doc-src/IsarRef/pure.tex
author wenzelm
Wed Jan 10 20:18:55 2001 +0100 (2001-01-10)
changeset 10858 479dad7b3b41
parent 10686 60c795d6bd9e
child 10899 5de31ddf9c03
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 of these markup elements corresponds to a {\LaTeX} command with the name
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prefixed by \verb,\isamarkup,.  For the sectioning commands this is a plain
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macro with a single argument, e.g.\ \verb,\isamarkupchapter{,\dots\verb,}, for
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$\isarkeyword{chapter}$.  The $\isarkeyword{text}$ markup results in a
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{\LaTeX} environment \verb,\begin{isamarkuptext}, {\dots}
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  \verb,\end{isamarkuptext},, while $\isarkeyword{text_raw}$ causes the text
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to be inserted directly into the {\LaTeX} source.
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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 section markup just
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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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  $\INSTANCE$ command (see \S\ref{sec:axclass}) provides a way to introduce
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  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 $\INSTANCE$ command (see \S\ref{sec:axclass}) provides a
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  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' ('(overloaded)')? (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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  The $overloaded$ option declares definitions to be potentially overloaded.
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  Unless this option is given, a warning message would be issued for any
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  definitional equation with a more special type than that of the
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  corresponding constant declaration.
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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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\railalias{rightleftharpoons}{\isasymrightleftharpoons}
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\railterm{rightleftharpoons}
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\railalias{rightharpoonup}{\isasymrightharpoonup}
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\railterm{rightharpoonup}
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\railalias{leftharpoondown}{\isasymleftharpoondown}
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\railterm{leftharpoondown}
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\begin{rail}
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  'syntax' ('(' ( name | 'output' | name 'output' ) ')')? (constdecl +)
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  ;
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  'translations' (transpat ('==' | '=>' | '<=' | rightleftharpoons | rightharpoonup | leftharpoondown) 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{==} or
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  \isasymrightleftharpoons), parse rules (\texttt{=>} or
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  \isasymrightharpoonup), or print rules (\texttt{<=} or
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  \isasymleftharpoondown).  Translation patterns may be prefixed by the
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  syntactic category to be used for parsing; the default is \texttt{logic}.
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\end{descr}
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\subsection{Axioms and theorems}\label{sec:axms-thms}
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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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   317
  ('theorems' | 'lemmas') (thmdef? thmrefs comment? + 'and')
wenzelm@7134
   318
  ;
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   319
\end{rail}
wenzelm@7134
   320
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   321
\begin{descr}
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   322
\item [$\isarkeyword{axioms}~a: \phi$] introduces arbitrary statements as
wenzelm@7895
   323
  axioms of the meta-logic.  In fact, axioms are ``axiomatic theorems'', and
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   324
  may be referred later just as any other theorem.
wenzelm@7134
   325
  
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   326
  Axioms are usually only introduced when declaring new logical systems.
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   327
  Everyday work is typically done the hard way, with proper definitions and
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   328
  actual proven theorems.
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   329
\item [$\isarkeyword{theorems}~a = \vec b$] stores lists of existing theorems.
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   330
  Typical applications would also involve attributes, to declare Simplifier
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   331
  rules, for example.
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   332
\item [$\isarkeyword{lemmas}$] is similar to $\isarkeyword{theorems}$, but
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   333
  tags the results as ``lemma''.
wenzelm@7167
   334
\end{descr}
wenzelm@7134
   335
wenzelm@7134
   336
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   337
\subsection{Name spaces}
wenzelm@7134
   338
wenzelm@8726
   339
\indexisarcmd{global}\indexisarcmd{local}\indexisarcmd{hide}
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   340
\begin{matharray}{rcl}
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   341
  \isarcmd{global} & : & \isartrans{theory}{theory} \\
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   342
  \isarcmd{local} & : & \isartrans{theory}{theory} \\
wenzelm@8726
   343
  \isarcmd{hide} & : & \isartrans{theory}{theory} \\
wenzelm@7134
   344
\end{matharray}
wenzelm@7134
   345
wenzelm@8726
   346
\begin{rail}
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   347
  'global' comment?
