{\isasymColon}nat{\isachardoublequoteclose}\ Dig{\isadigit{0}}\ Dig{\isadigit{1}}%
-\begin{isamarkuptext}%
-\noindent For the former constructor \isa{Suc}, we provide a code
-  equation and remove some parts of the default code generator setup
-  which are an obstacle here:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{lemma}\isamarkupfalse%
-\ Suc{\isacharunderscore}Dig\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\isanewline
-\ \ {\isachardoublequoteopen}Suc\ n\ {\isacharequal}\ n\ {\isacharplus}\ {\isadigit{1}}{\isachardoublequoteclose}\isanewline
-%
-\isadelimproof
-\ \ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ simp%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-\isanewline
-%
-\endisadelimproof
-\isanewline
-\isacommand{declare}\isamarkupfalse%
-\ One{\isacharunderscore}nat{\isacharunderscore}def\ {\isacharbrackleft}code\ inline\ del{\isacharbrackright}\isanewline
-\isacommand{declare}\isamarkupfalse%
-\ add{\isacharunderscore}Suc{\isacharunderscore}shift\ {\isacharbrackleft}code\ func\ del{\isacharbrackright}%
-\begin{isamarkuptext}%
-\noindent This yields the following code:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ {\isacharplus}\ {\isasymColon}\ nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ nat{\isachardoublequoteclose}\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}nat{\isacharunderscore}binary{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/nat_binary.ML}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-\medskip
-
-  From this example, it can be easily glimpsed that using own constructor sets
-  is a little delicate since it changes the set of valid patterns for values
-  of that type.  Without going into much detail, here some practical hints:
-
-  \begin{itemize}
-    \item When changing the constuctor set for datatypes, take care to
-      provide an alternative for the \isa{case} combinator (e.g. by replacing
-      it using the preprocessor).
-    \item Values in the target language need not to be normalized -- different
-      values in the target language may represent the same value in the
-      logic (e.g. \isa{Dig{\isadigit{1}}\ {\isadigit{0}}\ {\isacharequal}\ {\isadigit{1}}}).
-    \item Usually, a good methodology to deal with the subleties of pattern
-      matching is to see the type as an abstract type: provide a set
-      of operations which operate on the concrete representation of the type,
-      and derive further operations by combinations of these primitive ones,
-      without relying on a particular representation.
-  \end{itemize}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadeliminvisible
-%
-\endisadeliminvisible
-%
-\isataginvisible
-\isacommand{code{\isacharunderscore}datatype}\isamarkupfalse%
-\ {\isachardoublequoteopen}{\isadigit{0}}{\isacharcolon}{\isacharcolon}nat{\isachardoublequoteclose}\ Suc\isanewline
-\isacommand{declare}\isamarkupfalse%
-\ plus{\isacharunderscore}Dig\ {\isacharbrackleft}code\ func\ del{\isacharbrackright}\isanewline
-\isacommand{declare}\isamarkupfalse%
-\ One{\isacharunderscore}nat{\isacharunderscore}def\ {\isacharbrackleft}code\ inline{\isacharbrackright}\isanewline
-\isacommand{declare}\isamarkupfalse%
-\ add{\isacharunderscore}Suc{\isacharunderscore}shift\ {\isacharbrackleft}code\ func{\isacharbrackright}\ \isanewline
-\isacommand{lemma}\isamarkupfalse%
-\ {\isacharbrackleft}code\ func{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}{\isadigit{0}}\ {\isacharplus}\ n\ {\isacharequal}\ {\isacharparenleft}n\ {\isasymColon}\ nat{\isacharparenright}{\isachardoublequoteclose}\ \isacommand{by}\isamarkupfalse%
-\ simp%
-\endisataginvisible
-{\isafoldinvisible}%
-%
-\isadeliminvisible
-%
-\endisadeliminvisible
-%
-\isamarkupsubsection{Customizing serialization%
-}
-\isamarkuptrue%
-%
-\isamarkupsubsubsection{Basics%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Consider the following function and its corresponding
-  SML code:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{primrec}\isamarkupfalse%
-\isanewline
-\ \ in{\isacharunderscore}interval\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ {\isasymtimes}\ nat\ {\isasymRightarrow}\ nat\ {\isasymRightarrow}\ bool{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
-\ \ {\isachardoublequoteopen}in{\isacharunderscore}interval\ {\isacharparenleft}k{\isacharcomma}\ l{\isacharparenright}\ n\ {\isasymlongleftrightarrow}\ k\ {\isasymle}\ n\ {\isasymand}\ n\ {\isasymle}\ l{\isachardoublequoteclose}%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isatagtt
-%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ in{\isacharunderscore}interval\ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}bool{\isacharunderscore}literal{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/bool_literal.ML}
