clarified verbatim vs. typewriter
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\begin{isabellebody}%
\def\isabellecontext{Adaption}%
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\isadelimtheory
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\ Adaption\isanewline
\isakeyword{imports}\ Setup\isanewline
\isakeyword{begin}%
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\ {\isacharverbatimopen}\ Code{\isacharunderscore}Target{\isachardot}extend{\isacharunderscore}target\ {\isacharparenleft}{\isachardoublequote}{\isasymSML}{\isachardoublequote}{\isacharcomma}\ {\isacharparenleft}{\isachardoublequote}SML{\isachardoublequote}{\isacharcomma}\ K\ I{\isacharparenright}{\isacharparenright}\ {\isacharverbatimclose}%
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\isamarkupsection{Adaption to target languages \label{sec:adaption}%
}
\isamarkuptrue%
%
\isamarkupsubsection{Adapting code generation%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The aspects of code generation introduced so far have two aspects
in common:
\begin{itemize}
\item They act uniformly, without reference to a specific
target language.
\item They are \emph{safe} in the sense that as long as you trust
the code generator meta theory and implementation, you cannot
produce programs that yield results which are not derivable
in the logic.
\end{itemize}
\noindent In this section we will introduce means to \emph{adapt} the serialiser
to a specific target language, i.e.~to print program fragments
in a way which accommodates \qt{already existing} ingredients of
a target language environment, for three reasons:
\begin{itemize}
\item improving readability and aesthetics of generated code
\item gaining efficiency
\item interface with language parts which have no direct counterpart
in \isa{HOL} (say, imperative data structures)
\end{itemize}
\noindent Generally, you should avoid using those features yourself
\emph{at any cost}:
\begin{itemize}
\item The safe configuration methods act uniformly on every target language,
whereas for adaption you have to treat each target language separate.
\item Application is extremely tedious since there is no abstraction
which would allow for a static check, making it easy to produce garbage.
\item More or less subtle errors can be introduced unconsciously.
\end{itemize}
\noindent However, even if you ought refrain from setting up adaption
yourself, already the \isa{HOL} comes with some reasonable default
adaptions (say, using target language list syntax). There also some
common adaption cases which you can setup by importing particular
library theories. In order to understand these, we provide some clues here;
these however are not supposed to replace a careful study of the sources.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{The adaption principle%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The following figure illustrates what \qt{adaption} is conceptually
supposed to be:
\begin{figure}[here]
\begin{tikzpicture}[scale = 0.5]
\tikzstyle water=[color = blue, thick]
\tikzstyle ice=[color = black, very thick, cap = round, join = round, fill = white]
\tikzstyle process=[color = green, semithick, ->]
\tikzstyle adaption=[color = red, semithick, ->]
\tikzstyle target=[color = black]
\foreach \x in {0, ..., 24}
\draw[style=water] (\x, 0.25) sin + (0.25, 0.25) cos + (0.25, -0.25) sin
+ (0.25, -0.25) cos + (0.25, 0.25);
\draw[style=ice] (1, 0) --
(3, 6) node[above, fill=white] {logic} -- (5, 0) -- cycle;
\draw[style=ice] (9, 0) --
(11, 6) node[above, fill=white] {intermediate language} -- (13, 0) -- cycle;
\draw[style=ice] (15, -6) --
(19, 6) node[above, fill=white] {target language} -- (23, -6) -- cycle;
\draw[style=process]
(3.5, 3) .. controls (7, 5) .. node[fill=white] {translation} (10.5, 3);
\draw[style=process]
(11.5, 3) .. controls (15, 5) .. node[fill=white] (serialisation) {serialisation} (18.5, 3);
\node (adaption) at (11, -2) [style=adaption] {adaption};
\node at (19, 3) [rotate=90] {generated};
\node at (19.5, -5) {language};
\node at (19.5, -3) {library};
\node (includes) at (19.5, -1) {includes};
\node (reserved) at (16.5, -3) [rotate=72] {reserved}; % proper 71.57
\draw[style=process]
(includes) -- (serialisation);
\draw[style=process]
(reserved) -- (serialisation);
\draw[style=adaption]
(adaption) -- (serialisation);
\draw[style=adaption]
(adaption) -- (includes);
\draw[style=adaption]
(adaption) -- (reserved);
\end{tikzpicture}
\caption{The adaption principle}
\label{fig:adaption}
\end{figure}
\noindent In the tame view, code generation acts as broker between
\isa{logic}, \isa{intermediate\ language} and
\isa{target\ language} by means of \isa{translation} and
\isa{serialisation}; for the latter, the serialiser has to observe
the structure of the \isa{language} itself plus some \isa{reserved}
keywords which have to be avoided for generated code.