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   348
  ;
wenzelm@8726
   349
  'local' comment?
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   350
  ;
wenzelm@8726
   351
  'hide' name (nameref + ) comment?
wenzelm@8726
   352
  ;
wenzelm@8726
   353
\end{rail}
wenzelm@8726
   354
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   355
Isabelle organizes any kind of name declarations (of types, constants,
wenzelm@8547
   356
theorems etc.) by separate hierarchically structured name spaces.  Normally
wenzelm@8726
   357
the user does not have to control the behavior of name spaces by hand, yet the
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   358
following commands provide some way to do so.
wenzelm@7175
   359
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   360
\begin{descr}
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   361
\item [$\isarkeyword{global}$ and $\isarkeyword{local}$] change the current
wenzelm@7167
   362
  name declaration mode.  Initially, theories start in $\isarkeyword{local}$
wenzelm@7167
   363
  mode, causing all names to be automatically qualified by the theory name.
wenzelm@7895
   364
  Changing this to $\isarkeyword{global}$ causes all names to be declared
wenzelm@7895
   365
  without the theory prefix, until $\isarkeyword{local}$ is declared again.
wenzelm@8726
   366
  
wenzelm@8726
   367
  Note that global names are prone to get hidden accidently later, when
wenzelm@8726
   368
  qualified names of the same base name are introduced.
wenzelm@8726
   369
  
wenzelm@8726
   370
\item [$\isarkeyword{hide}~space~names$] removes declarations from a given
wenzelm@8726
   371
  name space (which may be $class$, $type$, or $const$).  Hidden objects
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   372
  remain valid within the logic, but are inaccessible from user input.  In
wenzelm@8726
   373
  output, the special qualifier ``$\mathord?\mathord?$'' is prefixed to the
wenzelm@8726
   374
  full internal name.
wenzelm@8726
   375
  
wenzelm@8726
   376
  Unqualified (global) names may not be hidden deliberately.
wenzelm@7167
   377
\end{descr}
wenzelm@7134
   378
wenzelm@7134
   379
wenzelm@7167
   380
\subsection{Incorporating ML code}\label{sec:ML}
wenzelm@7134
   381
wenzelm@8682
   382
\indexisarcmd{use}\indexisarcmd{ML}\indexisarcmd{ML-command}
wenzelm@8682
   383
\indexisarcmd{ML-setup}\indexisarcmd{setup}
wenzelm@9199
   384
\indexisarcmd{method-setup}
wenzelm@7134
   385
\begin{matharray}{rcl}
wenzelm@7134
   386
  \isarcmd{use} & : & \isartrans{\cdot}{\cdot} \\
wenzelm@7134
   387
  \isarcmd{ML} & : & \isartrans{\cdot}{\cdot} \\
wenzelm@8682
   388
  \isarcmd{ML_command} & : & \isartrans{\cdot}{\cdot} \\
wenzelm@7895
   389
  \isarcmd{ML_setup} & : & \isartrans{theory}{theory} \\
wenzelm@7175
   390
  \isarcmd{setup} & : & \isartrans{theory}{theory} \\
wenzelm@9199
   391
  \isarcmd{method_setup} & : & \isartrans{theory}{theory} \\
wenzelm@7134
   392
\end{matharray}
wenzelm@7134
   393
wenzelm@7895
   394
\railalias{MLsetup}{ML\_setup}
wenzelm@7895
   395
\railterm{MLsetup}
wenzelm@7895
   396
wenzelm@9199
   397
\railalias{methodsetup}{method\_setup}
wenzelm@9199
   398
\railterm{methodsetup}
wenzelm@9199
   399
wenzelm@8682
   400
\railalias{MLcommand}{ML\_command}
wenzelm@8682
   401
\railterm{MLcommand}
wenzelm@8682
   402
wenzelm@7134
   403
\begin{rail}
wenzelm@9273
   404
  'use' name comment?