-
-  \noindent Though this is correct code, it is a little bit unsatisfactory:
-  boolean values and operators are materialized as distinguished
-  entities with have nothing to do with the SML-builtin notion
-  of \qt{bool}.  This results in less readable code;
-  additionally, eager evaluation may cause programs to
-  loop or break which would perfectly terminate when
-  the existing SML \qt{bool} would be used.  To map
-  the HOL \qt{bool} on SML \qt{bool}, we may use
-  \qn{custom serializations}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isatagtt
-\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
-\ bool\isanewline
-\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}bool{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ True\ \isakeyword{and}\ False\ \isakeyword{and}\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}true{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}false{\isachardoublequoteclose}\ \isakeyword{and}\ {\isachardoublequoteopen}{\isacharunderscore}\ andalso\ {\isacharunderscore}{\isachardoublequoteclose}{\isacharparenright}%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\begin{isamarkuptext}%
-The \isa{{\isasymCODETYPE}} commad takes a type constructor
-  as arguments together with a list of custom serializations.
-  Each custom serialization starts with a target language
-  identifier followed by an expression, which during
-  code serialization is inserted whenever the type constructor
-  would occur.  For constants, \isa{{\isasymCODECONST}} implements
-  the corresponding mechanism.  Each ``\verb|_|'' in
-  a serialization expression is treated as a placeholder
-  for the type constructor's (the constant's) arguments.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ in{\isacharunderscore}interval\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}bool{\isacharunderscore}mlbool{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/bool_mlbool.ML}
-
-  \noindent This still is not perfect: the parentheses
-  around the \qt{andalso} expression are superfluous.
-  Though the serializer
-  by no means attempts to imitate the rich Isabelle syntax
-  framework, it provides some common idioms, notably
-  associative infixes with precedences which may be used here:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isatagtt
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharparenleft}SML\ \isakeyword{infixl}\ {\isadigit{1}}\ {\isachardoublequoteopen}andalso{\isachardoublequoteclose}{\isacharparenright}%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-\isanewline
-\isanewline
-\isacommand{export{\isacharunderscore}code}\isamarkupfalse%
-\ in{\isacharunderscore}interval\ \ \isakeyword{in}\ SML\ \isakeyword{file}\ {\isachardoublequoteopen}examples{\isacharslash}bool{\isacharunderscore}infix{\isachardot}ML{\isachardoublequoteclose}%
-\begin{isamarkuptext}%
-\lstsml{Thy/examples/bool_infix.ML}
-
-  \medskip
-
-  Next, we try to map HOL pairs to SML pairs, using the
-  infix ``\verb|*|'' type constructor and parentheses:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isatagtt
-\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
-\ {\isacharasterisk}\isanewline
-\ \ {\isacharparenleft}SML\ \isakeyword{infix}\ {\isadigit{2}}\ {\isachardoublequoteopen}{\isacharasterisk}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ Pair\isanewline
-\ \ {\isacharparenleft}SML\ {\isachardoublequoteopen}{\isacharbang}{\isacharparenleft}{\isacharparenleft}{\isacharunderscore}{\isacharparenright}{\isacharcomma}{\isacharslash}\ {\isacharparenleft}{\isacharunderscore}{\isacharparenright}{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\begin{isamarkuptext}%
-The initial bang ``\verb|!|'' tells the serializer to never put
-  parentheses around the whole expression (they are already present),
-  while the parentheses around argument place holders
-  tell not to put parentheses around the arguments.
-  The slash ``\verb|/|'' (followed by arbitrary white space)
-  inserts a space which may be used as a break if necessary
-  during pretty printing.
-
-  These examples give a glimpse what mechanisms
-  custom serializations provide; however their usage
-  requires careful thinking in order not to introduce
-  inconsistencies -- or, in other words:
-  custom serializations are completely axiomatic.
-
-  A further noteworthy details is that any special
-  character in a custom serialization may be quoted
-  using ``\verb|'|''; thus, in
-  ``\verb|fn '_ => _|'' the first
-  ``\verb|_|'' is a proper underscore while the
-  second ``\verb|_|'' is a placeholder.
