doc-src/IsarRef/pure.tex
author wenzelm
Tue Mar 21 17:32:43 2000 +0100 (2000-03-21)
changeset 8547 93b8685d004b
parent 8533 d534ddf14076
child 8620 3786d47f5570
permissions -rw-r--r--
tuned;
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\chapter{Basic Isar Language Elements}\label{ch:pure-syntax}
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Subsequently, we introduce the main part of Pure Isar theory and proof
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commands, together with fundamental proof methods and attributes.
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Chapter~\ref{ch:gen-tools} describes further Isar elements provided by generic
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tools and packages (such as the Simplifier) that are either part of Pure
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Isabelle or pre-installed by most object logics.  Chapter~\ref{ch:hol-tools}
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refers to actual object-logic specific elements of Isabelle/HOL.
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\medskip
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Isar commands may be either \emph{proper} document constructors, or
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\emph{improper commands}.  Some proof methods and attributes introduced later
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are classified as improper as well.  Improper Isar language elements, which
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are subsequently marked by $^*$, are often helpful when developing proof
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documents, while their use is discouraged for the final outcome.  Typical
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examples are diagnostic commands that print terms or theorems according to the
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current context; other commands even emulate old-style tactical theorem
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proving.
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\section{Theory commands}
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\subsection{Defining theories}\label{sec:begin-thy}
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\indexisarcmd{header}\indexisarcmd{theory}\indexisarcmd{end}\indexisarcmd{context}
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\begin{matharray}{rcl}
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  \isarcmd{header} & : & \isarkeep{toplevel} \\
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  \isarcmd{theory} & : & \isartrans{toplevel}{theory} \\
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  \isarcmd{context}^* & : & \isartrans{toplevel}{theory} \\
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  \isarcmd{end} & : & \isartrans{theory}{toplevel} \\
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\end{matharray}
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Isabelle/Isar ``new-style'' theories are either defined via theory files or
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interactively.  Both theory-level specifications and proofs are handled
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uniformly --- occasionally definitional mechanisms even require some explicit
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proof as well.  In contrast, ``old-style'' Isabelle theories support batch
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processing only, with the proof scripts collected in separate ML files.
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The first actual command of any theory has to be $\THEORY$, starting a new
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theory based on the merge of existing ones.  Just preceding $\THEORY$, there
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may be an optional $\isarkeyword{header}$ declaration, which is relevant to
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document preparation only; it acts very much like a special pre-theory markup
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command (cf.\ \S\ref{sec:markup-thy} and \S\ref{sec:markup-thy}).  The theory
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context may be also changed by $\CONTEXT$ without creating a new theory.  In
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both cases, $\END$ concludes the theory development; it has to be the very
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last command of any theory file.
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\begin{rail}
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  'header' text
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  ;
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  'theory' name '=' (name + '+') filespecs? ':'
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  ;
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  'context' name
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  ;
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  'end'
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  ;;
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  filespecs: 'files' ((name | parname) +);
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{header}~text$] provides plain text markup just preceding
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  the formal beginning of a theory.  In actual document preparation the
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  corresponding {\LaTeX} macro \verb,\isamarkupheader, may be redefined to
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  produce chapter or section headings.  See also \S\ref{sec:markup-thy} and
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  \S\ref{sec:markup-prf} for further markup commands.
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\item [$\THEORY~A = B@1 + \cdots + B@n\colon$] commences a new theory $A$
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  based on existing ones $B@1 + \cdots + B@n$.  Isabelle's theory loader
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  system ensures that any of the base theories are properly loaded (and fully
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  up-to-date when $\THEORY$ is executed interactively).  The optional
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  $\isarkeyword{files}$ specification declares additional dependencies on ML
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  files.  Unless put in parentheses, any file will be loaded immediately via
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  $\isarcmd{use}$ (see also \S\ref{sec:ML}).  The optional ML file
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  \texttt{$A$.ML} that may be associated with any theory should \emph{not} be
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  included in $\isarkeyword{files}$, though.
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\item [$\CONTEXT~B$] enters an existing theory context, basically in read-only
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  mode, so only a limited set of commands may be performed without destroying
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  the theory.  Just as for $\THEORY$, the theory loader ensures that $B$ is
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  loaded and up-to-date.
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\item [$\END$] concludes the current theory definition or context switch.
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Note that this command cannot be undone, but the whole theory definition has
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to be retracted.
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\end{descr}
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\subsection{Theory markup commands}\label{sec:markup-thy}
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\indexisarcmd{chapter}\indexisarcmd{section}\indexisarcmd{subsection}
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\indexisarcmd{subsubsection}\indexisarcmd{text}\indexisarcmd{text-raw}
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\begin{matharray}{rcl}
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  \isarcmd{chapter} & : & \isartrans{theory}{theory} \\
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  \isarcmd{section} & : & \isartrans{theory}{theory} \\
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  \isarcmd{subsection} & : & \isartrans{theory}{theory} \\
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  \isarcmd{subsubsection} & : & \isartrans{theory}{theory} \\
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  \isarcmd{text} & : & \isartrans{theory}{theory} \\
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  \isarcmd{text_raw} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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Apart from formal comments (see \S\ref{sec:comments}), markup commands provide
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a structured way to insert text into the document generated from a theory (see
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\cite{isabelle-sys} for more information on Isabelle's document preparation
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tools).
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\railalias{textraw}{text\_raw}
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\railterm{textraw}
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\begin{rail}
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  ('chapter' | 'section' | 'subsection' | 'subsubsection' | 'text' | textraw) text
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  ;
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{chapter}$, $\isarkeyword{section}$,
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  $\isarkeyword{subsection}$, and $\isarkeyword{subsubsection}$] mark chapter
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  and section headings.
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\item [$\TEXT$] specifies paragraphs of plain text, including references to
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  formal entities.\footnote{The latter feature is not yet supported.
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    Nevertheless, any source text of the form
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    ``\texttt{\at\ttlbrace$\dots$\ttrbrace}'' should be considered as reserved
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    for future use.}
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\item [$\isarkeyword{text_raw}$] inserts {\LaTeX} source into the output,
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  without additional markup.  Thus the full range of document manipulations
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  becomes available.  A typical application would be to emit
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  \verb,\begin{comment}, and \verb,\end{comment}, commands to exclude certain
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  parts from the final document.\footnote{This requires the \texttt{comment}
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    package to be included in {\LaTeX}, of course.}
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\end{descr}
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Any markup command (except $\isarkeyword{text_raw}$) corresponds to a {\LaTeX}
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macro with the name prefixed by \verb,\isamarkup, (e.g.\ 
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\verb,\isamarkupchapter, for $\isarkeyword{chapter}$). The \railqtoken{text}
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argument is passed to that macro unchanged, i.e.\ further {\LaTeX} commands
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may be included here as well.
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\medskip
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Additional markup commands are available for proofs (see
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\S\ref{sec:markup-prf}).  Also note that the $\isarkeyword{header}$
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declaration (see \S\ref{sec:begin-thy}) admits to insert document markup
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elements just preceding the actual theory definition.
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\subsection{Type classes and sorts}\label{sec:classes}
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\indexisarcmd{classes}\indexisarcmd{classrel}\indexisarcmd{defaultsort}
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\begin{matharray}{rcl}
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  \isarcmd{classes} & : & \isartrans{theory}{theory} \\
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  \isarcmd{classrel} & : & \isartrans{theory}{theory} \\
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  \isarcmd{defaultsort} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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\begin{rail}
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  'classes' (classdecl comment? +)
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  ;
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  'classrel' nameref '<' nameref comment?
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  ;
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  'defaultsort' sort comment?
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  ;
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{classes}~c<\vec c$] declares class $c$ to be a subclass
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  of existing classes $\vec c$.  Cyclic class structures are ruled out.
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\item [$\isarkeyword{classrel}~c@1<c@2$] states a subclass relation between
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  existing classes $c@1$ and $c@2$.  This is done axiomatically!  The
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  $\isarkeyword{instance}$ command (see \S\ref{sec:axclass}) provides a way to
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  introduce proven class relations.
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\item [$\isarkeyword{defaultsort}~s$] makes sort $s$ the new default sort for
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  any type variables given without sort constraints.  Usually, the default
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  sort would be only changed when defining new object-logics.
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\end{descr}
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\subsection{Primitive types and type abbreviations}\label{sec:types-pure}
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\indexisarcmd{typedecl}\indexisarcmd{types}\indexisarcmd{nonterminals}\indexisarcmd{arities}
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\begin{matharray}{rcl}
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  \isarcmd{types} & : & \isartrans{theory}{theory} \\
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  \isarcmd{typedecl} & : & \isartrans{theory}{theory} \\
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  \isarcmd{nonterminals} & : & \isartrans{theory}{theory} \\
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  \isarcmd{arities} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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\begin{rail}
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  'types' (typespec '=' type infix? comment? +)
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  ;
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  'typedecl' typespec infix? comment?
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  ;
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  'nonterminals' (name +) comment?
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  ;
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  'arities' (nameref '::' arity comment? +)
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  ;
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\end{rail}
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\begin{descr}
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\item [$\TYPES~(\vec\alpha)t = \tau$] introduces \emph{type synonym}
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  $(\vec\alpha)t$ for existing type $\tau$.  Unlike actual type definitions,
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  as are available in Isabelle/HOL for example, type synonyms are just purely
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  syntactic abbreviations without any logical significance.  Internally, type
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  synonyms are fully expanded.
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\item [$\isarkeyword{typedecl}~(\vec\alpha)t$] declares a new type constructor
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  $t$, intended as an actual logical type.  Note that object-logics such as
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  Isabelle/HOL override $\isarkeyword{typedecl}$ by their own version.
