%
\begin{isabellebody}%
\def\isabellecontext{Further}%
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\isadelimtheory
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\endisadelimtheory
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\isatagtheory
\isacommand{theory}\isamarkupfalse%
\ Further\isanewline
\isakeyword{imports}\ Setup\isanewline
\isakeyword{begin}%
\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
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\isamarkupsection{Further issues \label{sec:further}%
}
\isamarkuptrue%
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\isamarkupsubsection{Modules namespace%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
When invoking the \hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}} command it is possible to leave
out the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} part; then code is distributed over
different modules, where the module name space roughly is induced
by the Isabelle theory name space.
Then sometimes the awkward situation occurs that dependencies between
definitions introduce cyclic dependencies between modules, which in the
\isa{Haskell} world leaves you to the mercy of the \isa{Haskell} implementation
you are using, while for \isa{SML}/\isa{OCaml} 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%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{code{\isacharunderscore}modulename}\isamarkupfalse%
\ SML\isanewline
\ \ A\ ABC\isanewline
\ \ B\ ABC\isanewline
\ \ C\ ABC%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent
we explicitly map all those modules on \emph{ABC},
resulting in an ad-hoc merge of this three modules
at serialisation time.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Locales and interpretation%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
A technical issue comes to surface when generating code from
specifications stemming from locale interpretation.
Let us assume a locale specifying a power operation
on arbitrary types:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{locale}\isamarkupfalse%
\ power\ {\isacharequal}\isanewline
\ \ \isakeyword{fixes}\ power\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isachardoublequoteclose}\isanewline
\ \ \isakeyword{assumes}\ power{\isacharunderscore}commute{\isacharcolon}\ {\isachardoublequoteopen}power\ x\ {\isasymcirc}\ power\ y\ {\isacharequal}\ power\ y\ {\isasymcirc}\ power\ x{\isachardoublequoteclose}\isanewline
\isakeyword{begin}%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent Inside that locale we can lift \isa{power} to exponent lists
by means of specification relative to that locale:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{primrec}\isamarkupfalse%
\ powers\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}powers\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ id{\isachardoublequoteclose}\isanewline
{\isacharbar}\ {\isachardoublequoteopen}powers\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharequal}\ power\ x\ {\isasymcirc}\ powers\ xs{\isachardoublequoteclose}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ powers{\isacharunderscore}append{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}powers\ {\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ powers\ xs\ {\isasymcirc}\ powers\ ys{\isachardoublequoteclose}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ powers{\isacharunderscore}power{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}powers\ xs\ {\isasymcirc}\ power\ x\ {\isacharequal}\ power\ x\ {\isasymcirc}\ powers\ xs{\isachardoublequoteclose}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\isanewline
\ \ \ \ {\isacharparenleft}simp{\isacharunderscore}all\ del{\isacharcolon}\ o{\isacharunderscore}apply\ id{\isacharunderscore}apply\ add{\isacharcolon}\ o{\isacharunderscore}assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcomma}\isanewline
\ \ \ \ \ \ simp\ del{\isacharcolon}\ o{\isacharunderscore}apply\ add{\isacharcolon}\ o{\isacharunderscore}assoc\ power{\isacharunderscore}commute{\isacharparenright}\isanewline
\isanewline
\isacommand{lemma}\isamarkupfalse%
\ powers{\isacharunderscore}rev{\isacharcolon}\isanewline
\ \ {\isachardoublequoteopen}powers\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ powers\ xs{\isachardoublequoteclose}\isanewline
\ \ \ \ \isacommand{by}\isamarkupfalse%
\ {\isacharparenleft}induct\ xs{\isacharparenright}\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ powers{\isacharunderscore}append\ powers{\isacharunderscore}power{\isacharparenright}\isanewline
\isanewline
\isacommand{end}\isamarkupfalse%
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\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
After an interpretation of this locale (say, \hyperlink{command.interpretation}{\mbox{\isa{\isacommand{interpretation}}}} \isa{fun{\isacharunderscore}power{\isacharcolon}} \isa{{\isachardoublequote}power\ {\isacharparenleft}{\isasymlambda}n\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequote}}), one would expect to have a constant \isa{fun{\isacharunderscore}power{\isachardot}powers\ {\isacharcolon}{\isacharcolon}\ nat\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a} for which code
can be generated. But this not the case: internally, the term
\isa{fun{\isacharunderscore}power{\isachardot}powers} is an abbreviation for the foundational
term \isa{{\isachardoublequote}power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequote}}
(see \cite{isabelle-locale} for the details behind).
Fortunately, with minor effort the desired behaviour can be achieved.
First, a dedicated definition of the constant on which the local \isa{powers}
after interpretation is supposed to be mapped on:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{definition}\isamarkupfalse%
\ funpows\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isacharbrackleft}code\ del{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}funpows\ {\isacharequal}\ power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ f{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequoteclose}%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent In general, the pattern is \isa{c\ {\isacharequal}\ t} where \isa{c} is
the name of the future constant and \isa{t} the foundational term
corresponding to the local constant after interpretation.