wenzelm@7134
   405
  ;
wenzelm@9273
   406
  ('ML' | MLcommand | MLsetup | 'setup') text comment?
wenzelm@7134
   407
  ;
wenzelm@9199
   408
  methodsetup name '=' text text comment?
wenzelm@9199
   409
  ;
wenzelm@7134
   410
\end{rail}
wenzelm@7134
   411
wenzelm@7167
   412
\begin{descr}
wenzelm@7175
   413
\item [$\isarkeyword{use}~file$] reads and executes ML commands from $file$.
wenzelm@7466
   414
  The current theory context (if present) is passed down to the ML session,
wenzelm@7981
   415
  but may not be modified.  Furthermore, the file name is checked with the
wenzelm@7466
   416
  $\isarkeyword{files}$ dependency declaration given in the theory header (see
wenzelm@7466
   417
  also \S\ref{sec:begin-thy}).
wenzelm@7466
   418
  
wenzelm@8682
   419
\item [$\isarkeyword{ML}~text$ and $\isarkeyword{ML_command}~text$] execute ML
wenzelm@8682
   420
  commands from $text$.  The theory context is passed in the same way as for
wenzelm@10858
   421
  $\isarkeyword{use}$, but may not be changed.  Note that the output of
wenzelm@8682
   422
  $\isarkeyword{ML_command}$ is less verbose than plain $\isarkeyword{ML}$.
wenzelm@7895
   423
  
wenzelm@7895
   424
\item [$\isarkeyword{ML_setup}~text$] executes ML commands from $text$.  The
wenzelm@7895
   425
  theory context is passed down to the ML session, and fetched back
wenzelm@7895
   426
  afterwards.  Thus $text$ may actually change the theory as a side effect.
wenzelm@7895
   427
  
wenzelm@7167
   428
\item [$\isarkeyword{setup}~text$] changes the current theory context by
wenzelm@8379
   429
  applying $text$, which refers to an ML expression of type
wenzelm@8379
   430
  \texttt{(theory~->~theory)~list}.  The $\isarkeyword{setup}$ command is the
wenzelm@8547
   431
  canonical way to initialize any object-logic specific tools and packages
wenzelm@8547
   432
  written in ML.
wenzelm@9199
   433
  
wenzelm@9199
   434
\item [$\isarkeyword{method_setup}~name = text~description$] defines a proof
wenzelm@9199
   435
  method in the current theory.  The given $text$ has to be an ML expression
wenzelm@9199
   436
  of type \texttt{Args.src -> Proof.context -> Proof.method}.  Parsing
wenzelm@9199
   437
  concrete method syntax from \texttt{Args.src} input can be quite tedious in
wenzelm@9199
   438
  general.  The following simple examples are for methods without any explicit
wenzelm@9199
   439
  arguments, or a list of theorems, respectively.
wenzelm@9199
   440
wenzelm@9199
   441
{\footnotesize
wenzelm@9199
   442
\begin{verbatim}
wenzelm@9605
   443
 Method.no_args (Method.METHOD (fn facts => foobar_tac))
wenzelm@9605
   444
 Method.thms_args (fn thms => Method.METHOD (fn facts => foobar_tac))
wenzelm@9199
   445
\end{verbatim}
wenzelm@9199
   446
}
wenzelm@9199
   447
wenzelm@9199
   448
Note that mere tactic emulations may ignore the \texttt{facts} parameter
wenzelm@9199
   449
above.  Proper proof methods would do something ``appropriate'' with the list
wenzelm@9199
   450
of current facts, though.  Single-rule methods usually do strict
wenzelm@9199
   451
forward-chaining (e.g.\ by using \texttt{Method.multi_resolves}), while
wenzelm@9199
   452
automatic ones just insert the facts using \texttt{Method.insert_tac} before
wenzelm@9199
   453
applying the main tactic.