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\item [$\isarkeyword{nonterminals}~\vec c$] declares $0$-ary type constructors
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  $\vec c$ to act as purely syntactic types, i.e.\ nonterminal symbols of
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  Isabelle's inner syntax of terms or types.
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\item [$\isarkeyword{arities}~t::(\vec s)s$] augments Isabelle's order-sorted
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  signature of types by new type constructor arities.  This is done
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  axiomatically!  The $\isarkeyword{instance}$ command (see
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  \S\ref{sec:axclass}) provides a way to introduce proven type arities.
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\end{descr}
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\subsection{Constants and simple definitions}\label{sec:consts}
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\indexisarcmd{consts}\indexisarcmd{defs}\indexisarcmd{constdefs}\indexoutertoken{constdecl}
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\begin{matharray}{rcl}
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  \isarcmd{consts} & : & \isartrans{theory}{theory} \\
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  \isarcmd{defs} & : & \isartrans{theory}{theory} \\
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  \isarcmd{constdefs} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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\begin{rail}
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  'consts' (constdecl +)
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  ;
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  'defs' (axmdecl prop comment? +)
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  ;
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  'constdefs' (constdecl prop comment? +)
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  ;
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  constdecl: name '::' type mixfix? comment?
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  ;
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\end{rail}
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\begin{descr}
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\item [$\CONSTS~c::\sigma$] declares constant $c$ to have any instance of type
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  scheme $\sigma$.  The optional mixfix annotations may attach concrete syntax
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  to the constants declared.
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\item [$\DEFS~name: eqn$] introduces $eqn$ as a definitional axiom for some
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  existing constant.  See \cite[\S6]{isabelle-ref} for more details on the
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  form of equations admitted as constant definitions.
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\item [$\isarkeyword{constdefs}~c::\sigma~eqn$] combines declarations and
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  definitions of constants, using the canonical name $c_def$ for the
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  definitional axiom.
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\end{descr}
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\subsection{Syntax and translations}\label{sec:syn-trans}
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\indexisarcmd{syntax}\indexisarcmd{translations}
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\begin{matharray}{rcl}
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  \isarcmd{syntax} & : & \isartrans{theory}{theory} \\
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  \isarcmd{translations} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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\begin{rail}
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  'syntax' ('(' name 'output'? ')')? (constdecl +)
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  ;
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  'translations' (transpat ('==' | '=>' | '<=') transpat comment? +)
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  ;
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  transpat: ('(' nameref ')')? string
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  ;
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{syntax}~(mode)~decls$] is similar to $\CONSTS~decls$,
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  except that the actual logical signature extension is omitted.  Thus the
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  context free grammar of Isabelle's inner syntax may be augmented in
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  arbitrary ways, independently of the logic.  The $mode$ argument refers to
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  the print mode that the grammar rules belong; unless the \texttt{output}
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  flag is given, all productions are added both to the input and output
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  grammar.
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\item [$\isarkeyword{translations}~rules$] specifies syntactic translation
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  rules (i.e.\ \emph{macros}): parse~/ print rules (\texttt{==}), parse rules
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  (\texttt{=>}), or print rules (\texttt{<=}).  Translation patterns may be
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  prefixed by the syntactic category to be used for parsing; the default is
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  \texttt{logic}.
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\end{descr}
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\subsection{Axioms and theorems}
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\indexisarcmd{axioms}\indexisarcmd{theorems}\indexisarcmd{lemmas}
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\begin{matharray}{rcl}
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  \isarcmd{axioms} & : & \isartrans{theory}{theory} \\
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  \isarcmd{theorems} & : & \isartrans{theory}{theory} \\
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  \isarcmd{lemmas} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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\begin{rail}
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  'axioms' (axmdecl prop comment? +)
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  ;
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  ('theorems' | 'lemmas') thmdef? thmrefs
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  ;
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{axioms}~a: \phi$] introduces arbitrary statements as
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  axioms of the meta-logic.  In fact, axioms are ``axiomatic theorems'', and
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  may be referred later just as any other theorem.
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  Axioms are usually only introduced when declaring new logical systems.
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  Everyday work is typically done the hard way, with proper definitions and
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  actual proven theorems.
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\item [$\isarkeyword{theorems}~a = \vec b$] stores lists of existing theorems.
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  Typical applications would also involve attributes, to declare Simplifier
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  rules, for example.
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\item [$\isarkeyword{lemmas}$] is similar to $\isarkeyword{theorems}$, but
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  tags the results as ``lemma''.
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\end{descr}
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\subsection{Name spaces}
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\indexisarcmd{global}\indexisarcmd{local}
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   321
\begin{matharray}{rcl}
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   322
  \isarcmd{global} & : & \isartrans{theory}{theory} \\
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   323
  \isarcmd{local} & : & \isartrans{theory}{theory} \\
wenzelm@7134
   324
\end{matharray}
wenzelm@7134
   325
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   326
Isabelle organizes any kind of name declarations (of types, constants,
wenzelm@8547
   327
theorems etc.) by separate hierarchically structured name spaces.  Normally
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   328
the user never has to control the behavior of name space entry by hand, yet
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   329
the following commands provide some way to do so.
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   330
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   331
\begin{descr}
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   332
\item [$\isarkeyword{global}$ and $\isarkeyword{local}$] change the current
wenzelm@7167
   333
  name declaration mode.  Initially, theories start in $\isarkeyword{local}$
wenzelm@7167
   334
  mode, causing all names to be automatically qualified by the theory name.
wenzelm@7895
   335
  Changing this to $\isarkeyword{global}$ causes all names to be declared
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   336
  without the theory prefix, until $\isarkeyword{local}$ is declared again.
wenzelm@7167
   337
\end{descr}
wenzelm@7134
   338
wenzelm@7134
   339
wenzelm@7167
   340
\subsection{Incorporating ML code}\label{sec:ML}
wenzelm@7134
   341
wenzelm@7895
   342
\indexisarcmd{use}\indexisarcmd{ML}\indexisarcmd{ML-setup}\indexisarcmd{setup}
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   343
\begin{matharray}{rcl}
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   344
  \isarcmd{use} & : & \isartrans{\cdot}{\cdot} \\
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   345
  \isarcmd{ML} & : & \isartrans{\cdot}{\cdot} \\
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   346
  \isarcmd{ML_setup} & : & \isartrans{theory}{theory} \\
wenzelm@7175
   347
  \isarcmd{setup} & : & \isartrans{theory}{theory} \\
wenzelm@7134
   348
\end{matharray}
wenzelm@7134
   349
wenzelm@7895
   350
\railalias{MLsetup}{ML\_setup}
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   351
\railterm{MLsetup}
wenzelm@7895
   352
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   353
\begin{rail}
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   354
  'use' name
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   355
  ;
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   356
  ('ML' | MLsetup | 'setup') text
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   357
  ;
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   358
\end{rail}
wenzelm@7134
   359
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   360
\begin{descr}
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   361
\item [$\isarkeyword{use}~file$] reads and executes ML commands from $file$.
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   362
  The current theory context (if present) is passed down to the ML session,
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   363
  but may not be modified.  Furthermore, the file name is checked with the
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   364
  $\isarkeyword{files}$ dependency declaration given in the theory header (see
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   365
  also \S\ref{sec:begin-thy}).
wenzelm@7466
   366
  
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   367
\item [$\isarkeyword{ML}~text$] executes ML commands from $text$.  The theory
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   368
  context is passed in the same way as for $\isarkeyword{use}$.
wenzelm@7895
   369
  
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   370
\item [$\isarkeyword{ML_setup}~text$] executes ML commands from $text$.  The
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   371
  theory context is passed down to the ML session, and fetched back
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   372
  afterwards.  Thus $text$ may actually change the theory as a side effect.
wenzelm@7895
   373
  
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   374
\item [$\isarkeyword{setup}~text$] changes the current theory context by
wenzelm@8379
   375
  applying $text$, which refers to an ML expression of type
wenzelm@8379
   376
  \texttt{(theory~->~theory)~list}.  The $\isarkeyword{setup}$ command is the
wenzelm@8547
   377
  canonical way to initialize any object-logic specific tools and packages
wenzelm@8547
   378
  written in ML.
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   379
\end{descr}
wenzelm@7134
   380
wenzelm@7134
   381
wenzelm@8250
   382
\subsection{Syntax translation functions}
wenzelm@7134
   383
wenzelm@8250
   384
\indexisarcmd{parse-ast-translation}\indexisarcmd{parse-translation}
wenzelm@8250
   385
\indexisarcmd{print-translation}\indexisarcmd{typed-print-translation}
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   386
\indexisarcmd{print-ast-translation}\indexisarcmd{token-translation}
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   387
\begin{matharray}{rcl}
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   388
  \isarcmd{parse_ast_translation} & : & \isartrans{theory}{theory} \\
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   389
  \isarcmd{parse_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   390
  \isarcmd{print_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   391
  \isarcmd{typed_print_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   392
  \isarcmd{print_ast_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   393
  \isarcmd{token_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   394
\end{matharray}
wenzelm@7134
   395
wenzelm@8250
   396
Syntax translation functions written in ML admit almost arbitrary
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   397
manipulations of Isabelle's inner syntax.  Any of the above commands have a
wenzelm@8250
   398
single \railqtoken{text} argument that refers to an ML expression of
wenzelm@8379
   399
appropriate type.
wenzelm@8379
   400
wenzelm@8379
   401
\begin{ttbox}
wenzelm@8379
   402
val parse_ast_translation   : (string * (ast list -> ast)) list
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   403
val parse_translation       : (string * (term list -> term)) list
wenzelm@8379
   404
val print_translation       : (string * (term list -> term)) list
wenzelm@8379
   405
val typed_print_translation :
wenzelm@8379
   406
  (string * (bool -> typ -> term list -> term)) list
wenzelm@8379
   407
val print_ast_translation   : (string * (ast list -> ast)) list
wenzelm@8379
   408
val token_translation       :
wenzelm@8379
   409
  (string * string * (string -> string * real)) list
wenzelm@8379
   410
\end{ttbox}
wenzelm@8379
   411
See \cite[\S8]{isabelle-ref} for more information on syntax transformations.
