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\begin{isabellebody}%
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\def\isabellecontext{Further}%
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\isadelimtheory
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\isatagtheory
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\isacommand{theory}\isamarkupfalse%
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\ Further\isanewline
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\isakeyword{imports}\ Setup\isanewline
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\isakeyword{begin}%
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\endisatagtheory
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{\isafoldtheory}%
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%
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\isamarkupsection{Further issues \label{sec:further}%
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}
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\isamarkuptrue%
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%
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\isamarkupsubsection{Modules namespace%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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When invoking the \hyperlink{command.export-code}{\mbox{\isa{\isacommand{export{\isacharunderscore}code}}}} command it is possible to leave
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out the \hyperlink{keyword.module-name}{\mbox{\isa{\isakeyword{module{\isacharunderscore}name}}}} part; then code is distributed over
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different modules, where the module name space roughly is induced
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by the Isabelle theory name space.
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Then sometimes the awkward situation occurs that dependencies between
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definitions introduce cyclic dependencies between modules, which in the
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\isa{Haskell} world leaves you to the mercy of the \isa{Haskell} implementation
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you are using, while for \isa{SML}/\isa{OCaml} code generation is not possible.
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A solution is to declare module names explicitly.
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Let use assume the three cyclically dependent
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modules are named \emph{A}, \emph{B} and \emph{C}.
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Then, by stating%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
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\isacommand{code{\isacharunderscore}modulename}\isamarkupfalse%
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\ SML\isanewline
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\ \ A\ ABC\isanewline
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\ \ B\ ABC\isanewline
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\ \ C\ ABC%
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\endisatagquote
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{\isafoldquote}%
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\isadelimquote
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%
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\begin{isamarkuptext}%
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\noindent
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we explicitly map all those modules on \emph{ABC},
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resulting in an ad-hoc merge of this three modules
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at serialisation time.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{Locales and interpretation%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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A technical issue comes to surface when generating code from
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specifications stemming from locale interpretation.
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Let us assume a locale specifying a power operation
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on arbitrary types:%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isadelimquote
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\isatagquote
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\isacommand{locale}\isamarkupfalse%
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\ power\ {\isacharequal}\isanewline
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\ \ \isakeyword{fixes}\ power\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isachardoublequoteclose}\isanewline
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\ \ \isakeyword{assumes}\ power{\isacharunderscore}commute{\isacharcolon}\ {\isachardoublequoteopen}power\ x\ {\isasymcirc}\ power\ y\ {\isacharequal}\ power\ y\ {\isasymcirc}\ power\ x{\isachardoublequoteclose}\isanewline
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\isakeyword{begin}%
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\endisatagquote
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{\isafoldquote}%
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\begin{isamarkuptext}%
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\noindent Inside that locale we can lift \isa{power} to exponent lists
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by means of specification relative to that locale:%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isadelimquote
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\isatagquote
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\isacommand{primrec}\isamarkupfalse%
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\ powers\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}{\isacharprime}a\ list\ {\isasymRightarrow}\ {\isacharprime}b\ {\isasymRightarrow}\ {\isacharprime}b{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
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\ \ {\isachardoublequoteopen}powers\ {\isacharbrackleft}{\isacharbrackright}\ {\isacharequal}\ id{\isachardoublequoteclose}\isanewline
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{\isacharbar}\ {\isachardoublequoteopen}powers\ {\isacharparenleft}x\ {\isacharhash}\ xs{\isacharparenright}\ {\isacharequal}\ power\ x\ {\isasymcirc}\ powers\ xs{\isachardoublequoteclose}\isanewline
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\isanewline