wenzelm@7167
   454
\end{descr}
wenzelm@7134
   455
wenzelm@7134
   456
wenzelm@8250
   457
\subsection{Syntax translation functions}
wenzelm@7134
   458
wenzelm@8250
   459
\indexisarcmd{parse-ast-translation}\indexisarcmd{parse-translation}
wenzelm@8250
   460
\indexisarcmd{print-translation}\indexisarcmd{typed-print-translation}
wenzelm@8250
   461
\indexisarcmd{print-ast-translation}\indexisarcmd{token-translation}
wenzelm@8250
   462
\begin{matharray}{rcl}
wenzelm@8250
   463
  \isarcmd{parse_ast_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   464
  \isarcmd{parse_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   465
  \isarcmd{print_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   466
  \isarcmd{typed_print_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   467
  \isarcmd{print_ast_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   468
  \isarcmd{token_translation} & : & \isartrans{theory}{theory} \\
wenzelm@8250
   469
\end{matharray}
wenzelm@7134
   470
wenzelm@9273
   471
\railalias{parseasttranslation}{parse\_ast\_translation}
wenzelm@9273
   472
\railterm{parseasttranslation}
wenzelm@9273
   473
wenzelm@9273
   474
\railalias{parsetranslation}{parse\_translation}
wenzelm@9273
   475
\railterm{parsetranslation}
wenzelm@9273
   476
wenzelm@9273
   477
\railalias{printtranslation}{print\_translation}
wenzelm@9273
   478
\railterm{printtranslation}
wenzelm@9273
   479
wenzelm@9273
   480
\railalias{typedprinttranslation}{typed\_print\_translation}
wenzelm@9273
   481
\railterm{typedprinttranslation}
wenzelm@9273
   482
wenzelm@9273
   483
\railalias{printasttranslation}{print\_ast\_translation}
wenzelm@9273
   484
\railterm{printasttranslation}
wenzelm@9273
   485
wenzelm@9273
   486
\railalias{tokentranslation}{token\_translation}
wenzelm@9273
   487
\railterm{tokentranslation}
wenzelm@9273
   488
wenzelm@9273
   489
\begin{rail}
wenzelm@9273
   490
  ( parseasttranslation | parsetranslation | printtranslation | typedprinttranslation |
wenzelm@9273
   491
  printasttranslation | tokentranslation ) text comment?
wenzelm@9273
   492
\end{rail}
wenzelm@9273
   493
wenzelm@8250
   494
Syntax translation functions written in ML admit almost arbitrary
wenzelm@8250
   495
manipulations of Isabelle's inner syntax.  Any of the above commands have a
wenzelm@8250
   496
single \railqtoken{text} argument that refers to an ML expression of
wenzelm@8379
   497
appropriate type.
wenzelm@8379
   498
wenzelm@8379
   499
\begin{ttbox}
wenzelm@8379
   500
val parse_ast_translation   : (string * (ast list -> ast)) list
wenzelm@8379
   501
val parse_translation       : (string * (term list -> term)) list
wenzelm@8379
   502
val print_translation       : (string * (term list -> term)) list
wenzelm@8379
   503
val typed_print_translation :
wenzelm@8379
   504
  (string * (bool -> typ -> term list -> term)) list
wenzelm@8379
   505
val print_ast_translation   : (string * (ast list -> ast)) list
wenzelm@8379
   506
val token_translation       :
wenzelm@8379
   507
  (string * string * (string -> string * real)) list
wenzelm@8379
   508
\end{ttbox}
wenzelm@8379
   509
See \cite[\S8]{isabelle-ref} for more information on syntax transformations.
wenzelm@7134
   510
wenzelm@7134
   511
wenzelm@7134
   512
\subsection{Oracles}
wenzelm@7134
   513
wenzelm@7134
   514
\indexisarcmd{oracle}
wenzelm@7134
   515
\begin{matharray}{rcl}
wenzelm@7134
   516
  \isarcmd{oracle} & : & \isartrans{theory}{theory} \\
wenzelm@7134
   517
\end{matharray}
wenzelm@7134
   518
wenzelm@7175
   519
Oracles provide an interface to external reasoning systems, without giving up
wenzelm@7175
   520
control completely --- each theorem carries a derivation object recording any
wenzelm@7175
   521
oracle invocation.  See \cite[\S6]{isabelle-ref} for more information.