wenzelm@7134
   412
wenzelm@7134
   413
wenzelm@7134
   414
\subsection{Oracles}
wenzelm@7134
   415
wenzelm@7134
   416
\indexisarcmd{oracle}
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   417
\begin{matharray}{rcl}
wenzelm@7134
   418
  \isarcmd{oracle} & : & \isartrans{theory}{theory} \\
wenzelm@7134
   419
\end{matharray}
wenzelm@7134
   420
wenzelm@7175
   421
Oracles provide an interface to external reasoning systems, without giving up
wenzelm@7175
   422
control completely --- each theorem carries a derivation object recording any
wenzelm@7175
   423
oracle invocation.  See \cite[\S6]{isabelle-ref} for more information.
wenzelm@7175
   424
wenzelm@7134
   425
\begin{rail}
wenzelm@7134
   426
  'oracle' name '=' text comment?
wenzelm@7134
   427
  ;
wenzelm@7134
   428
\end{rail}
wenzelm@7134
   429
wenzelm@7167
   430
\begin{descr}
wenzelm@7175
   431
\item [$\isarkeyword{oracle}~name=text$] declares oracle $name$ to be ML
wenzelm@8379
   432
  function $text$, which has to be of type
wenzelm@8379
   433
  \texttt{Sign.sg~*~Object.T~->~term}.
wenzelm@7167
   434
\end{descr}
wenzelm@7134
   435
wenzelm@7134
   436
wenzelm@7134
   437
\section{Proof commands}
wenzelm@7134
   438
wenzelm@7987
   439
Proof commands perform transitions of Isar/VM machine configurations, which
wenzelm@7315
   440
are block-structured, consisting of a stack of nodes with three main
wenzelm@7335
   441
components: logical proof context, current facts, and open goals.  Isar/VM
wenzelm@8547
   442
transitions are \emph{typed} according to the following three different modes
wenzelm@8547
   443
of operation:
wenzelm@7167
   444
\begin{descr}
wenzelm@7167
   445
\item [$proof(prove)$] means that a new goal has just been stated that is now
wenzelm@8547
   446
  to be \emph{proven}; the next command may refine it by some proof method,
wenzelm@8547
   447
  and enter a sub-proof to establish the actual result.
wenzelm@7167
   448
\item [$proof(state)$] is like an internal theory mode: the context may be
wenzelm@7987
   449
  augmented by \emph{stating} additional assumptions, intermediate results
wenzelm@7987
   450
  etc.
wenzelm@7895
   451
\item [$proof(chain)$] is intermediate between $proof(state)$ and
wenzelm@7987
   452
  $proof(prove)$: existing facts (i.e.\ the contents of the special ``$this$''
wenzelm@7987
   453
  register) have been just picked up in order to be used when refining the
wenzelm@7987
   454
  goal claimed next.
wenzelm@7167
   455
\end{descr}
wenzelm@7134
   456
wenzelm@7167
   457
wenzelm@7895
   458
\subsection{Proof markup commands}\label{sec:markup-prf}
wenzelm@7167
   459
wenzelm@7987
   460
\indexisarcmd{sect}\indexisarcmd{subsect}\indexisarcmd{subsubsect}
wenzelm@7895
   461
\indexisarcmd{txt}\indexisarcmd{txt-raw}
wenzelm@7134
   462
\begin{matharray}{rcl}
wenzelm@8101
   463
  \isarcmd{sect} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   464
  \isarcmd{subsect} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   465
  \isarcmd{subsubsect} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   466
  \isarcmd{txt} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   467
  \isarcmd{txt_raw} & : & \isartrans{proof}{proof} \\
wenzelm@7134
   468
\end{matharray}
wenzelm@7134
   469
wenzelm@7895
   470
These markup commands for proof mode closely correspond to the ones of theory
wenzelm@7895
   471
mode (see \S\ref{sec:markup-thy}).  Note that $\isarkeyword{txt_raw}$ is
wenzelm@7895
   472
special in the same way as $\isarkeyword{text_raw}$.
wenzelm@7895
   473
wenzelm@7895
   474
\railalias{txtraw}{txt\_raw}
wenzelm@7895
   475
\railterm{txtraw}
wenzelm@7175
   476
wenzelm@7134
   477
\begin{rail}
wenzelm@7895
   478
  ('sect' | 'subsect' | 'subsubsect' | 'txt' | txtraw) text
wenzelm@7134
   479
  ;
wenzelm@7134
   480
\end{rail}
wenzelm@7134
   481
wenzelm@7134
   482
wenzelm@7315
   483
\subsection{Proof context}\label{sec:proof-context}
wenzelm@7134
   484
wenzelm@7315
   485
\indexisarcmd{fix}\indexisarcmd{assume}\indexisarcmd{presume}\indexisarcmd{def}
wenzelm@7134
   486
\begin{matharray}{rcl}
wenzelm@7134
   487
  \isarcmd{fix} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   488
  \isarcmd{assume} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   489
  \isarcmd{presume} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   490
  \isarcmd{def} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   491
\end{matharray}
wenzelm@7134
   492
wenzelm@7315
   493
The logical proof context consists of fixed variables and assumptions.  The
wenzelm@7315
   494
former closely correspond to Skolem constants, or meta-level universal
wenzelm@7315
   495
quantification as provided by the Isabelle/Pure logical framework.
wenzelm@7315
   496
Introducing some \emph{arbitrary, but fixed} variable via $\FIX x$ results in
wenzelm@7987
   497
a local value that may be used in the subsequent proof as any other variable
wenzelm@7895
   498
or constant.  Furthermore, any result $\edrv \phi[x]$ exported from the
wenzelm@7987
   499
context will be universally closed wrt.\ $x$ at the outermost level: $\edrv
wenzelm@7987
   500
\All x \phi$ (this is expressed using Isabelle's meta-variables).
wenzelm@7315
   501
wenzelm@7315
   502
Similarly, introducing some assumption $\chi$ has two effects.  On the one
wenzelm@7315
   503
hand, a local theorem is created that may be used as a fact in subsequent
wenzelm@7895
   504
proof steps.  On the other hand, any result $\chi \drv \phi$ exported from the
wenzelm@7895
   505
context becomes conditional wrt.\ the assumption: $\edrv \chi \Imp \phi$.
wenzelm@7895
   506
Thus, solving an enclosing goal using such a result would basically introduce
wenzelm@7895
   507
a new subgoal stemming from the assumption.  How this situation is handled
wenzelm@7895
   508
depends on the actual version of assumption command used: while $\ASSUMENAME$
wenzelm@7895
   509
insists on solving the subgoal by unification with some premise of the goal,
wenzelm@7895
   510
$\PRESUMENAME$ leaves the subgoal unchanged in order to be proved later by the
wenzelm@7895
   511
user.
wenzelm@7315
   512
wenzelm@7319
   513
Local definitions, introduced by $\DEF{}{x \equiv t}$, are achieved by
wenzelm@7987
   514
combining $\FIX x$ with another version of assumption that causes any
wenzelm@7987
   515
hypothetical equation $x \equiv t$ to be eliminated by the reflexivity rule.
wenzelm@7987
   516
Thus, exporting some result $x \equiv t \drv \phi[x]$ yields $\edrv \phi[t]$.
wenzelm@7175
   517
wenzelm@7134
   518
\begin{rail}
wenzelm@7431
   519
  'fix' (vars + 'and') comment?
wenzelm@7134
   520
  ;
wenzelm@7315
   521
  ('assume' | 'presume') (assm comment? + 'and')
wenzelm@7134
   522
  ;
wenzelm@7175
   523
  'def' thmdecl? \\ var '==' term termpat? comment?
wenzelm@7134
   524
  ;
wenzelm@7134
   525
wenzelm@7134
   526
  var: name ('::' type)?
wenzelm@7134
   527
  ;
wenzelm@7458
   528
  vars: (name+) ('::' type)?
wenzelm@7431
   529
  ;
wenzelm@7315
   530
  assm: thmdecl? (prop proppat? +)
wenzelm@7315
   531
  ;
wenzelm@7134
   532
\end{rail}
wenzelm@7134
   533
wenzelm@7167
   534
\begin{descr}
wenzelm@8547
   535
\item [$\FIX{\vec x}$] introduces local \emph{arbitrary, but fixed} variables
wenzelm@8547
   536
  $\vec x$.
wenzelm@8515
   537
\item [$\ASSUME{a}{\vec\phi}$ and $\PRESUME{a}{\vec\phi}$] introduce local
wenzelm@8515
   538
  theorems $\vec\phi$ by assumption.  Subsequent results applied to an
wenzelm@8515
   539
  enclosing goal (e.g.\ by $\SHOWNAME$) are handled as follows: $\ASSUMENAME$
wenzelm@8515
   540
  expects to be able to unify with existing premises in the goal, while
wenzelm@8515
   541
  $\PRESUMENAME$ leaves $\vec\phi$ as new subgoals.
wenzelm@7335
   542
  
wenzelm@7335
   543
  Several lists of assumptions may be given (separated by
wenzelm@7895
   544
  $\isarkeyword{and}$); the resulting list of current facts consists of all of
wenzelm@7895
   545
  these concatenated.
wenzelm@7315
   546
\item [$\DEF{a}{x \equiv t}$] introduces a local (non-polymorphic) definition.
wenzelm@7315
   547
  In results exported from the context, $x$ is replaced by $t$.  Basically,
wenzelm@7987
   548
  $\DEF{}{x \equiv t}$ abbreviates $\FIX{x}~\ASSUME{}{x \equiv t}$, with the
wenzelm@7335
   549
  resulting hypothetical equation solved by reflexivity.