However, if you consider \isa{adaption} mechanisms, the code generated
by the serializer is just the tip of the iceberg:
\begin{itemize}
\item \isa{serialisation} can be \emph{parametrised} such that
logical entities are mapped to target-specific ones
(e.g. target-specific list syntax,
see also \secref{sec:adaption_mechanisms})
\item Such parametrisations can involve references to a
target-specific standard \isa{library} (e.g. using
the \isa{Haskell} \verb|Maybe| type instead
of the \isa{HOL} \isa{option} type);
if such are used, the corresponding identifiers
(in our example, \verb|Maybe|, \verb|Nothing|
and \verb|Just|) also have to be considered \isa{reserved}.
\item Even more, the user can enrich the library of the
target-language by providing code snippets
(\qt{\isa{includes}}) which are prepended to
any generated code (see \secref{sec:include}); this typically
also involves further \isa{reserved} identifiers.
\end{itemize}
\noindent As figure \ref{fig:adaption} illustrates, all these adaption mechanisms
have to act consistently; it is at the discretion of the user
to take care for this.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isamarkupsubsection{Common adaption patterns%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
The \hyperlink{theory.HOL}{\mbox{\isa{HOL}}} \hyperlink{theory.Main}{\mbox{\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 customising the code generator setup (see below
\secref{sec:adaption_mechanisms}).
\begin{description}
\item[\hyperlink{theory.Code-Integer}{\mbox{\isa{Code{\isacharunderscore}Integer}}}] represents \isa{HOL} integers by big
integer literals in target languages.
\item[\hyperlink{theory.Code-Char}{\mbox{\isa{Code{\isacharunderscore}Char}}}] represents \isa{HOL} characters by
character literals in target languages.
\item[\hyperlink{theory.Code-Char-chr}{\mbox{\isa{Code{\isacharunderscore}Char{\isacharunderscore}chr}}}] like \isa{Code{\isacharunderscore}Char},
but also offers treatment of character codes; includes
\hyperlink{theory.Code-Char}{\mbox{\isa{Code{\isacharunderscore}Char}}}.
\item[\hyperlink{theory.Efficient-Nat}{\mbox{\isa{Efficient{\isacharunderscore}Nat}}}] \label{eff_nat} implements natural numbers by integers,
which in general will result in higher efficiency; pattern
matching with \isa{{\isadigit{0}}} / \isa{Suc}
is eliminated; includes \hyperlink{theory.Code-Integer}{\mbox{\isa{Code{\isacharunderscore}Integer}}}
and \hyperlink{theory.Code-Index}{\mbox{\isa{Code{\isacharunderscore}Index}}}.
\item[\hyperlink{theory.Code-Index}{\mbox{\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[\hyperlink{theory.Code-Message}{\mbox{\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{Parametrising serialisation \label{sec:adaption_mechanisms}%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
Consider the following function and its corresponding
SML code:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\isatagquote
\isacommand{primrec}\isamarkupfalse%
\ 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}%
\endisatagquote
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\begin{isamarkuptext}%
\isatypewriter%
\noindent%
\hspace*{0pt}structure Example = \\
\hspace*{0pt}struct\\
\hspace*{0pt}\\
\hspace*{0pt}datatype nat = Suc of nat | Zero{\char95}nat;\\
\hspace*{0pt}\\
\hspace*{0pt}datatype boola = False | True;\\
\hspace*{0pt}\\
\hspace*{0pt}fun anda x True = x\\
\hspace*{0pt} ~| anda x False = False\\
\hspace*{0pt} ~| anda True x = x\\
\hspace*{0pt} ~| anda False x = False;\\
\hspace*{0pt}\\
\hspace*{0pt}fun less{\char95}nat m (Suc n) = less{\char95}eq{\char95}nat m n\\
\hspace*{0pt} ~| less{\char95}nat n Zero{\char95}nat = False\\
\hspace*{0pt}and less{\char95}eq{\char95}nat (Suc m) n = less{\char95}nat m n\\
\hspace*{0pt} ~| less{\char95}eq{\char95}nat Zero{\char95}nat n = True;\\
\hspace*{0pt}\\
\hspace*{0pt}fun in{\char95}interval (k, l) n = anda (less{\char95}eq{\char95}nat k n) (less{\char95}eq{\char95}nat n l);\\
\hspace*{0pt}\\
\hspace*{0pt}end; (*struct Example*)%
\end{isamarkuptext}%
\isamarkuptrue%
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\endisatagquote
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\begin{isamarkuptext}%
\noindent Though this is correct code, it is a little bit unsatisfactory:
boolean values and operators are materialised as distinguished
entities with have nothing to do with the SML-built-in 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 \verb|bool| would be used. To map
the HOL \isa{bool} on SML \verb|bool|, we may use
\qn{custom serialisations}:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquotett
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\endisadelimquotett
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\isatagquotett
\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}%
\endisatagquotett
{\isafoldquotett}%
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\isadelimquotett
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\endisadelimquotett
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\begin{isamarkuptext}%
\noindent The \hyperlink{command.code-type}{\mbox{\isa{\isacommand{code{\isacharunderscore}type}}}} command takes a type constructor
as arguments together with a list of custom serialisations.