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\isacommand{lemma}\isamarkupfalse%
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\ powers{\isacharunderscore}append{\isacharcolon}\isanewline
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\ \ {\isachardoublequoteopen}powers\ {\isacharparenleft}xs\ {\isacharat}\ ys{\isacharparenright}\ {\isacharequal}\ powers\ xs\ {\isasymcirc}\ powers\ ys{\isachardoublequoteclose}\isanewline
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\ \ \isacommand{by}\isamarkupfalse%
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\ {\isacharparenleft}induct\ xs{\isacharparenright}\ simp{\isacharunderscore}all\isanewline
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\isanewline
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\isacommand{lemma}\isamarkupfalse%
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\ powers{\isacharunderscore}power{\isacharcolon}\isanewline
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\ \ {\isachardoublequoteopen}powers\ xs\ {\isasymcirc}\ power\ x\ {\isacharequal}\ power\ x\ {\isasymcirc}\ powers\ xs{\isachardoublequoteclose}\isanewline
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\ \ \isacommand{by}\isamarkupfalse%
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\ {\isacharparenleft}induct\ xs{\isacharparenright}\isanewline
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\ \ \ \ {\isacharparenleft}simp{\isacharunderscore}all\ del{\isacharcolon}\ o{\isacharunderscore}apply\ id{\isacharunderscore}apply\ add{\isacharcolon}\ o{\isacharunderscore}assoc\ {\isacharbrackleft}symmetric{\isacharbrackright}{\isacharcomma}\isanewline
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\ \ \ \ \ \ simp\ del{\isacharcolon}\ o{\isacharunderscore}apply\ add{\isacharcolon}\ o{\isacharunderscore}assoc\ power{\isacharunderscore}commute{\isacharparenright}\isanewline
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\isanewline
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\isacommand{lemma}\isamarkupfalse%
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\ powers{\isacharunderscore}rev{\isacharcolon}\isanewline
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\ \ {\isachardoublequoteopen}powers\ {\isacharparenleft}rev\ xs{\isacharparenright}\ {\isacharequal}\ powers\ xs{\isachardoublequoteclose}\isanewline
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\ \ \ \ \isacommand{by}\isamarkupfalse%
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\ {\isacharparenleft}induct\ xs{\isacharparenright}\ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ powers{\isacharunderscore}append\ powers{\isacharunderscore}power{\isacharparenright}\isanewline
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\isanewline
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\isacommand{end}\isamarkupfalse%
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\begin{isamarkuptext}%
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After an interpretation of this locale (say, \indexdef{}{command}{interpretation}\hypertarget{command.interpretation}{\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
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can be generated. But this not the case: internally, the term
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\isa{fun{\isacharunderscore}power{\isachardot}powers} is an abbreviation for the foundational
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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}}
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(see \cite{isabelle-locale} for the details behind).
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Fortunately, with minor effort the desired behaviour can be achieved.
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First, a dedicated definition of the constant on which the local \isa{powers}
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after interpretation is supposed to be mapped on:%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isacommand{definition}\isamarkupfalse%
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\ funpows\ {\isacharcolon}{\isacharcolon}\ {\isachardoublequoteopen}nat\ list\ {\isasymRightarrow}\ {\isacharparenleft}{\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isacharparenright}\ {\isasymRightarrow}\ {\isacharprime}a\ {\isasymRightarrow}\ {\isacharprime}a{\isachardoublequoteclose}\ \isakeyword{where}\isanewline
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\ \ {\isacharbrackleft}code\ del{\isacharbrackright}{\isacharcolon}\ {\isachardoublequoteopen}funpows\ {\isacharequal}\ power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ f{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}{\isachardoublequoteclose}%
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\begin{isamarkuptext}%
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\noindent In general, the pattern is \isa{c\ {\isacharequal}\ t} where \isa{c} is
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the name of the future constant and \isa{t} the foundational term
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corresponding to the local constant after interpretation.
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The interpretation itself is enriched with an equation \isa{t\ {\isacharequal}\ c}:%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\isacommand{interpretation}\isamarkupfalse%
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\ 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
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\ \ {\isachardoublequoteopen}power{\isachardot}powers\ {\isacharparenleft}{\isasymlambda}n\ f{\isachardot}\ f\ {\isacharcircum}{\isacharcircum}\ n{\isacharparenright}\ {\isacharequal}\ funpows{\isachardoublequoteclose}\isanewline
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\ \ \isacommand{by}\isamarkupfalse%
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\ unfold{\isacharunderscore}locales\isanewline
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\ \ \ \ {\isacharparenleft}simp{\isacharunderscore}all\ add{\isacharcolon}\ expand{\isacharunderscore}fun{\isacharunderscore}eq\ funpow{\isacharunderscore}mult\ mult{\isacharunderscore}commute\ funpows{\isacharunderscore}def{\isacharparenright}%
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\begin{isamarkuptext}%
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\noindent This additional equation is trivially proved by the definition
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itself.