wenzelm@7431
   550
  
wenzelm@7431
   551
  The default name for the definitional equation is $x_def$.
wenzelm@7167
   552
\end{descr}
wenzelm@7167
   553
wenzelm@7895
   554
The special name $prems$\indexisarthm{prems} refers to all assumptions of the
wenzelm@7895
   555
current context as a list of theorems.
wenzelm@7315
   556
wenzelm@7167
   557
wenzelm@7167
   558
\subsection{Facts and forward chaining}
wenzelm@7167
   559
wenzelm@7167
   560
\indexisarcmd{note}\indexisarcmd{then}\indexisarcmd{from}\indexisarcmd{with}
wenzelm@7167
   561
\begin{matharray}{rcl}
wenzelm@7167
   562
  \isarcmd{note} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7167
   563
  \isarcmd{then} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm@7167
   564
  \isarcmd{from} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm@7167
   565
  \isarcmd{with} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm@7167
   566
\end{matharray}
wenzelm@7167
   567
wenzelm@7319
   568
New facts are established either by assumption or proof of local statements.
wenzelm@7335
   569
Any fact will usually be involved in further proofs, either as explicit
wenzelm@8547
   570
arguments of proof methods, or when forward chaining towards the next goal via
wenzelm@7335
   571
$\THEN$ (and variants).  Note that the special theorem name
wenzelm@7987
   572
$this$\indexisarthm{this} refers to the most recently established facts.
wenzelm@7167
   573
\begin{rail}
wenzelm@7167
   574
  'note' thmdef? thmrefs comment?
wenzelm@7167
   575
  ;
wenzelm@7167
   576
  'then' comment?
wenzelm@7167
   577
  ;
wenzelm@7167
   578
  ('from' | 'with') thmrefs comment?
wenzelm@7167
   579
  ;
wenzelm@7167
   580
\end{rail}
wenzelm@7167
   581
wenzelm@7167
   582
\begin{descr}
wenzelm@7175
   583
\item [$\NOTE{a}{\vec b}$] recalls existing facts $\vec b$, binding the result
wenzelm@7175
   584
  as $a$.  Note that attributes may be involved as well, both on the left and
wenzelm@7175
   585
  right hand sides.
wenzelm@7167
   586
\item [$\THEN$] indicates forward chaining by the current facts in order to
wenzelm@7895
   587
  establish the goal to be claimed next.  The initial proof method invoked to
wenzelm@7895
   588
  refine that will be offered the facts to do ``anything appropriate'' (cf.\ 
wenzelm@7895
   589
  also \S\ref{sec:proof-steps}).  For example, method $rule$ (see
wenzelm@8515
   590
  \S\ref{sec:pure-meth-att}) would typically do an elimination rather than an
wenzelm@7895
   591
  introduction.  Automatic methods usually insert the facts into the goal
wenzelm@8547
   592
  state before operation.  This provides a simple scheme to control relevance
wenzelm@8547
   593
  of facts in automated proof search.
wenzelm@7335
   594
\item [$\FROM{\vec b}$] abbreviates $\NOTE{}{\vec b}~\THEN$; thus $\THEN$ is
wenzelm@7458
   595
  equivalent to $\FROM{this}$.
wenzelm@7175
   596
\item [$\WITH{\vec b}$] abbreviates $\FROM{\vec b~facts}$; thus the forward
wenzelm@7175
   597
  chaining is from earlier facts together with the current ones.
wenzelm@7167
   598
\end{descr}
wenzelm@7167
   599
wenzelm@8515
   600
Basic proof methods (such as $rule$, see \S\ref{sec:pure-meth-att}) expect
wenzelm@7895
   601
multiple facts to be given in their proper order, corresponding to a prefix of
wenzelm@7895
   602
the premises of the rule involved.  Note that positions may be easily skipped
wenzelm@8547
   603
using something like $\FROM{\text{\texttt{_}}~a~b}$, for example.  This
wenzelm@8547
   604
involves the trivial rule $\PROP\psi \Imp \PROP\psi$, which happens to be
wenzelm@8547
   605
bound in Isabelle/Pure as ``\texttt{_}''
wenzelm@8547
   606
(underscore).\indexisarthm{_@\texttt{_}}
wenzelm@7389
   607
wenzelm@7167
   608
wenzelm@7167
   609
\subsection{Goal statements}
wenzelm@7167
   610
wenzelm@7167
   611
\indexisarcmd{theorem}\indexisarcmd{lemma}
wenzelm@7167
   612
\indexisarcmd{have}\indexisarcmd{show}\indexisarcmd{hence}\indexisarcmd{thus}
wenzelm@7167
   613
\begin{matharray}{rcl}
wenzelm@7167
   614
  \isarcmd{theorem} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@7167
   615
  \isarcmd{lemma} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@7987
   616
  \isarcmd{have} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\
wenzelm@7987
   617
  \isarcmd{show} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\
wenzelm@7167
   618
  \isarcmd{hence} & : & \isartrans{proof(state)}{proof(prove)} \\
wenzelm@7167
   619
  \isarcmd{thus} & : & \isartrans{proof(state)}{proof(prove)} \\
wenzelm@7167
   620
\end{matharray}
wenzelm@7167
   621
wenzelm@7175
   622
Proof mode is entered from theory mode by initial goal commands $\THEOREMNAME$
wenzelm@7895
   623
and $\LEMMANAME$.  New local goals may be claimed within proof mode as well.
wenzelm@7895
   624
Four variants are available, indicating whether the result is meant to solve
wenzelm@8547
   625
some pending goal or whether forward chaining is indicated.
wenzelm@7175
   626
wenzelm@7167
   627
\begin{rail}
wenzelm@7167
   628
  ('theorem' | 'lemma') goal
wenzelm@7167
   629
  ;
wenzelm@7167
   630
  ('have' | 'show' | 'hence' | 'thus') goal
wenzelm@7167
   631
  ;
wenzelm@7167
   632
wenzelm@7167
   633
  goal: thmdecl? proppat comment?
wenzelm@7167
   634
  ;
wenzelm@7167
   635
\end{rail}
wenzelm@7167
   636
wenzelm@7167
   637
\begin{descr}
wenzelm@7335
   638
\item [$\THEOREM{a}{\phi}$] enters proof mode with $\phi$ as main goal,
wenzelm@8547
   639
  eventually resulting in some theorem $\turn \phi$ to be put back into the
wenzelm@8547
   640
  theory.
wenzelm@7987
   641
\item [$\LEMMA{a}{\phi}$] is similar to $\THEOREMNAME$, but tags the result as
wenzelm@7167
   642
  ``lemma''.
wenzelm@7335
   643
\item [$\HAVE{a}{\phi}$] claims a local goal, eventually resulting in a
wenzelm@7167
   644
  theorem with the current assumption context as hypotheses.
wenzelm@7335
   645
\item [$\SHOW{a}{\phi}$] is similar to $\HAVE{a}{\phi}$, but solves some
wenzelm@7895
   646
  pending goal with the result \emph{exported} into the corresponding context
wenzelm@7895
   647
  (cf.\ \S\ref{sec:proof-context}).
wenzelm@7895
   648
\item [$\HENCENAME$] abbreviates $\THEN~\HAVENAME$, i.e.\ claims a local goal
wenzelm@7895
   649
  to be proven by forward chaining the current facts.  Note that $\HENCENAME$
wenzelm@7895
   650
  is also equivalent to $\FROM{this}~\HAVENAME$.
wenzelm@7895
   651
\item [$\THUSNAME$] abbreviates $\THEN~\SHOWNAME$.  Note that $\THUSNAME$ is
wenzelm@7895
   652
  also equivalent to $\FROM{this}~\SHOWNAME$.
wenzelm@7167
   653
\end{descr}
wenzelm@7167
   654
wenzelm@7167
   655
wenzelm@7167
   656
\subsection{Initial and terminal proof steps}\label{sec:proof-steps}
wenzelm@7167
   657
wenzelm@7175
   658
\indexisarcmd{proof}\indexisarcmd{qed}\indexisarcmd{by}
wenzelm@7175
   659
\indexisarcmd{.}\indexisarcmd{..}\indexisarcmd{sorry}
wenzelm@7175
   660
\begin{matharray}{rcl}
wenzelm@7175
   661
  \isarcmd{proof} & : & \isartrans{proof(prove)}{proof(state)} \\
wenzelm@7175
   662
  \isarcmd{qed} & : & \isartrans{proof(state)}{proof(state) ~|~ theory} \\
wenzelm@7175
   663
  \isarcmd{by} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   664
  \isarcmd{.\,.} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   665
  \isarcmd{.} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   666
  \isarcmd{sorry} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   667
\end{matharray}
wenzelm@7175
   668
wenzelm@8547
   669
Arbitrary goal refinement via tactics is considered harmful.  Properly, the
wenzelm@7335
   670
Isar framework admits proof methods to be invoked in two places only.
wenzelm@7167
   671
\begin{enumerate}
wenzelm@7175
   672
\item An \emph{initial} refinement step $\PROOF{m@1}$ reduces a newly stated
wenzelm@7335
   673
  goal to a number of sub-goals that are to be solved later.  Facts are passed
wenzelm@7895
   674
  to $m@1$ for forward chaining, if so indicated by $proof(chain)$ mode.
wenzelm@7167
   675
  
wenzelm@7987
   676
\item A \emph{terminal} conclusion step $\QED{m@2}$ is intended to solve
wenzelm@7987
   677
  remaining goals.  No facts are passed to $m@2$.
wenzelm@7167
   678
\end{enumerate}
wenzelm@7167
   679
wenzelm@8547
   680
The only other proper way to affect pending goals is by $\SHOWNAME$, which
wenzelm@8547
   681
involves an explicit statement of what is to be solved.