Each custom serialisation starts with a target language
identifier followed by an expression, which during
code serialisation is inserted whenever the type constructor
would occur. For constants, \hyperlink{command.code-const}{\mbox{\isa{\isacommand{code{\isacharunderscore}const}}}} implements
the corresponding mechanism. Each ``\verb|_|'' in
a serialisation expression is treated as a placeholder
for the type constructor's (the constant's) arguments.%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\begin{isamarkuptext}%
\isatypewriter%
\noindent%
\hspace*{0pt}structure Example = \\
\hspace*{0pt}struct\\
\hspace*{0pt}\\
\hspace*{0pt}datatype nat = Suc of nat | Zero{\char95}nat;\\
\hspace*{0pt}\\
\hspace*{0pt}fun less{\char95}nat m (Suc n) = less{\char95}eq{\char95}nat m n\\
\hspace*{0pt} ~| less{\char95}nat n Zero{\char95}nat = false\\
\hspace*{0pt}and less{\char95}eq{\char95}nat (Suc m) n = less{\char95}nat m n\\
\hspace*{0pt} ~| less{\char95}eq{\char95}nat Zero{\char95}nat n = true;\\
\hspace*{0pt}\\
\hspace*{0pt}fun in{\char95}interval (k, l) n = (less{\char95}eq{\char95}nat k n) andalso (less{\char95}eq{\char95}nat n l);\\
\hspace*{0pt}\\
\hspace*{0pt}end; (*struct Example*)%
\end{isamarkuptext}%
\isamarkuptrue%
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\endisatagquote
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\begin{isamarkuptext}%
\noindent This still is not perfect: the parentheses
around the \qt{andalso} expression are superfluous.
Though the serialiser
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%
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\isadelimquotett
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\isatagquotett
\isacommand{code{\isacharunderscore}const}\isamarkupfalse%
\ {\isachardoublequoteopen}op\ {\isasymand}{\isachardoublequoteclose}\isanewline
\ \ {\isacharparenleft}SML\ \isakeyword{infixl}\ {\isadigit{1}}\ {\isachardoublequoteopen}andalso{\isachardoublequoteclose}{\isacharparenright}%
\endisatagquotett
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\begin{isamarkuptext}%
\isatypewriter%
\noindent%
\hspace*{0pt}structure Example = \\
\hspace*{0pt}struct\\
\hspace*{0pt}\\
\hspace*{0pt}datatype nat = Suc of nat | Zero{\char95}nat;\\
\hspace*{0pt}\\
\hspace*{0pt}fun less{\char95}nat m (Suc n) = less{\char95}eq{\char95}nat m n\\
\hspace*{0pt} ~| less{\char95}nat n Zero{\char95}nat = false\\
\hspace*{0pt}and less{\char95}eq{\char95}nat (Suc m) n = less{\char95}nat m n\\
\hspace*{0pt} ~| less{\char95}eq{\char95}nat Zero{\char95}nat n = true;\\
\hspace*{0pt}\\
\hspace*{0pt}fun in{\char95}interval (k, l) n = less{\char95}eq{\char95}nat k n andalso less{\char95}eq{\char95}nat n l;\\
\hspace*{0pt}\\
\hspace*{0pt}end; (*struct Example*)%
\end{isamarkuptext}%
\isamarkuptrue%
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\endisatagquote
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\begin{isamarkuptext}%
\noindent The attentive reader may ask how we assert that no generated
code will accidentally overwrite. For this reason the serialiser has
an internal table of identifiers which have to be avoided to be used
for new declarations. Initially, this table typically contains the
keywords of the target language. It can be extended manually, thus avoiding
accidental overwrites, using the \hyperlink{command.code-reserved}{\mbox{\isa{\isacommand{code{\isacharunderscore}reserved}}}} command:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\isacommand{code{\isacharunderscore}reserved}\isamarkupfalse%
\ {\isachardoublequoteopen}{\isasymSML}{\isachardoublequoteclose}\ bool\ true\ false\ andalso%
\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
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\begin{isamarkuptext}%
\noindent Next, we try to map HOL pairs to SML pairs, using the
infix ``\verb|*|'' type constructor and parentheses:%
\end{isamarkuptext}%
\isamarkuptrue%
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\endisataginvisible
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\isatagquotett
\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}%
\endisatagquotett
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\begin{isamarkuptext}%
\noindent The initial bang ``\verb|!|'' tells the serialiser
never to 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 serialisations provide; however their usage
requires careful thinking in order not to introduce
inconsistencies -- or, in other words:
custom serialisations are completely axiomatic.
A further noteworthy details is that any special
character in a custom serialisation may be quoted
using ``\verb|'|''; thus, in
``\verb|fn '_ => _|'' the first
``\verb|_|'' is a proper underscore while the
second ``\verb|_|'' is a placeholder.%
\end{isamarkuptext}%
\isamarkuptrue%
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\isamarkupsubsection{\isa{Haskell} serialisation%
}
\isamarkuptrue%
%
\begin{isamarkuptext}%
For convenience, the default
\isa{HOL} setup for \isa{Haskell} maps the \isa{eq} class to
its counterpart in \isa{Haskell}, giving custom serialisations
for the class \isa{eq} (by command \hyperlink{command.code-class}{\mbox{\isa{\isacommand{code{\isacharunderscore}class}}}}) and its operation
\isa{eq{\isacharunderscore}class{\isachardot}eq}%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquotett
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\endisadelimquotett
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\isatagquotett
\isacommand{code{\isacharunderscore}class}\isamarkupfalse%
\ eq\isanewline
\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Eq{\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}%
\endisatagquotett
{\isafoldquotett}%
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\isadelimquotett
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\begin{isamarkuptext}%
\noindent A problem now occurs whenever a type which
is an instance of \isa{eq} in \isa{HOL} is mapped
on a \isa{Haskell}-built-in type which is also an instance
of \isa{Haskell} \isa{Eq}:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquote
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\endisadelimquote
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\isatagquote
\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%
\ \isacommand{by}\isamarkupfalse%
\ default\ {\isacharparenleft}simp\ add{\isacharcolon}\ eq{\isacharunderscore}bar{\isacharunderscore}def{\isacharparenright}\isanewline
\isanewline
\isacommand{end}\isamarkupfalse%
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\endisatagquote
{\isafoldquote}%
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\isadelimquote
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\endisadelimquote
\isanewline
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\isadelimquotett
\isanewline
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\endisadelimquotett
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\isatagquotett
\isacommand{code{\isacharunderscore}type}\isamarkupfalse%
\ bar\isanewline
\ \ {\isacharparenleft}Haskell\ {\isachardoublequoteopen}Integer{\isachardoublequoteclose}{\isacharparenright}%
\endisatagquotett
{\isafoldquotett}%
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\isadelimquotett
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\endisadelimquotett
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\begin{isamarkuptext}%
\noindent The code generator would produce
an additional instance, which of course is rejected by the \isa{Haskell}
compiler.
To suppress this additional instance, use
\isa{code{\isacharunderscore}instance}:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquotett
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\endisadelimquotett
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\isatagquotett
\isacommand{code{\isacharunderscore}instance}\isamarkupfalse%
\ bar\ {\isacharcolon}{\isacharcolon}\ eq\isanewline
\ \ {\isacharparenleft}Haskell\ {\isacharminus}{\isacharparenright}%
\endisatagquotett
{\isafoldquotett}%
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\isadelimquotett
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\endisadelimquotett
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\isamarkupsubsection{Enhancing the target language context \label{sec:include}%
}
\isamarkuptrue%
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\begin{isamarkuptext}%
In rare cases it is necessary to \emph{enrich} the context of a
target language; this is accomplished using the \hyperlink{command.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}}
command:%
\end{isamarkuptext}%
\isamarkuptrue%
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\isadelimquotett
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\endisadelimquotett
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\isatagquotett
\isacommand{code{\isacharunderscore}include}\isamarkupfalse%
\ Haskell\ {\isachardoublequoteopen}Errno{\isachardoublequoteclose}\isanewline
{\isacharverbatimopen}errno\ i\ {\isacharequal}\ error\ {\isacharparenleft}{\isachardoublequote}Error\ number{\isacharcolon}\ {\isachardoublequote}\ {\isacharplus}{\isacharplus}\ show\ i{\isacharparenright}{\isacharverbatimclose}\isanewline
\isanewline
\isacommand{code{\isacharunderscore}reserved}\isamarkupfalse%
\ Haskell\ Errno%
\endisatagquotett
{\isafoldquotett}%
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\isadelimquotett
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\endisadelimquotett
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\begin{isamarkuptext}%
\noindent Such named \isa{include}s are then prepended to every generated code.
Inspect such code in order to find out how \hyperlink{command.code-include}{\mbox{\isa{\isacommand{code{\isacharunderscore}include}}}} behaves
with respect to a particular target language.%
\end{isamarkuptext}%
\isamarkuptrue%
%
\isadelimtheory
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\endisadelimtheory
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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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