wenzelm@7175
   522
wenzelm@7134
   523
\begin{rail}
wenzelm@7134
   524
  'oracle' name '=' text comment?
wenzelm@7134
   525
  ;
wenzelm@7134
   526
\end{rail}
wenzelm@7134
   527
wenzelm@7167
   528
\begin{descr}
wenzelm@7175
   529
\item [$\isarkeyword{oracle}~name=text$] declares oracle $name$ to be ML
wenzelm@8379
   530
  function $text$, which has to be of type
wenzelm@8379
   531
  \texttt{Sign.sg~*~Object.T~->~term}.
wenzelm@7167
   532
\end{descr}
wenzelm@7134
   533
wenzelm@7134
   534
wenzelm@7134
   535
\section{Proof commands}
wenzelm@7134
   536
wenzelm@7987
   537
Proof commands perform transitions of Isar/VM machine configurations, which
wenzelm@7315
   538
are block-structured, consisting of a stack of nodes with three main
wenzelm@7335
   539
components: logical proof context, current facts, and open goals.  Isar/VM
wenzelm@8547
   540
transitions are \emph{typed} according to the following three different modes
wenzelm@8547
   541
of operation:
wenzelm@7167
   542
\begin{descr}
wenzelm@7167
   543
\item [$proof(prove)$] means that a new goal has just been stated that is now
wenzelm@8547
   544
  to be \emph{proven}; the next command may refine it by some proof method,
wenzelm@8547
   545
  and enter a sub-proof to establish the actual result.
wenzelm@10858
   546
\item [$proof(state)$] is like a nested theory mode: the context may be
wenzelm@7987
   547
  augmented by \emph{stating} additional assumptions, intermediate results
wenzelm@7987
   548
  etc.
wenzelm@7895
   549
\item [$proof(chain)$] is intermediate between $proof(state)$ and
wenzelm@7987
   550
  $proof(prove)$: existing facts (i.e.\ the contents of the special ``$this$''
wenzelm@7987
   551
  register) have been just picked up in order to be used when refining the
wenzelm@7987
   552
  goal claimed next.
wenzelm@7167
   553
\end{descr}
wenzelm@7134
   554
wenzelm@7167
   555
wenzelm@7895
   556
\subsection{Proof markup commands}\label{sec:markup-prf}
wenzelm@7167
   557
wenzelm@7987
   558
\indexisarcmd{sect}\indexisarcmd{subsect}\indexisarcmd{subsubsect}
wenzelm@7895
   559
\indexisarcmd{txt}\indexisarcmd{txt-raw}
wenzelm@7134
   560
\begin{matharray}{rcl}
wenzelm@8101
   561
  \isarcmd{sect} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   562
  \isarcmd{subsect} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   563
  \isarcmd{subsubsect} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   564
  \isarcmd{txt} & : & \isartrans{proof}{proof} \\
wenzelm@8101
   565
  \isarcmd{txt_raw} & : & \isartrans{proof}{proof} \\
wenzelm@7134
   566
\end{matharray}
wenzelm@7134
   567
wenzelm@7895
   568
These markup commands for proof mode closely correspond to the ones of theory
wenzelm@8684
   569
mode (see \S\ref{sec:markup-thy}).