wenzelm@7167
   682
wenzelm@7175
   683
\medskip
wenzelm@7175
   684
wenzelm@7167
   685
Also note that initial proof methods should either solve the goal completely,
wenzelm@7895
   686
or constitute some well-understood reduction to new sub-goals.  Arbitrary
wenzelm@7895
   687
automatic proof tools that are prone leave a large number of badly structured
wenzelm@7895
   688
sub-goals are no help in continuing the proof document in any intelligible
wenzelm@7987
   689
way.
wenzelm@7167
   690
wenzelm@7175
   691
\medskip
wenzelm@7175
   692
wenzelm@8547
   693
Unless given explicitly by the user, the default initial method is ``$rule$'',
wenzelm@8547
   694
which applies a single standard elimination or introduction rule according to
wenzelm@8547
   695
the topmost symbol involved.  There is no separate default terminal method.
wenzelm@8547
   696
Any remaining goals are always solved by assumption in the very last step.
wenzelm@7167
   697
wenzelm@7167
   698
\begin{rail}
wenzelm@7167
   699
  'proof' interest? meth? comment?
wenzelm@7167
   700
  ;
wenzelm@7167
   701
  'qed' meth? comment?
wenzelm@7167
   702
  ;
wenzelm@7167
   703
  'by' meth meth? comment?
wenzelm@7167
   704
  ;
wenzelm@7167
   705
  ('.' | '..' | 'sorry') comment?
wenzelm@7167
   706
  ;
wenzelm@7167
   707
wenzelm@7167
   708
  meth: method interest?
wenzelm@7167
   709
  ;
wenzelm@7167
   710
\end{rail}
wenzelm@7167
   711
wenzelm@7167
   712
\begin{descr}
wenzelm@7335
   713
\item [$\PROOF{m@1}$] refines the goal by proof method $m@1$; facts for
wenzelm@7335
   714
  forward chaining are passed if so indicated by $proof(chain)$ mode.
wenzelm@7335
   715
\item [$\QED{m@2}$] refines any remaining goals by proof method $m@2$ and
wenzelm@7895
   716
  concludes the sub-proof by assumption.  If the goal had been $\SHOWNAME$ (or
wenzelm@7895
   717
  $\THUSNAME$), some pending sub-goal is solved as well by the rule resulting
wenzelm@7895
   718
  from the result \emph{exported} into the enclosing goal context.  Thus
wenzelm@7895
   719
  $\QEDNAME$ may fail for two reasons: either $m@2$ fails, or the resulting
wenzelm@7895
   720
  rule does not fit to any pending goal\footnote{This includes any additional
wenzelm@7895
   721
    ``strong'' assumptions as introduced by $\ASSUMENAME$.} of the enclosing
wenzelm@7895
   722
  context.  Debugging such a situation might involve temporarily changing
wenzelm@7895
   723
  $\SHOWNAME$ into $\HAVENAME$, or weakening the local context by replacing
wenzelm@7895
   724
  some occurrences of $\ASSUMENAME$ by $\PRESUMENAME$.
wenzelm@7895
   725
\item [$\BYY{m@1}{m@2}$] is a \emph{terminal proof}\index{proof!terminal}; it
wenzelm@7987
   726
  abbreviates $\PROOF{m@1}~\QED{m@2}$, with backtracking across both methods,
wenzelm@7987
   727
  though.  Debugging an unsuccessful $\BYY{m@1}{m@2}$ commands might be done
wenzelm@7895
   728
  by expanding its definition; in many cases $\PROOF{m@1}$ is already
wenzelm@7175
   729
  sufficient to see what is going wrong.
wenzelm@7895
   730
\item [``$\DDOT$''] is a \emph{default proof}\index{proof!default}; it
wenzelm@8515
   731
  abbreviates $\BY{rule}$.
wenzelm@7895
   732
\item [``$\DOT$''] is a \emph{trivial proof}\index{proof!trivial}; it
wenzelm@8195
   733
  abbreviates $\BY{this}$.
wenzelm@8379
   734
\item [$\SORRY$] is a \emph{fake proof}\index{proof!fake}; provided that the
wenzelm@8379
   735
  \texttt{quick_and_dirty} flag is enabled, $\SORRY$ pretends to solve the
wenzelm@8515
   736
  goal without further ado.  Of course, the result would be a fake theorem
wenzelm@8515
   737
  only, involving some oracle in its internal derivation object (this is
wenzelm@8515
   738
  indicated as ``$[!]$'' in the printed result).  The main application of
wenzelm@8515
   739
  $\SORRY$ is to support experimentation and top-down proof development.
wenzelm@8515
   740
\end{descr}
wenzelm@8515
   741
wenzelm@8515
   742
wenzelm@8515
   743
\subsection{Fundamental methods and attributes}\label{sec:pure-meth-att}
wenzelm@8515
   744
wenzelm@8547
   745
The following proof methods and attributes refer to basic logical operations
wenzelm@8547
   746
of Isar.  Further methods and attributes are provided by several generic and
wenzelm@8547
   747
object-logic specific tools and packages (see chapters \ref{ch:gen-tools} and
wenzelm@8547
   748
\ref{ch:hol-tools}).
wenzelm@8515
   749
wenzelm@8515
   750
\indexisarmeth{assumption}\indexisarmeth{this}\indexisarmeth{rule}\indexisarmeth{$-$}
wenzelm@8515
   751
\indexisaratt{intro}\indexisaratt{elim}\indexisaratt{dest}
wenzelm@8515
   752
\indexisaratt{OF}\indexisaratt{of}
wenzelm@8515
   753
\begin{matharray}{rcl}
wenzelm@8515
   754
  assumption & : & \isarmeth \\
wenzelm@8515
   755
  this & : & \isarmeth \\
wenzelm@8515
   756
  rule & : & \isarmeth \\
wenzelm@8515
   757
  - & : & \isarmeth \\
wenzelm@8515
   758
  OF & : & \isaratt \\
wenzelm@8515
   759
  of & : & \isaratt \\
wenzelm@8515
   760
  intro & : & \isaratt \\
wenzelm@8515
   761
  elim & : & \isaratt \\
wenzelm@8515
   762
  dest & : & \isaratt \\
wenzelm@8515
   763
  delrule & : & \isaratt \\
wenzelm@8515
   764
\end{matharray}
wenzelm@8515
   765
wenzelm@8515
   766
\begin{rail}
wenzelm@8547
   767
  'rule' thmrefs?
wenzelm@8515
   768
  ;
wenzelm@8515
   769
  'OF' thmrefs
wenzelm@8515
   770
  ;
wenzelm@8515
   771
  'of' (inst * ) ('concl' ':' (inst * ))?
wenzelm@8515
   772
  ;
wenzelm@8515
   773
wenzelm@8515
   774
  inst: underscore | term
wenzelm@8515
   775
  ;
wenzelm@8515
   776
\end{rail}
wenzelm@8515
   777
wenzelm@8515
   778
\begin{descr}
wenzelm@8515
   779
\item [$assumption$] solves some goal by a single assumption step.  Any facts
wenzelm@8515
   780
  given (${} \le 1$) are guaranteed to participate in the refinement.  Recall
wenzelm@8515
   781
  that $\QEDNAME$ (see \S\ref{sec:proof-steps}) already concludes any
wenzelm@8515
   782
  remaining sub-goals by assumption.
wenzelm@8515
   783
\item [$this$] applies all of the current facts directly as rules.  Recall
wenzelm@8515
   784
  that ``$\DOT$'' (dot) abbreviates $\BY{this}$.
wenzelm@8547
   785
\item [$rule~\vec a$] applies some rule given as argument in backward manner;
wenzelm@8515
   786
  facts are used to reduce the rule before applying it to the goal.  Thus
wenzelm@8515
   787
  $rule$ without facts is plain \emph{introduction}, while with facts it
wenzelm@8515
   788
  becomes \emph{elimination}.
wenzelm@8515
   789
  
wenzelm@8547
   790
  When no arguments are given, the $rule$ method tries to pick appropriate
wenzelm@8547
   791
  rules automatically, as declared in the current context using the $intro$,
wenzelm@8547
   792
  $elim$, $dest$ attributes (see below).  This is the default behavior of
wenzelm@8547
   793
  $\PROOFNAME$ and ``$\DDOT$'' (double-dot) steps (see
wenzelm@8515
   794
  \S\ref{sec:proof-steps}).
wenzelm@8515
   795
\item [``$-$''] does nothing but insert the forward chaining facts as premises
wenzelm@8515
   796
  into the goal.  Note that command $\PROOFNAME$ without any method actually
wenzelm@8515
   797
  performs a single reduction step using the $rule$ method; thus a plain
wenzelm@8515
   798
  \emph{do-nothing} proof step would be $\PROOF{-}$ rather than $\PROOFNAME$
wenzelm@8515
   799
  alone.
wenzelm@8547
   800
\item [$OF~\vec a$] applies some theorem to given rules $\vec a$ (in
wenzelm@8547
   801
  parallel).  This corresponds to the \texttt{MRS} operator in ML
wenzelm@8547
   802
  \cite[\S5]{isabelle-ref}, but note the reversed order.  Positions may be
wenzelm@8547
   803
  skipped by including ``$\_$'' (underscore) as argument.
wenzelm@8547
   804
\item [$of~\vec t$] performs positional instantiation.  The terms $\vec t$ are
wenzelm@8515
   805
  substituted for any schematic variables occurring in a theorem from left to
wenzelm@8515
   806
  right; ``\texttt{_}'' (underscore) indicates to skip a position.  Arguments
wenzelm@8515
   807
  following a ``$concl\colon$'' specification refer to positions of the
wenzelm@8515
   808
  conclusion of a rule.