The interpretation itself is enriched with an equation \isa{t\ {\isacharequal}\ c}:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{interpretation}\isamarkupfalse%
\ fun{\isacharunderscore}power{\isacharcolon}\ power\ {\isachardoublequoteopen}{\isasymlambda}n\ {\isacharparenleft}f\ {\isacharcolon}{\isacharcolon}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
\ \ {\isachardoublequoteopen}power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ f{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}\ {\isacharequal}\ funpows{\isachardoublequoteclose}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
\ unfold{\isacharunderscore}locales\isanewline
\ \ \ \ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ expand{\isacharunderscore}fun{\isacharunderscore}eq\ funpow{\isacharunderscore}mult\ mult{\isacharunderscore}commute\ funpows{\isacharunderscore}def{\isacharparenright}%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent This additional equation is trivially proved by the definition
itself.
After this setup procedure, code generation can continue as usual:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
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\begin{isamarkuptext}%
\isatypewriter%
\noindent%
\hspace*{0pt}funpow ::~forall a.~Nat -> (a -> a) -> a -> a;\\
\hspace*{0pt}funpow Zero{\char95}nat f = id;\\
\hspace*{0pt}funpow (Suc n) f = f .~funpow n f;\\
\hspace*{0pt}\\
\hspace*{0pt}funpows ::~forall a.~[Nat] -> (a -> a) -> a -> a;\\
\hspace*{0pt}funpows [] = id;\\
\hspace*{0pt}funpows (x :~xs) = funpow x .~funpows xs;%
\end{isamarkuptext}%
\isamarkuptrue%
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\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\isamarkupsubsection{Imperative data structures%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
If you consider imperative data structures as inevitable for a
specific application, you should consider \emph{Imperative
Functional Programming with Isabelle/HOL}
\cite{bulwahn-et-al:2008:imperative}; the framework described there
is available in session \hyperlink{theory.Imperative-HOL}{\mbox{\isa{Imperative{\isacharunderscore}HOL}}}.%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsection{Evaluation oracle%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
Code generation may also be used to \emph{evaluate} expressions
(using \isa{SML} as target language of course).
For instance, the \hyperlink{command.value}{\mbox{\isa{\isacommand{value}}}} reduces an expression to a
normal form with respect to the underlying code equations:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{value}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isadigit{4}}{\isadigit{2}}\ {\isacharslash}\ {\isacharparenleft}{\isadigit{1}}{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ rat{\isacharparenright}{\isachardoublequoteclose}%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent will display \isa{{\isadigit{7}}\ {\isacharslash}\ {\isadigit{2}}}.
The \hyperlink{method.eval}{\mbox{\isa{eval}}} method tries to reduce a goal by code generation to \isa{True}
and solves it in that case, but fails otherwise:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{lemma}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isadigit{4}}{\isadigit{2}}\ {\isacharslash}\ {\isacharparenleft}{\isadigit{1}}{\isadigit{2}}\ {\isacharcolon}{\isacharcolon}\ rat{\isacharparenright}\ {\isacharequal}\ {\isadigit{7}}\ {\isacharslash}\ {\isadigit{2}}{\isachardoublequoteclose}\isanewline
\ \ \isacommand{by}\isamarkupfalse%
\ eval%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent The soundness of the \hyperlink{method.eval}{\mbox{\isa{eval}}} method depends crucially
on the correctness of the code generator; this is one of the reasons
why you should not use adaptation (see \secref{sec:adaptation}) frivolously.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Building evaluators%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
FIXME%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsubsection{Code antiquotation%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
In scenarios involving techniques like reflection it is quite common
that code generated from a theory forms the basis for implementing
a proof procedure in \isa{SML}. To facilitate interfacing of generated code
with system code, the code generator provides a \isa{code} antiquotation:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{datatype}\isamarkupfalse%
\ form\ {\isacharequal}\ T\ {\isacharbar}\ F\ {\isacharbar}\ And\ form\ form\ {\isacharbar}\ Or\ form\ form\ %
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\isadelimquotett
\ %
\endisadelimquotett
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\isatagquotett
\isacommand{ML}\isamarkupfalse%
\ {\isacharverbatimopen}\isanewline
\ \ fun\ eval{\isacharunderscore}form\ %
\isaantiq
code\ T%
\endisaantiq
\ {\isacharequal}\ true\isanewline
\ \ \ \ {\isacharbar}\ eval{\isacharunderscore}form\ %
\isaantiq
code\ F%
\endisaantiq
\ {\isacharequal}\ false\isanewline
\ \ \ \ {\isacharbar}\ eval{\isacharunderscore}form\ {\isacharparenleft}%
\isaantiq
code\ And%
\endisaantiq
\ {\isacharparenleft}p{\isacharcomma}\ q{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
\ \ \ \ \ \ \ \ eval{\isacharunderscore}form\ p\ andalso\ eval{\isacharunderscore}form\ q\isanewline
\ \ \ \ {\isacharbar}\ eval{\isacharunderscore}form\ {\isacharparenleft}%
\isaantiq
code\ Or%
\endisaantiq
\ {\isacharparenleft}p{\isacharcomma}\ q{\isacharparenright}{\isacharparenright}\ {\isacharequal}\isanewline
\ \ \ \ \ \ \ \ eval{\isacharunderscore}form\ p\ orelse\ eval{\isacharunderscore}form\ q{\isacharsemicolon}\isanewline
{\isacharverbatimclose}%
\endisatagquotett
{\isafoldquotett}%
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\isadelimquotett
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\endisadelimquotett
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\begin{isamarkuptext}%
\noindent \isa{code} takes as argument the name of a constant; after the
whole \isa{SML} is read, the necessary code is generated transparently
and the corresponding constant names are inserted. This technique also
allows to use pattern matching on constructors stemming from compiled
\isa{datatypes}.