-
-  The HOL theories provide further
-  examples for custom serializations.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsubsection{Haskell serialization%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-For convenience, the default
-  HOL setup for Haskell maps the \isa{eq} class to
-  its counterpart in Haskell, giving custom serializations
-  for the class (\isa{{\isasymCODECLASS}}) and its operation:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isatagtt
-\isacommand{code{\isacharunderscore}class}\isamarkupfalse%
-\ eq\isanewline
-\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Eq{\isachardoublequoteclose}\ \isakeyword{where}\ {\isachardoublequoteopen}op\ {\isacharequal}{\isachardoublequoteclose}\ {\isasymequiv}\ {\isachardoublequoteopen}{\isacharparenleft}{\isacharequal}{\isacharequal}{\isacharparenright}{\isachardoublequoteclose}{\isacharparenright}\isanewline
-\isanewline
-\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
-\ {\isachardoublequoteopen}op\ {\isacharequal}{\isachardoublequoteclose}\isanewline
-\ \ {\isacharparenleft}Haskell\ \isakeyword{infixl}\ {\isadigit{4}}\ {\isachardoublequoteopen}{\isacharequal}{\isacharequal}{\isachardoublequoteclose}{\isacharparenright}%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\begin{isamarkuptext}%
-A problem now occurs whenever a type which
-  is an instance of \isa{eq} in HOL is mapped
-  on a Haskell-builtin type which is also an instance
-  of Haskell \isa{Eq}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{typedecl}\isamarkupfalse%
-\ bar\isanewline
-\isanewline
-\isacommand{instantiation}\isamarkupfalse%
-\ bar\ {\isacharcolon}{\isacharcolon}\ eq\isanewline
-\isakeyword{begin}\isanewline
-\isanewline
-\isacommand{definition}\isamarkupfalse%
-\ {\isachardoublequoteopen}eq{\isacharunderscore}class{\isachardot}eq\ {\isacharparenleft}x{\isasymColon}bar{\isacharparenright}\ y\ {\isasymlongleftrightarrow}\ x\ {\isacharequal}\ y{\isachardoublequoteclose}\isanewline
-\isanewline
-\isacommand{instance}\isamarkupfalse%
-%
-\isadelimproof
-\ %
-\endisadelimproof
-%
-\isatagproof
-\isacommand{by}\isamarkupfalse%
-\ default\ {\isacharparenleft}simp\ add{\isacharcolon}\ eq{\isacharunderscore}bar{\isacharunderscore}def{\isacharparenright}%
-\endisatagproof
-{\isafoldproof}%
-%
-\isadelimproof
-%
-\endisadelimproof
-\isanewline
-\isanewline
-\isacommand{end}\isamarkupfalse%
-\isanewline
-%
-\isadelimtt
-\isanewline
-%
-\endisadelimtt
-%
-\isatagtt
-\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
-\ bar\isanewline
-\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Integer{\isachardoublequoteclose}{\isacharparenright}%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\begin{isamarkuptext}%
-The code generator would produce
-  an additional instance, which of course is rejected.
-  To suppress this additional instance, use
-  \isa{{\isasymCODEINSTANCE}}:%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isatagtt
-\isacommand{code{\isacharunderscore}instance}\isamarkupfalse%
-\ bar\ {\isacharcolon}{\isacharcolon}\ eq\isanewline
-\ \ {\isacharparenleft}Haskell\ {\isacharminus}{\isacharparenright}%
-\endisatagtt
-{\isafoldtt}%
-%
-\isadelimtt
-%
-\endisadelimtt
-%
-\isamarkupsubsubsection{Pretty printing%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-The serializer provides ML interfaces to set up
-  pretty serializations for expressions like lists, numerals
-  and characters;  these are
-  monolithic stubs and should only be used with the
-  theories introduced in \secref{sec:library}.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Cyclic module dependencies%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Sometimes the awkward situation occurs that dependencies
-  between definitions introduce cyclic dependencies
-  between modules, which in the Haskell world leaves
-  you to the mercy of the Haskell implementation you are using,
-  while for SML code generation is not possible.
-
-  A solution is to declare module names explicitly.
-  Let use assume the three cyclically dependent
-  modules are named \emph{A}, \emph{B} and \emph{C}.