wenzelm@8515
   809
\item [$intro$, $elim$, and $dest$] declare introduction, elimination, and
wenzelm@8515
   810
  destruct rules, respectively.  Note that the classical reasoner (see
wenzelm@8515
   811
  \S\ref{sec:classical-basic}) introduces different versions of these
wenzelm@8515
   812
  attributes, and the $rule$ method, too.  In object-logics with classical
wenzelm@8515
   813
  reasoning enabled, the latter version should be used all the time to avoid
wenzelm@8515
   814
  confusion!
wenzelm@8515
   815
\item [$delrule$] undeclares introduction or elimination rules.
wenzelm@7315
   816
\end{descr}
wenzelm@7315
   817
wenzelm@7315
   818
wenzelm@7315
   819
\subsection{Term abbreviations}\label{sec:term-abbrev}
wenzelm@7315
   820
wenzelm@7315
   821
\indexisarcmd{let}
wenzelm@7315
   822
\begin{matharray}{rcl}
wenzelm@7315
   823
  \isarcmd{let} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7315
   824
  \isarkeyword{is} & : & syntax \\
wenzelm@7315
   825
\end{matharray}
wenzelm@7315
   826
wenzelm@7315
   827
Abbreviations may be either bound by explicit $\LET{p \equiv t}$ statements,
wenzelm@7987
   828
or by annotating assumptions or goal statements with a list of patterns
wenzelm@7987
   829
$\ISS{p@1\;\dots}{p@n}$.  In both cases, higher-order matching is invoked to
wenzelm@7987
   830
bind extra-logical term variables, which may be either named schematic
wenzelm@7987
   831
variables of the form $\Var{x}$, or nameless dummies ``\texttt{_}''
wenzelm@7987
   832
(underscore).\indexisarvar{_@\texttt{_}} Note that in the $\LETNAME$ form the
wenzelm@7987
   833
patterns occur on the left-hand side, while the $\ISNAME$ patterns are in
wenzelm@7987
   834
postfix position.
wenzelm@7315
   835
wenzelm@7319
   836
Term abbreviations are quite different from actual local definitions as
wenzelm@7319
   837
introduced via $\DEFNAME$ (see \S\ref{sec:proof-context}).  The latter are
wenzelm@7315
   838
visible within the logic as actual equations, while abbreviations disappear
wenzelm@7315
   839
during the input process just after type checking.
wenzelm@7315
   840
wenzelm@7315
   841
\begin{rail}
wenzelm@7315
   842
  'let' ((term + 'as') '=' term comment? + 'and')
wenzelm@7315
   843
  ;  
wenzelm@7315
   844
\end{rail}
wenzelm@7315
   845
wenzelm@7315
   846
The syntax of $\ISNAME$ patterns follows \railnonterm{termpat} or
wenzelm@7315
   847
\railnonterm{proppat} (see \S\ref{sec:term-pats}).
wenzelm@7315
   848
wenzelm@7315
   849
\begin{descr}
wenzelm@7315
   850
\item [$\LET{\vec p = \vec t}$] binds any text variables in patters $\vec p$
wenzelm@7315
   851
  by simultaneous higher-order matching against terms $\vec t$.
wenzelm@7315
   852
\item [$\IS{\vec p}$] resembles $\LETNAME$, but matches $\vec p$ against the
wenzelm@7315
   853
  preceding statement.  Also note that $\ISNAME$ is not a separate command,
wenzelm@7315
   854
  but part of others (such as $\ASSUMENAME$, $\HAVENAME$ etc.).
wenzelm@7315
   855
\end{descr}
wenzelm@7315
   856
wenzelm@7988
   857
A few \emph{automatic} term abbreviations\index{term abbreviations} for goals
wenzelm@7988
   858
and facts are available as well.  For any open goal,
wenzelm@7466
   859
$\Var{thesis_prop}$\indexisarvar{thesis-prop} refers to the full proposition
wenzelm@7466
   860
(which may be a rule), $\Var{thesis_concl}$\indexisarvar{thesis-concl} to its
wenzelm@7466
   861
(atomic) conclusion, and $\Var{thesis}$\indexisarvar{thesis} to its
wenzelm@8547
   862
object-level statement.  The latter two abstract over any meta-level
wenzelm@7987
   863
parameters.
wenzelm@7315
   864
wenzelm@7466
   865
Fact statements resulting from assumptions or finished goals are bound as
wenzelm@7466
   866
$\Var{this_prop}$\indexisarvar{this-prop},
wenzelm@7466
   867
$\Var{this_concl}$\indexisarvar{this-concl}, and
wenzelm@7466
   868
$\Var{this}$\indexisarvar{this}, similar to $\Var{thesis}$ above.  In case
wenzelm@7466
   869
$\Var{this}$ refers to an object-logic statement that is an application
wenzelm@7895
   870
$f(t)$, then $t$ is bound to the special text variable
wenzelm@7466
   871
``$\dots$''\indexisarvar{\dots} (three dots).  The canonical application of
wenzelm@7987
   872
the latter are calculational proofs (see \S\ref{sec:calculation}).
wenzelm@7315
   873
wenzelm@7315
   874
wenzelm@7134
   875
\subsection{Block structure}
wenzelm@7134
   876
wenzelm@7397
   877
\indexisarcmd{next}\indexisarcmd{\{\{}\indexisarcmd{\}\}}
wenzelm@7397
   878
\begin{matharray}{rcl}
wenzelm@8448
   879
  \NEXT & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7974
   880
  \BG & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7974
   881
  \EN & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7397
   882
\end{matharray}
wenzelm@7397
   883
wenzelm@7167
   884
While Isar is inherently block-structured, opening and closing blocks is
wenzelm@7167
   885
mostly handled rather casually, with little explicit user-intervention.  Any
wenzelm@7167
   886
local goal statement automatically opens \emph{two} blocks, which are closed
wenzelm@7167
   887
again when concluding the sub-proof (by $\QEDNAME$ etc.).  Sections of
wenzelm@8448
   888
different context within a sub-proof may be switched via $\NEXT$, which is
wenzelm@8448
   889
just a single block-close followed by block-open again.  Thus the effect of
wenzelm@8448
   890
$\NEXT$ to reset the local proof context. There is no goal focus involved
wenzelm@8448
   891
here!
wenzelm@7167
   892
wenzelm@7175
   893
For slightly more advanced applications, there are explicit block parentheses
wenzelm@7895
   894
as well.  These typically achieve a stronger forward style of reasoning.
wenzelm@7167
   895
wenzelm@7167
   896
\begin{descr}
wenzelm@8448
   897
\item [$\NEXT$] switches to a fresh block within a sub-proof, resetting the
wenzelm@8448
   898
  local context to the initial one.
wenzelm@7167
   899
\item [$\isarkeyword{\{\{}$ and $\isarkeyword{\}\}}$] explicitly open and
wenzelm@7895
   900
  close blocks.  Any current facts pass through ``$\isarkeyword{\{\{}$''
wenzelm@7895
   901
  unchanged, while ``$\isarkeyword{\}\}}$'' causes any result to be
wenzelm@7895
   902
  \emph{exported} into the enclosing context.  Thus fixed variables are
wenzelm@7895
   903
  generalized, assumptions discharged, and local definitions unfolded (cf.\ 
wenzelm@7895
   904
  \S\ref{sec:proof-context}).  There is no difference of $\ASSUMENAME$ and
wenzelm@7895
   905
  $\PRESUMENAME$ in this mode of forward reasoning --- in contrast to plain
wenzelm@7895
   906
  backward reasoning with the result exported at $\SHOWNAME$ time.
wenzelm@7167
   907
\end{descr}
wenzelm@7134
   908
wenzelm@7134
   909
wenzelm@8533
   910
\subsection{Emulating tactic scripts}\label{sec:tactical-proof}
wenzelm@8515
   911
wenzelm@8515
   912
The following elements emulate unstructured tactic scripts to some extent.
wenzelm@8515
   913
While these are anathema for writing proper Isar proof documents, they might
wenzelm@8515
   914
come in handy for interactive exploration and debugging, or even actual
wenzelm@8515
   915
tactical proof within new-style theories (to benefit from document
wenzelm@8515
   916
preparation, for example).
wenzelm@8515
   917
wenzelm@8515
   918
\indexisarcmd{apply}\indexisarcmd{apply-end}
wenzelm@8515
   919
\indexisarcmd{defer}\indexisarcmd{prefer}\indexisarcmd{back}
wenzelm@8515
   920
\indexisarmeth{tactic}
wenzelm@8533
   921
\indexisarmeth{res-inst-tac}\indexisarmeth{eres-inst-tac}
wenzelm@8533
   922
\indexisarmeth{dres-inst-tac}\indexisarmeth{forw-inst-tac}
wenzelm@8533
   923
\indexisarmeth{subgoal-tac}
wenzelm@8515
   924
\begin{matharray}{rcl}
wenzelm@8533
   925
  \isarcmd{apply}^* & : & \isartrans{proof(prove)}{proof(prove)} \\
wenzelm@8533
   926
  \isarcmd{apply_end}^* & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@8533
   927
  \isarcmd{defer}^* & : & \isartrans{proof}{proof} \\
wenzelm@8533
   928
  \isarcmd{prefer}^* & : & \isartrans{proof}{proof} \\
wenzelm@8533
   929
  \isarcmd{back}^* & : & \isartrans{proof}{proof} \\
wenzelm@8533
   930
  tactic^* & : & \isarmeth \\
wenzelm@8533
   931
  res_inst_tac^* & : & \isarmeth \\
wenzelm@8533
   932
  eres_inst_tac^* & : & \isarmeth \\
wenzelm@8533
   933
  dres_inst_tac^* & : & \isarmeth \\
wenzelm@8533
   934
  forw_inst_tac^* & : & \isarmeth \\
wenzelm@8533
   935
  subgoal_tac^* & : & \isarmeth \\
wenzelm@8515
   936
\end{matharray}
wenzelm@8515
   937
wenzelm@8515
   938
\railalias{applyend}{apply\_end}
wenzelm@8515
   939
\railterm{applyend}
wenzelm@8515
   940
wenzelm@8533
   941
\railalias{resinsttac}{res\_inst\_tac}
wenzelm@8533
   942
\railterm{resinsttac}
wenzelm@8533
   943
wenzelm@8533
   944
\railalias{eresinsttac}{eres\_inst\_tac}
wenzelm@8533
   945
\railterm{eresinsttac}
wenzelm@8533
   946
wenzelm@8533
   947
\railalias{dresinsttac}{dres\_inst\_tac}
wenzelm@8533
   948
\railterm{dresinsttac}
wenzelm@8533
   949
wenzelm@8533
   950
\railalias{forwinsttac}{forw\_inst\_tac}
wenzelm@8533
   951
\railterm{forwinsttac}
wenzelm@8533
   952
wenzelm@8533
   953
\railalias{subgoaltac}{subgoal\_tac}
wenzelm@8533
   954
\railterm{subgoaltac}
wenzelm@8533
   955
wenzelm@8515
   956
\begin{rail}
wenzelm@8515
   957
  'apply' method
wenzelm@8515
   958
  ;
wenzelm@8515
   959
  applyend method
wenzelm@8515
   960
  ;
wenzelm@8515
   961
  'defer' nat?