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After this setup procedure, code generation can continue as usual:%
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\end{isamarkuptext}%
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\isamarkuptrue%
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\begin{isamarkuptext}%
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\isatypewriter%
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\noindent%
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\hspace*{0pt}funpow ::~forall a.~Example.Nat -> (a -> a) -> a -> a;\\
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\hspace*{0pt}funpow Example.Zero{\char95}nat f = id;\\
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\hspace*{0pt}funpow (Example.Suc n) f = f .~Example.funpow n f;\\
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\hspace*{0pt}\\
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\hspace*{0pt}funpows ::~forall a.~[Example.Nat] -> (a -> a) -> a -> a;\\
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\hspace*{0pt}funpows [] = id;\\
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\hspace*{0pt}funpows (x :~xs) = Example.funpow x .~Example.funpows xs;%
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\end{isamarkuptext}%
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\isamarkuptrue%
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{\isafoldquote}%
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\isamarkupsubsection{Imperative data structures%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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If you consider imperative data structures as inevitable for a
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specific application, you should consider \emph{Imperative
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Functional Programming with Isabelle/HOL}
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\cite{bulwahn-et-al:2008:imperative}; the framework described there
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is available in session \isa{Imperative{\isacharunderscore}HOL}.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsection{ML system interfaces \label{sec:ml}%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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Since the code generator framework not only aims to provide a nice
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Isar interface but also to form a base for code-generation-based
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applications, here a short description of the most fundamental ML
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interfaces.%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\isamarkupsubsubsection{Managing executable content%
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}
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\isamarkuptrue%
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\isadelimmlref
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%
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\begin{isamarkuptext}%
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\begin{mldecls}
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\indexdef{}{ML}{Code.read\_const}\verb|Code.read_const: theory -> string -> string| \\
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\indexdef{}{ML}{Code.add\_eqn}\verb|Code.add_eqn: thm -> theory -> theory| \\
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\indexdef{}{ML}{Code.del\_eqn}\verb|Code.del_eqn: thm -> theory -> theory| \\
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\indexdef{}{ML}{Code\_Preproc.map\_pre}\verb|Code_Preproc.map_pre: (simpset -> simpset) -> theory -> theory| \\
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\indexdef{}{ML}{Code\_Preproc.map\_post}\verb|Code_Preproc.map_post: (simpset -> simpset) -> theory -> theory| \\
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\indexdef{}{ML}{Code\_Preproc.add\_functrans}\verb|Code_Preproc.add_functrans: |\isasep\isanewline%
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\verb| string * (theory -> (thm * bool) list -> (thm * bool) list option)|\isasep\isanewline%
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\verb| -> theory -> theory| \\
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\indexdef{}{ML}{Code\_Preproc.del\_functrans}\verb|Code_Preproc.del_functrans: string -> theory -> theory| \\
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\indexdef{}{ML}{Code.add\_datatype}\verb|Code.add_datatype: (string * typ) list -> theory -> theory| \\
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\indexdef{}{ML}{Code.get\_type}\verb|Code.get_type: theory -> string|\isasep\isanewline%
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\verb| -> (string * sort) list * ((string * string list) * typ list) list| \\
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\indexdef{}{ML}{Code.get\_type\_of\_constr\_or\_abstr}\verb|Code.get_type_of_constr_or_abstr: theory -> string -> (string * bool) option|
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\end{mldecls}
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\begin{description}
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\item \verb|Code.read_const|~\isa{thy}~\isa{s}
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reads a constant as a concrete term expression \isa{s}.
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\item \verb|Code.add_eqn|~\isa{thm}~\isa{thy} adds function
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theorem \isa{thm} to executable content.
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\item \verb|Code.del_eqn|~\isa{thm}~\isa{thy} removes function
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theorem \isa{thm} from executable content, if present.
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\item \verb|Code_Preproc.map_pre|~\isa{f}~\isa{thy} changes
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the preprocessor simpset.