-  Then, by stating%
-\end{isamarkuptext}%
-\isamarkuptrue%
-\isacommand{code{\isacharunderscore}modulename}\isamarkupfalse%
-\ SML\isanewline
-\ \ A\ ABC\isanewline
-\ \ B\ ABC\isanewline
-\ \ C\ ABC%
-\begin{isamarkuptext}%
-we explicitly map all those modules on \emph{ABC},
-  resulting in an ad-hoc merge of this three modules
-  at serialization time.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Incremental code generation%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Code generation is \emph{incremental}: theorems
-  and abstract intermediate code are cached and extended on demand.
-  The cache may be partially or fully dropped if the underlying
-  executable content of the theory changes.
-  Implementation of caching is supposed to transparently
-  hid away the details from the user.  Anyway, caching
-  reaches the surface by using a slightly more general form
-  of the \isa{{\isasymCODETHMS}}, \isa{{\isasymCODEDEPS}}
-  and \isa{{\isasymEXPORTCODE}} commands: the list of constants
-  may be omitted.  Then, all constants with code theorems
-  in the current cache are referred to.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsection{ML interfaces \label{sec:ml}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Since the code generator framework not only aims to provide
-  a nice Isar interface but also to form a base for
-  code-generation-based applications, here a short
-  description of the most important ML interfaces.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsection{Executable theory content: \isa{Code}%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-This Pure module implements the core notions of
-  executable content of a theory.%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsubsection{Managing executable content%
-}
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
-  \indexml{Code.add\_func}\verb|Code.add_func: thm -> theory -> theory| \\
-  \indexml{Code.del\_func}\verb|Code.del_func: thm -> theory -> theory| \\
-  \indexml{Code.add\_funcl}\verb|Code.add_funcl: string * thm list Susp.T -> theory -> theory| \\
-  \indexml{Code.map\_pre}\verb|Code.map_pre: (MetaSimplifier.simpset -> MetaSimplifier.simpset) -> theory -> theory| \\
-  \indexml{Code.map\_post}\verb|Code.map_post: (MetaSimplifier.simpset -> MetaSimplifier.simpset) -> theory -> theory| \\
-  \indexml{Code.add\_functrans}\verb|Code.add_functrans: string * (theory -> thm list -> thm list option)|\isasep\isanewline%
-\verb|    -> theory -> theory| \\
-  \indexml{Code.del\_functrans}\verb|Code.del_functrans: string -> theory -> theory| \\
-  \indexml{Code.add\_datatype}\verb|Code.add_datatype: (string * typ) list -> theory -> theory| \\
-  \indexml{Code.get\_datatype}\verb|Code.get_datatype: theory -> string|\isasep\isanewline%
-\verb|    -> (string * sort) list * (string * typ list) list| \\
-  \indexml{Code.get\_datatype\_of\_constr}\verb|Code.get_datatype_of_constr: theory -> string -> string option|
-  \end{mldecls}
-
-  \begin{description}
-
-  \item \verb|Code.add_func|~\isa{thm}~\isa{thy} adds function
-     theorem \isa{thm} to executable content.
-
-  \item \verb|Code.del_func|~\isa{thm}~\isa{thy} removes function
-     theorem \isa{thm} from executable content, if present.
-
-  \item \verb|Code.add_funcl|~\isa{{\isacharparenleft}const{\isacharcomma}\ lthms{\isacharparenright}}~\isa{thy} adds
-     suspended defining equations \isa{lthms} for constant
-     \isa{const} to executable content.
-
-  \item \verb|Code.map_pre|~\isa{f}~\isa{thy} changes
-     the preprocessor simpset.
-
-  \item \verb|Code.add_functrans|~\isa{{\isacharparenleft}name{\isacharcomma}\ f{\isacharparenright}}~\isa{thy} adds
-     function transformer \isa{f} (named \isa{name}) to executable content;
-     \isa{f} is a transformer of the defining equations belonging
-     to a certain function definition, depending on the
-     current theory context.  Returning \isa{NONE} indicates that no
-     transformation took place;  otherwise, the whole process will be iterated
-     with the new defining equations.
-
-  \item \verb|Code.del_functrans|~\isa{name}~\isa{thy} removes
-     function transformer named \isa{name} from executable content.
-
-  \item \verb|Code.add_datatype|~\isa{cs}~\isa{thy} adds
-     a datatype to executable content, with generation
-     set \isa{cs}.
-
-  \item \verb|Code.get_datatype_of_constr|~\isa{thy}~\isa{const}
-     returns type constructor corresponding to
-     constructor \isa{const}; returns \isa{NONE}
-     if \isa{const} is no constructor.
-
-  \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsubsection{Auxiliary%
-}
-\isamarkuptrue%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isatagmlref
-%
-\begin{isamarkuptext}%
-\begin{mldecls}
-  \indexml{Code\_Unit.read\_const}\verb|Code.read_const: theory -> string -> string| \\
-  \indexml{Code\_Unit.head\_func}\verb|Code.head_func: thm -> string * ((string * sort) list * typ)| \\
-  \indexml{Code\_Unit.rewrite\_func}\verb|Code.rewrite_func: MetaSimplifier.simpset -> thm -> thm| \\
-  \end{mldecls}
-
-  \begin{description}
-
-  \item \verb|Code.read_const|~\isa{thy}~\isa{s}
-     reads a constant as a concrete term expression \isa{s}.
-
-  \item \verb|Code.head_func|~\isa{thm}
-     extracts the constant and its type from a defining equation \isa{thm}.
-
-  \item \verb|Code.rewrite_func|~\isa{ss}~\isa{thm}
-     rewrites a defining equation \isa{thm} with a simpset \isa{ss};
-     only arguments and right hand side are rewritten,
-     not the head of the defining equation.
-
-  \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\endisatagmlref
-{\isafoldmlref}%
-%
-\isadelimmlref
-%
-\endisadelimmlref
-%
-\isamarkupsubsection{Implementing code generator applications%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Implementing code generator applications on top
-  of the framework set out so far usually not only
-  involves using those primitive interfaces
-  but also storing code-dependent data and various
-  other things.
-
-  \begin{warn}
-    Some interfaces discussed here have not reached
-    a final state yet.
-    Changes likely to occur in future.
-  \end{warn}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\isamarkupsubsubsection{Data depending on the theory's executable content%
-}
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-Due to incrementality of code generation, changes in the
-  theory's executable content have to be propagated in a
-  certain fashion.  Additionally, such changes may occur
-  not only during theory extension but also during theory
-  merge, which is a little bit nasty from an implementation
-  point of view.  The framework provides a solution
-  to this technical challenge by providing a functorial
-  data slot \verb|CodeDataFun|; on instantiation
-  of this functor, the following types and operations
-  are required:
-
-  \medskip
-  \begin{tabular}{l}
-  \isa{type\ T} \\
-  \isa{val\ empty{\isacharcolon}\ T} \\
-  \isa{val\ merge{\isacharcolon}\ Pretty{\isachardot}pp\ {\isasymrightarrow}\ T\ {\isacharasterisk}\ T\ {\isasymrightarrow}\ T} \\
-  \isa{val\ purge{\isacharcolon}\ theory\ option\ {\isasymrightarrow}\ CodeUnit{\isachardot}const\ list\ option\ {\isasymrightarrow}\ T\ {\isasymrightarrow}\ T}
-  \end{tabular}
-
-  \begin{description}
-
-  \item \isa{T} the type of data to store.
-
-  \item \isa{empty} initial (empty) data.
-
-  \item \isa{merge} merging two data slots.
-
-  \item \isa{purge}~\isa{thy}~\isa{consts} propagates changes in executable content;
-    if possible, the current theory context is handed over
-    as argument \isa{thy} (if there is no current theory context (e.g.~during
-    theory merge, \verb|NONE|); \isa{consts} indicates the kind
-    of change: \verb|NONE| stands for a fundamental change
-    which invalidates any existing code, \isa{SOME\ consts}
-    hints that executable content for constants \isa{consts}
-    has changed.
-
-  \end{description}
-
-  An instance of \verb|CodeDataFun| provides the following
-  interface:
-
-  \medskip
-  \begin{tabular}{l}
-  \isa{get{\isacharcolon}\ theory\ {\isasymrightarrow}\ T} \\
-  \isa{change{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ T} \\
-  \isa{change{\isacharunderscore}yield{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T{\isacharparenright}\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T}
-  \end{tabular}
-
-  \begin{description}
-
-  \item \isa{get} retrieval of the current data.
-
-  \item \isa{change} update of current data (cached!)
-    by giving a continuation.
-
-  \item \isa{change{\isacharunderscore}yield} update with side result.
-
-  \end{description}%
-\end{isamarkuptext}%
-\isamarkuptrue%
-%
-\begin{isamarkuptext}%
-\emph{Happy proving, happy hacking!}%
-\end{isamarkuptext}%
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