wenzelm@8515
   962
  ;
wenzelm@8515
   963
  'prefer' nat
wenzelm@8515
   964
  ;
wenzelm@8515
   965
  'tactic' text
wenzelm@8515
   966
  ;
wenzelm@8533
   967
  ( resinsttac | eresinsttac | dresinsttac | forwinsttac ) goalspec? ((name '=' term) + 'and')
wenzelm@8533
   968
  ;
wenzelm@8533
   969
  subgoaltac goalspec? prop
wenzelm@8533
   970
  ;
wenzelm@8515
   971
\end{rail}
wenzelm@8515
   972
wenzelm@8515
   973
\begin{descr}
wenzelm@8547
   974
\item [$\isarkeyword{apply}~(m)$] applies proof method $m$ in initial
wenzelm@8547
   975
  position, but unlike $\PROOFNAME$ it retains ``$proof(prove)$'' mode.  Thus
wenzelm@8515
   976
  consecutive method applications may be given just as in tactic scripts.  In
wenzelm@8515
   977
  order to complete the proof properly, any of the actual structured proof
wenzelm@8515
   978
  commands (e.g.\ ``$\DOT$'') has to be given eventually.
wenzelm@8515
   979
  
wenzelm@8515
   980
  Facts are passed to $m$ as indicated by the goal's forward-chain mode.
wenzelm@8515
   981
  Common use of $\isarkeyword{apply}$ would be in a purely backward manner,
wenzelm@8515
   982
  though.
wenzelm@8515
   983
\item [$\isarkeyword{apply_end}~(m)$] applies proof method $m$ as if in
wenzelm@8515
   984
  terminal position.  Basically, this simulates a multi-step tactic script for
wenzelm@8515
   985
  $\QEDNAME$, but may be given anywhere within the proof body.
wenzelm@8515
   986
  
wenzelm@8515
   987
  No facts are passed to $m$.  Furthermore, the static context is that of the
wenzelm@8515
   988
  enclosing goal (as for actual $\QEDNAME$).  Thus the proof method may not
wenzelm@8515
   989
  refer to any assumptions introduced in the current body, for example.
wenzelm@8515
   990
\item [$\isarkeyword{defer}~n$ and $\isarkeyword{prefer}~n$] shuffle the list
wenzelm@8515
   991
  of pending goals: $defer$ puts off goal $n$ to the end of the list ($n = 1$
wenzelm@8515
   992
  by default), while $prefer$ brings goal $n$ to the top.
wenzelm@8515
   993
\item [$\isarkeyword{back}$] does back-tracking over the result sequence of
wenzelm@8515
   994
  the latest proof command.\footnote{Unlike the ML function \texttt{back}
wenzelm@8515
   995
    \cite{isabelle-ref}, the Isar command does not search upwards for further
wenzelm@8515
   996
    branch points.} Basically, any proof command may return multiple results.
wenzelm@8515
   997
\item [$tactic~text$] produces a proof method from any ML text of type
wenzelm@8547
   998
  \texttt{tactic}.  Apart from the usual ML environment and the current
wenzelm@8515
   999
  implicit theory context, the ML code may refer to the following locally
wenzelm@8515
  1000
  bound values:
wenzelm@8515
  1001
%%FIXME ttbox produces too much trailing space (why?)
wenzelm@8515
  1002
{\footnotesize\begin{verbatim}
wenzelm@8515
  1003
val ctxt  : Proof.context
wenzelm@8515
  1004
val facts : thm list
wenzelm@8515
  1005
val thm   : string -> thm
wenzelm@8515
  1006
val thms  : string -> thm list
wenzelm@8515
  1007
\end{verbatim}}
wenzelm@8515
  1008
  Here \texttt{ctxt} refers to the current proof context, \texttt{facts}
wenzelm@8515
  1009
  indicates any current facts for forward-chaining, and
wenzelm@8515
  1010
  \texttt{thm}~/~\texttt{thms} retrieve named facts (including global
wenzelm@8515
  1011
  theorems) from the context.
wenzelm@8533
  1012
\item [$res_inst_tac$ etc.] do resolution of rules with explicit
wenzelm@8533
  1013
  instantiation.  This works the same way as the corresponding ML tactics, see
wenzelm@8533
  1014
  \cite[\S3]{isabelle-ref}.
wenzelm@8533
  1015
  
wenzelm@8533
  1016
  It is very important to note that the instantiations are read and
wenzelm@8533
  1017
  type-checked according to the dynamic goal state, rather than the static
wenzelm@8533
  1018
  proof context!  In particular, locally fixed variables and term
wenzelm@8533
  1019
  abbreviations may not be included in the term specifications.
wenzelm@8547
  1020
\item [$subgoal_tac~\phi$] emulates the ML tactic of the same name, see
wenzelm@8533
  1021
  \cite[\S3]{isabelle-ref}.  Syntactically, the given proposition is handled
wenzelm@8533
  1022
  as the instantiations in $res_inst_tac$ etc.
wenzelm@8533
  1023
  
wenzelm@8533
  1024
  Note that the proper Isar command $\PRESUMENAME$ achieves a similar effect
wenzelm@8533
  1025
  as $subgoal_tac$.
wenzelm@8515
  1026
\end{descr}
wenzelm@8515
  1027
wenzelm@8515
  1028
wenzelm@8515
  1029
\subsection{Meta-linguistic features}
wenzelm@8515
  1030
wenzelm@8515
  1031
\indexisarcmd{oops}
wenzelm@8515
  1032
\begin{matharray}{rcl}
wenzelm@8515
  1033
  \isarcmd{oops} & : & \isartrans{proof}{theory} \\
wenzelm@8515
  1034
\end{matharray}
wenzelm@8515
  1035
wenzelm@8515
  1036
The $\OOPS$ command discontinues the current proof attempt, while considering
wenzelm@8515
  1037
the partial proof text as properly processed.  This is conceptually quite
wenzelm@8515
  1038
different from ``faking'' actual proofs via $\SORRY$ (see
wenzelm@8515
  1039
\S\ref{sec:proof-steps}): $\OOPS$ does not observe the proof structure at all,
wenzelm@8515
  1040
but goes back right to the theory level.  Furthermore, $\OOPS$ does not
wenzelm@8515
  1041
produce any result theorem --- there is no claim to be able to complete the
wenzelm@8515
  1042
proof anyhow.
wenzelm@8515
  1043
wenzelm@8515
  1044
A typical application of $\OOPS$ is to explain Isar proofs \emph{within} the
wenzelm@8515
  1045
system itself, in conjunction with the document preparation tools of Isabelle
wenzelm@8515
  1046
described in \cite{isabelle-sys}.  Thus partial or even wrong proof attempts
wenzelm@8515
  1047
can be discussed in a logically sound manner.  Note that the Isabelle {\LaTeX}
wenzelm@8515
  1048
macros can be easily adapted to print something like ``$\dots$'' instead of an
wenzelm@8515
  1049
``$\OOPS$'' keyword.
wenzelm@8515
  1050
wenzelm@8547
  1051
\medskip The $\OOPS$ command is undoable, unlike $\isarkeyword{kill}$ (see
wenzelm@8547
  1052
\S\ref{sec:history}).  The effect is to get back to the theory \emph{before}
wenzelm@8547
  1053
the opening of the proof.
wenzelm@8515
  1054
wenzelm@8515
  1055
wenzelm@7134
  1056
\section{Other commands}
wenzelm@7134
  1057
wenzelm@8448
  1058
\subsection{Diagnostics}\label{sec:diag}
wenzelm@7134
  1059
wenzelm@8485
  1060
\indexisarcmd{pr}\indexisarcmd{thm}\indexisarcmd{term}\indexisarcmd{prop}\indexisarcmd{typ}
wenzelm@8485
  1061
\indexisarcmd{print-facts}\indexisarcmd{print-binds}
wenzelm@7134
  1062
\begin{matharray}{rcl}
wenzelm@8515
  1063
  \isarcmd{help}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1064
  \isarcmd{pr}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1065
  \isarcmd{thm}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1066
  \isarcmd{term}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1067
  \isarcmd{prop}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1068
  \isarcmd{typ}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1069
  \isarcmd{print_facts}^* & : & \isarkeep{proof} \\
wenzelm@8515
  1070
  \isarcmd{print_binds}^* & : & \isarkeep{proof} \\
wenzelm@7134
  1071
\end{matharray}
wenzelm@7134
  1072
wenzelm@7335
  1073
These commands are not part of the actual Isabelle/Isar syntax, but assist
wenzelm@7335
  1074
interactive development.  Also note that $undo$ does not apply here, since the
wenzelm@7335
  1075
theory or proof configuration is not changed.