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\item \verb|Code_Preproc.add_functrans|~\isa{{\isacharparenleft}name{\isacharcomma}\ f{\isacharparenright}}~\isa{thy} adds
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function transformer \isa{f} (named \isa{name}) to executable content;
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\isa{f} is a transformer of the code equations belonging
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to a certain function definition, depending on the
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current theory context. Returning \isa{NONE} indicates that no
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transformation took place; otherwise, the whole process will be iterated
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with the new code equations.
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\item \verb|Code_Preproc.del_functrans|~\isa{name}~\isa{thy} removes
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function transformer named \isa{name} from executable content.
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\item \verb|Code.add_datatype|~\isa{cs}~\isa{thy} adds
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a datatype to executable content, with generation
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set \isa{cs}.
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\item \verb|Code.get_type_of_constr_or_abstr|~\isa{thy}~\isa{const}
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returns type constructor corresponding to
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constructor \isa{const}; returns \isa{NONE}
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if \isa{const} is no constructor.
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\end{description}%
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\end{isamarkuptext}%
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\isamarkuptrue%
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%
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\endisatagmlref
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{\isafoldmlref}%
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%
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\isadelimmlref
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%
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\endisadelimmlref
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%
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\isamarkupsubsubsection{Data depending on the theory's executable content%
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}
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\isamarkuptrue%
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%
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\begin{isamarkuptext}%
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Implementing code generator applications on top
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of the framework set out so far usually not only
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involves using those primitive interfaces
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but also storing code-dependent data and various
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other things.
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Due to incrementality of code generation, changes in the
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theory's executable content have to be propagated in a
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certain fashion. Additionally, such changes may occur
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not only during theory extension but also during theory
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|
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merge, which is a little bit nasty from an implementation
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|
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point of view. The framework provides a solution
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to this technical challenge by providing a functorial
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data slot \verb|Code_Data|; on instantiation
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of this functor, the following types and operations
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|
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are required:
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|
|
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\medskip
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|
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\begin{tabular}{l}
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\isa{type\ T} \\
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\isa{val\ empty{\isacharcolon}\ T} \\
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359 |
\end{tabular}
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|
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\begin{description}
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|
|
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\item \isa{T} the type of data to store.
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\item \isa{empty} initial (empty) data.
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|
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\end{description}
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|
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|
|
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\noindent An instance of \verb|Code_Data| provides the following
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|
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interface:
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|
|
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\medskip
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|
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\begin{tabular}{l}
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\isa{change{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ T{\isacharparenright}\ {\isasymrightarrow}\ T} \\
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|
375 |
\isa{change{\isacharunderscore}yield{\isacharcolon}\ theory\ {\isasymrightarrow}\ {\isacharparenleft}T\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T{\isacharparenright}\ {\isasymrightarrow}\ {\isacharprime}a\ {\isacharasterisk}\ T}
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|
376 |
\end{tabular}
|
|
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|
|
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\begin{description}
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|
379 |
|
|
380 |
\item \isa{change} update of current data (cached!)
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|
381 |
by giving a continuation.
|
|
382 |
|
|
383 |
\item \isa{change{\isacharunderscore}yield} update with side result.
|
|
384 |
|
|
385 |
\end{description}%
|
|
386 |
\end{isamarkuptext}%
|
|
387 |
\isamarkuptrue%
|
|
388 |
%
|
28447
|
389 |
\isadelimtheory
|
|
390 |
%
|
|
391 |
\endisadelimtheory
|
|
392 |
%
|
|
393 |
\isatagtheory
|
|
394 |
\isacommand{end}\isamarkupfalse%
|
|
395 |
%
|
|
396 |
\endisatagtheory
|
|
397 |
{\isafoldtheory}%
|
|
398 |
%
|
|
399 |
\isadelimtheory
|
|
400 |
%
|
|
401 |
\endisadelimtheory
|
|
402 |
\isanewline
|
|
403 |
\end{isabellebody}%
|
|
404 |
%%% Local Variables:
|
|
405 |
%%% mode: latex
|
|
406 |
%%% TeX-master: "root"
|
|
407 |
%%% End:
|