For a less simplistic example, theory \hyperlink{theory.Ferrack}{\mbox{\isa{Ferrack}}} is
a good reference.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{ML system 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%
%
\isamarkupsubsubsection{Managing executable content%
}
\isamarkuptrue%
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\isadelimmlref
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\endisadelimmlref
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\isatagmlref
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\begin{isamarkuptext}%
\begin{mldecls}
\indexdef{}{ML}{Code.add\_eqn}\verb|Code.add_eqn: thm -> theory -> theory| \\
\indexdef{}{ML}{Code.del\_eqn}\verb|Code.del_eqn: thm -> theory -> theory| \\
\indexdef{}{ML}{Code\_Preproc.map\_pre}\verb|Code_Preproc.map_pre: (simpset -> simpset) -> theory -> theory| \\
\indexdef{}{ML}{Code\_Preproc.map\_post}\verb|Code_Preproc.map_post: (simpset -> simpset) -> theory -> theory| \\
\indexdef{}{ML}{Code\_Preproc.add\_functrans}\verb|Code_Preproc.add_functrans: string * (theory -> (thm * bool) list -> (thm * bool) list option)|\isasep\isanewline%
\verb| -> theory -> theory| \\
\indexdef{}{ML}{Code\_Preproc.del\_functrans}\verb|Code_Preproc.del_functrans: string -> theory -> theory| \\
\indexdef{}{ML}{Code.add\_datatype}\verb|Code.add_datatype: (string * typ) list -> theory -> theory| \\
\indexdef{}{ML}{Code.get\_type}\verb|Code.get_type: theory -> string|\isasep\isanewline%
\verb| -> (string * sort) list * ((string * string list) * typ list) list| \\
\indexdef{}{ML}{Code.get\_type\_of\_constr\_or\_abstr}\verb|Code.get_type_of_constr_or_abstr: theory -> string -> (string * bool) option|
\end{mldecls}
\begin{description}
\item \verb|Code.add_eqn|~\isa{thm}~\isa{thy} adds function
theorem \isa{thm} to executable content.
\item \verb|Code.del_eqn|~\isa{thm}~\isa{thy} removes function
theorem \isa{thm} from executable content, if present.
\item \verb|Code_Preproc.map_pre|~\isa{f}~\isa{thy} changes
the preprocessor simpset.
\item \verb|Code_Preproc.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 code 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 code equations.
\item \verb|Code_Preproc.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_type_of_constr_or_abstr|~\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%
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\endisatagmlref
{\isafoldmlref}%
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\isadelimmlref
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\endisadelimmlref
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\isamarkupsubsubsection{Auxiliary%
}
\isamarkuptrue%
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\isadelimmlref
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\endisadelimmlref
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\isatagmlref
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\begin{isamarkuptext}%
\begin{mldecls}
\indexdef{}{ML}{Code.read\_const}\verb|Code.read_const: theory -> string -> string|
\end{mldecls}
\begin{description}
\item \verb|Code.read_const|~\isa{thy}~\isa{s}
reads a constant as a concrete term expression \isa{s}.
\end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
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\endisatagmlref
{\isafoldmlref}%
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\isadelimmlref
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\endisadelimmlref
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\isamarkupsubsubsection{Data depending on the theory's executable content%
}
\isamarkuptrue%
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\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.
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|Code_Data|; on instantiation
of this functor, the following types and operations
are required:
\medskip
\begin{tabular}{l}
\isa{type\ T} \\
\isa{val\ empty{\isacharcolon}\ T} \\
\end{tabular}
\begin{description}
\item \isa{T} the type of data to store.
\item \isa{empty} initial (empty) data.
\end{description}
\noindent An instance of \verb|Code_Data| provides the following
interface:
\medskip
\begin{tabular}{l}
\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{change} update of current data (cached!)
by giving a continuation.
\item \isa{change{\isacharunderscore}yield} update with side result.
\end{description}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimtheory
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\isatagtheory
\isacommand{end}\isamarkupfalse%
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\endisatagtheory
{\isafoldtheory}%
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\isadelimtheory
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\endisadelimtheory
\isanewline
\end{isabellebody}%
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