wenzelm@7335
  1076
wenzelm@7134
  1077
\begin{rail}
wenzelm@8485
  1078
  'pr' modes? nat?
wenzelm@7134
  1079
  ;
wenzelm@8485
  1080
  'thm' modes? thmrefs
wenzelm@8485
  1081
  ;
wenzelm@8485
  1082
  'term' modes? term
wenzelm@7134
  1083
  ;
wenzelm@8485
  1084
  'prop' modes? prop
wenzelm@7134
  1085
  ;
wenzelm@8485
  1086
  'typ' modes? type
wenzelm@8485
  1087
  ;
wenzelm@8485
  1088
wenzelm@8485
  1089
  modes: '(' (name + ) ')'
wenzelm@7134
  1090
  ;
wenzelm@7134
  1091
\end{rail}
wenzelm@7134
  1092
wenzelm@7167
  1093
\begin{descr}
wenzelm@8515
  1094
\item [$\isarkeyword{help}$] prints a list of available language elements.
wenzelm@8515
  1095
  Note that methods and attributes depend on the current theory context.
wenzelm@8485
  1096
\item [$\isarkeyword{pr}~n$] prints the current top-level state, i.e.\ the
wenzelm@8485
  1097
  theory identifier or proof state.  The latter includes the proof context,
wenzelm@8485
  1098
  current facts and goals.  The optional argument $n$ affects the implicit
wenzelm@8485
  1099
  limit of goals to be displayed, which is initially 10.  Omitting the limit
wenzelm@8485
  1100
  leaves the value unchanged.
wenzelm@8547
  1101
\item [$\isarkeyword{thm}~\vec a$] retrieves theorems from the current theory
wenzelm@8547
  1102
  or proof context.  Note that any attributes included in the theorem
wenzelm@7974
  1103
  specifications are applied to a temporary context derived from the current
wenzelm@8547
  1104
  theory or proof; the result is discarded, i.e.\ attributes involved in $\vec
wenzelm@8547
  1105
  a$ do not have any permanent effect.
wenzelm@7987
  1106
\item [$\isarkeyword{term}~t$, $\isarkeyword{prop}~\phi$] read, type-check and
wenzelm@7987
  1107
  print terms or propositions according to the current theory or proof
wenzelm@7895
  1108
  context; the inferred type of $t$ is output as well.  Note that these
wenzelm@7895
  1109
  commands are also useful in inspecting the current environment of term
wenzelm@7895
  1110
  abbreviations.
wenzelm@7974
  1111
\item [$\isarkeyword{typ}~\tau$] reads and prints types of the meta-logic
wenzelm@7974
  1112
  according to the current theory or proof context.
wenzelm@8379
  1113
\item [$\isarkeyword{print_facts}$] prints any named facts of the current
wenzelm@8379
  1114
  context, including assumptions and local results.
wenzelm@8379
  1115
\item [$\isarkeyword{print_binds}$] prints all term abbreviations present in
wenzelm@8379
  1116
  the context.
wenzelm@8485
  1117
\end{descr}
wenzelm@8485
  1118
wenzelm@8485
  1119
The basic diagnostic commands above admit a list of $modes$ to be specified,
wenzelm@8485
  1120
which is appended to the current print mode (see also \cite{isabelle-ref}).
wenzelm@8485
  1121
Thus the output behavior may be modified according particular print mode
wenzelm@8485
  1122
features.
wenzelm@8485
  1123
wenzelm@8485
  1124
For example, $\isarkeyword{pr}~(latex~xsymbols~symbols)$ would print the
wenzelm@8485
  1125
current proof state with mathematical symbols and special characters
wenzelm@8485
  1126
represented in {\LaTeX} source, according to the Isabelle style
wenzelm@8547
  1127
\cite{isabelle-sys}.  The resulting text can be directly pasted into a
wenzelm@8547
  1128
\verb,\begin{isabelle},\dots\verb,\end{isabelle}, environment.  Note that
wenzelm@8547
  1129
$\isarkeyword{pr}~(latex)$ is sufficient to achieve the same output, if the
wenzelm@8547
  1130
current Isabelle session has the other modes already activated, say due to
wenzelm@8547
  1131
some particular user interface configuration such as Proof~General
wenzelm@8510
  1132
\cite{proofgeneral,Aspinall:TACAS:2000} with X-Symbol mode \cite{x-symbol}.
wenzelm@8485
  1133
wenzelm@8485
  1134
wenzelm@8485
  1135
\subsection{History commands}\label{sec:history}
wenzelm@8485
  1136
wenzelm@8485
  1137
\indexisarcmd{undo}\indexisarcmd{redo}\indexisarcmd{kill}
wenzelm@8485
  1138
\begin{matharray}{rcl}
wenzelm@8485
  1139
  \isarcmd{undo}^{{*}{*}} & : & \isarkeep{\cdot} \\
wenzelm@8485
  1140
  \isarcmd{redo}^{{*}{*}} & : & \isarkeep{\cdot} \\
wenzelm@8485
  1141
  \isarcmd{kill}^{{*}{*}} & : & \isarkeep{\cdot} \\
wenzelm@8485
  1142
\end{matharray}
wenzelm@8485
  1143
wenzelm@8485
  1144
The Isabelle/Isar top-level maintains a two-stage history, for theory and
wenzelm@8485
  1145
proof state transformation.  Basically, any command can be undone using
wenzelm@8485
  1146
$\isarkeyword{undo}$, excluding mere diagnostic elements.  Its effect may be
wenzelm@8485
  1147
revoked via $\isarkeyword{redo}$, unless the corresponding the
wenzelm@8485
  1148
$\isarkeyword{undo}$ step has crossed the beginning of a proof or theory.  The
wenzelm@8485
  1149
$\isarkeyword{kill}$ command aborts the current history node altogether,
wenzelm@8485
  1150
discontinuing a proof or even the whole theory.  This operation is \emph{not}
wenzelm@8485
  1151
undoable.
wenzelm@8485
  1152
wenzelm@8485
  1153
\begin{warn}
wenzelm@8547
  1154
  History commands should never be used with user interfaces such as
wenzelm@8547
  1155
  Proof~General \cite{proofgeneral,Aspinall:TACAS:2000}, which takes care of
wenzelm@8547
  1156
  stepping forth and back itself.  Interfering by manual $\isarkeyword{undo}$,
wenzelm@8510
  1157
  $\isarkeyword{redo}$, or even $\isarkeyword{kill}$ commands would quickly
wenzelm@8510
  1158
  result in utter confusion.
wenzelm@8485
  1159
\end{warn}
wenzelm@8485
  1160
wenzelm@8515
  1161
%FIXME remove
wenzelm@8515
  1162
% \begin{descr}
wenzelm@8515
  1163
% \item [$\isarkeyword{undo}$] revokes the latest state-transforming command.
wenzelm@8515
  1164
% \item [$\isarkeyword{redo}$] undos the latest $\isarkeyword{undo}$.
wenzelm@8515
  1165
% \item [$\isarkeyword{kill}$] aborts the current history level.
wenzelm@8515
  1166
% \end{descr}
wenzelm@8485
  1167
wenzelm@8379
  1168
wenzelm@7134
  1169
\subsection{System operations}
wenzelm@7134
  1170
wenzelm@7167
  1171
\indexisarcmd{cd}\indexisarcmd{pwd}\indexisarcmd{use-thy}\indexisarcmd{use-thy-only}
wenzelm@7167
  1172
\indexisarcmd{update-thy}\indexisarcmd{update-thy-only}
wenzelm@7134
  1173
\begin{matharray}{rcl}
wenzelm@8515
  1174
  \isarcmd{cd}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1175
  \isarcmd{pwd}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1176
  \isarcmd{use_thy}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1177
  \isarcmd{use_thy_only}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1178
  \isarcmd{update_thy}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1179
  \isarcmd{update_thy_only}^* & : & \isarkeep{\cdot} \\
wenzelm@7134
  1180
\end{matharray}
wenzelm@7134
  1181
wenzelm@7167
  1182
\begin{descr}
wenzelm@7134
  1183
\item [$\isarkeyword{cd}~name$] changes the current directory of the Isabelle
wenzelm@7134
  1184
  process.
wenzelm@7134
  1185
\item [$\isarkeyword{pwd}~$] prints the current working directory.
wenzelm@7175
  1186
\item [$\isarkeyword{use_thy}$, $\isarkeyword{use_thy_only}$,
wenzelm@7987
  1187
  $\isarkeyword{update_thy}$, $\isarkeyword{update_thy_only}$] load some
wenzelm@7895
  1188
  theory given as $name$ argument.  These commands are basically the same as
wenzelm@7987
  1189
  the corresponding ML functions\footnote{The ML versions also change the
wenzelm@7987
  1190
    implicit theory context to that of the theory loaded.}  (see also
wenzelm@7987
  1191
  \cite[\S1,\S6]{isabelle-ref}).  Note that both the ML and Isar versions may
wenzelm@7987
  1192
  load new- and old-style theories alike.
wenzelm@7167
  1193
\end{descr}
wenzelm@7134
  1194
wenzelm@7987
  1195
These system commands are scarcely used when working with the Proof~General
wenzelm@7987
  1196
interface, since loading of theories is done fully transparently.
wenzelm@7134
  1197
wenzelm@8379
  1198
wenzelm@7046
  1199
%%% Local Variables: 
wenzelm@7046
  1200
%%% mode: latex
wenzelm@7046
  1201
%%% TeX-master: "isar-ref"
wenzelm@7046
  1202
%%% End: