\chapter{The Isabelle/Isar Conversion Guide}
Subsequently, we give a few practical hints on working in a mixed environment
with old Isabelle ML proof scripts and new Isabelle/Isar theories. There are
basically three ways to cope with this issue.
\begin{enumerate}
\item Do not convert old sources at all, but communicate directly at the level
of internal theory and theorem values.
\item Manually port old-style theory files to new-style ones (very easy), and
ML proof scripts to Isar tactic emulation scripts (quite easy).
\item Actually redo ML proof scripts as human readable Isar proof texts
(probably hard, depending who wrote the original scripts).
\end{enumerate}
\section{No conversion}
Internally, Isabelle handles both old and new-style theories at the same time;
the theory loader automatically detects the input format. In any case, this
results in certain internal ML values of type \texttt{theory} and
\texttt{thm}. These may be accessed from either the classic or Isar version,
provided that some minimal care is taken.
\subsection{Referring to theorem and theory values}
\begin{ttbox}
thm : xstring -> thm
thms : xstring -> thm list
the_context : unit -> theory
theory : string -> theory
\end{ttbox}
These above functions provide general means to refer to logical objects from
ML. While old-style theories used to emit many ML bindings to theorems (and
theories), this is no longer done for new-style Isabelle/Isar theories.
Nevertheless, it is often more appropriate to use these explicit functions in
any case, even if referring to old theories.
\begin{descr}
\item [$\mathtt{thm}~name$ and $\mathtt{thms}~name$] retrieve theorems stored
in the current theory context, including any ancestor node.
The convention of old-style theories was to bind any theorem as an ML value
as well. New-style theories no longer do this, so ML code may have to use
\texttt{thm~"foo"} rather than just \texttt{foo}.
\item [$\mathtt{the_context()}$] refers to the current theory context.
Old-style theories often use the ML binding \texttt{thy}, which is
dynamically created as part of producing ML code out of the theory source.
\item [$\mathtt{theory}~name$] retrieves the named theory from the global
theory loader database.
The ML code generated from old style theories would include an ML binding
$name\mathtt{.thy}$ as part of an ML structure.
\end{descr}
\subsection{Enabling new-style theories to retrieve theory values}
\begin{ttbox}
qed : string -> unit
bind_thm : string * thm -> unit
bind_thms : string * thm list -> unit
\end{ttbox}
ML proof scripts have to be well-behaved in storing theorems properly within
the current theory context, in order to enable new-style theories to retrieve
these these later.
\begin{descr}
\item [$\mathtt{qed}~name$] is the canonical way to conclude a proof script in
ML. This already manages entry in the theorem database of the current
theory context.
\item [$\mathtt{bind_thm}~(name, thm)$ and $\mathtt{bind_thms}~(name, thms)$]
store theorems that are produced in ML in an ad-hoc manner.
Note that the original ``LCF'' system approach of binding theorem values on
the ML toplevel only has long been given up in Isabelle. Nevertheless,
legacy proof scripts may occasionally contain ill-behaved code like this:
\texttt{val foo = result();} So far, this form did not give any immediate
feedback that there is something wrong, apart from theorems missing in the
WWW presentation, for example. Now it prevents such theorems to be referred
from new-style theories.
\end{descr}
\subsection{Providing legacy ML bindings}
\begin{matharray}{rcl}
\isarcmd{ML} & : & \isartrans{\cdot}{\cdot} \\
\end{matharray}
New-style theories may provide ML bindings to accommodate legacy ML scripts as
follows.
\[
\isarkeyword{ML}~\{*~\mbox{\texttt{val foo = thm "foo"}}~*\}
\]
Note that this command cannot be undone; invalid theorem bindings in ML may
persist.
By providing an old-style ML binding in the way that legacy proof scripts
usually expect, one may avoid to change all occurrences of a \texttt{foo}
reference into \texttt{thm~"foo"}.
\section{Porting proof scripts}
Porting legacy theory and ML files to proper Isabelle/Isar theories has
several advantages. For example, the Proof~General user interface
\cite{proofgeneral} for Isabelle/Isar is more robust and more comfortable than
the classic Isabelle version. This is due to the fact that the generic ML
toplevel has been replaced by the new Isar interaction loop, with full control
over input synchronization and errors.
Furthermore, the Isabelle document preparation system only properly with
new-style theories (see also \cite{isabelle-system}). There is only very
basic document output of the plain sources of legacy theories, lacking
theorems and proof scripts. Proper document markup is only available for
Isabelle/Isar theories.
\subsection{Theory syntax}
Basically, the new-style Isabelle/Isar theory syntax is a proper superset of
the old one. Only a few quirks and legacy problems have been eliminated,
resulting in simpler rules with less exceptions.
\medskip The main differences in the new syntax are as follows.
\begin{itemize}
\item Types and terms have to be \emph{atomic} as far as the theory syntax is
concerned; this usually requires proper quoting of input strings.
The old theory syntax used to fake part of the syntax of types in order to
require less quoting. This has caused too many strange effects and is no
longer supported.
Note that quotes are \emph{not} required for simple atomic terms, such as
plain identifiers (e.g.\ $x$), numerals (e.g.\ $1$), or non-ASCII symbols
(e.g.\ $\forall$, which is input as \verb,\<forall>,).
\item Every name may be quoted, if required. The old syntax would
occasionally demand plain identifiers vs.\ quoted strings to accommodate
certain (discontinued) syntactic features.
\item Theorem declarations now require an explicit colon to separate the name
and the statement (e.g.\ see the syntax of $\DEFS$ in \S\ref{sec:consts}, or
$\THEOREMNAME$ in \S\ref{sec:axms-thms}).
\end{itemize}
Isabelle/Isar error messages are usually quite explicit about the problem, so
doubtful cases of syntax may as well just tried interactively.
\subsection{Basic goal statements}\label{sec:conv-goal}
In ML scripts, the canonical a goal statement with completed proof script is
as follows.
\begin{ttbox}
Goal "\(\phi\)";
by \(tac@1\);
\(\vdots\);
by \(tac@n\);
qed "\(name\)";
\end{ttbox}
This form may be turned into an Isar tactic emulation script like this:
\begin{matharray}{l}
\LEMMA{name}\texttt"{\phi}\texttt" \\
\quad \isarkeyword{apply}~meth@1 \\
\quad \vdots \\
\quad \isarkeyword{apply}~meth@n \\
\quad \isarkeyword{done} \\
\end{matharray}
The main statement may be $\THEOREMNAME$ as well. See \S\ref{sec:conv-tac}
for further details on how to convert actual tactic expressions into proof
methods.
\medskip Classic Isabelle provides many variant forms of goal commands, see
\cite{isabelle-ref} for further details. The second most common one is
\texttt{Goalw}, which expands definitions before commencing the actual proof
script.
\begin{ttbox}
Goalw [defs] "\(\phi\)";
\(\vdots\)
\end{ttbox}
This may be replaced by an explicit invocation of the $unfold$ proof method.
\begin{matharray}{l}
\LEMMA{name}\texttt"{\phi}\texttt" \\
\quad \isarkeyword{apply}~(unfold~defs) \\
\quad \vdots \\
\end{matharray}
%FIXME "goal" and higher-order rules;
\subsection{Tactics vs.\ proof methods}\label{sec:conv-tac}
Proof methods closely resemble traditional tactics, when used in unstructured
sequences of $\isarkeyword{apply}$ commands (cf.\ \S\ref{sec:conv-goal}).
Unlike tactics, proof methods provide proper concrete syntax for additional
arguments, options, and modifiers. Thus a typical method text is usually more
concise than the corresponding tactic expression in ML.
Well-structured Isar proof texts usually demand much less diverse methods than
traditional proof scripts, so basically a few methods would be sufficient.
Isabelle/Isar provides emulations for any major ML tactic of classic Isabelle,
mostly for the sake of easy porting of existing developments. Nevertheless,
the Isar versions often cover several old-style tactics by a single method.
For example, $simp$ replaces all of \texttt{simp_tac}~/
\texttt{asm_simp_tac}~/ \texttt{full_simp_tac}~/ \texttt{asm_full_simp_tac},
including concrete syntax for augmenting the Simplifier context (the current
``simpset'').
\bigskip
FIXME
\begin{matharray}{llll}
\texttt{rtac}~a~1 & & rule~a \\
\texttt{resolve_tac}~[a@1, \dots, a@n]~1 & & rule~a@1~\dots~a@n \\
\texttt{res_inst_tac}~[(x@1, t@1), \dots, (x@n, t@n)]~a~1 & &
rule_tac~x@1 = t@1~\dots~x@n = t@n~\textrm{in}~a \\
% \texttt{} & & \\
\texttt{stac}~a~1 & & subst~a \\
\texttt{strip_tac}~1 & & intro~strip & \Text{(HOL)} \\
\texttt{split_all_tac} & & simp~(no_asm_simp)~only:~split_tupled_all & \Text{(HOL)} \\
& \approx & simp~only:~split_tupled_all & \Text{(HOL)} \\
& \ll & clarify & \Text{(HOL)} \\
\end{matharray}
\subsection{Declarations and ad-hoc operations}
%\section{Performing actual proof}
%FIXME
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