wenzelm@7895
   570
wenzelm@7895
   571
\railalias{txtraw}{txt\_raw}
wenzelm@7895
   572
\railterm{txtraw}
wenzelm@7175
   573
wenzelm@7134
   574
\begin{rail}
wenzelm@7895
   575
  ('sect' | 'subsect' | 'subsubsect' | 'txt' | txtraw) text
wenzelm@7134
   576
  ;
wenzelm@7134
   577
\end{rail}
wenzelm@7134
   578
wenzelm@7134
   579
wenzelm@7315
   580
\subsection{Proof context}\label{sec:proof-context}
wenzelm@7134
   581
wenzelm@7315
   582
\indexisarcmd{fix}\indexisarcmd{assume}\indexisarcmd{presume}\indexisarcmd{def}
wenzelm@7134
   583
\begin{matharray}{rcl}
wenzelm@7134
   584
  \isarcmd{fix} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   585
  \isarcmd{assume} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   586
  \isarcmd{presume} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   587
  \isarcmd{def} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7134
   588
\end{matharray}
wenzelm@7134
   589
wenzelm@7315
   590
The logical proof context consists of fixed variables and assumptions.  The
wenzelm@7315
   591
former closely correspond to Skolem constants, or meta-level universal
wenzelm@7315
   592
quantification as provided by the Isabelle/Pure logical framework.
wenzelm@7315
   593
Introducing some \emph{arbitrary, but fixed} variable via $\FIX x$ results in
wenzelm@7987
   594
a local value that may be used in the subsequent proof as any other variable
wenzelm@7895
   595
or constant.  Furthermore, any result $\edrv \phi[x]$ exported from the
wenzelm@7987
   596
context will be universally closed wrt.\ $x$ at the outermost level: $\edrv
wenzelm@7987
   597
\All x \phi$ (this is expressed using Isabelle's meta-variables).
wenzelm@7315
   598
wenzelm@7315
   599
Similarly, introducing some assumption $\chi$ has two effects.  On the one
wenzelm@7315
   600
hand, a local theorem is created that may be used as a fact in subsequent
wenzelm@7895
   601
proof steps.  On the other hand, any result $\chi \drv \phi$ exported from the
wenzelm@7895
   602
context becomes conditional wrt.\ the assumption: $\edrv \chi \Imp \phi$.
wenzelm@7895
   603
Thus, solving an enclosing goal using such a result would basically introduce
wenzelm@7895
   604
a new subgoal stemming from the assumption.  How this situation is handled
wenzelm@7895
   605
depends on the actual version of assumption command used: while $\ASSUMENAME$
wenzelm@7895
   606
insists on solving the subgoal by unification with some premise of the goal,
wenzelm@7895
   607
$\PRESUMENAME$ leaves the subgoal unchanged in order to be proved later by the
wenzelm@7895
   608
user.
wenzelm@7315
   609
wenzelm@7319
   610
Local definitions, introduced by $\DEF{}{x \equiv t}$, are achieved by
wenzelm@7987
   611
combining $\FIX x$ with another version of assumption that causes any
wenzelm@7987
   612
hypothetical equation $x \equiv t$ to be eliminated by the reflexivity rule.
wenzelm@7987
   613
Thus, exporting some result $x \equiv t \drv \phi[x]$ yields $\edrv \phi[t]$.
wenzelm@7175
   614
wenzelm@10686
   615
\railalias{equiv}{\isasymequiv}
wenzelm@10686
   616
\railterm{equiv}
wenzelm@10686
   617
wenzelm@7134
   618
\begin{rail}
wenzelm@7431
   619
  'fix' (vars + 'and') comment?
wenzelm@7134
   620
  ;
wenzelm@7315
   621
  ('assume' | 'presume') (assm comment? + 'and')
wenzelm@7134
   622
  ;
wenzelm@10686
   623
  'def' thmdecl? \\ name ('==' | equiv) term termpat? comment?
wenzelm@7134
   624
  ;
wenzelm@7134
   625
wenzelm@7134
   626
  var: name ('::' type)?
wenzelm@7134
   627
  ;
wenzelm@7458
   628
  vars: (name+) ('::' type)?
wenzelm@7431
   629
  ;
wenzelm@7315
   630
  assm: thmdecl? (prop proppat? +)
wenzelm@7315
   631
  ;
wenzelm@7134
   632
\end{rail}
wenzelm@7134
   633
wenzelm@7167
   634
\begin{descr}
wenzelm@8547
   635
\item [$\FIX{\vec x}$] introduces local \emph{arbitrary, but fixed} variables
wenzelm@8547
   636
  $\vec x$.
wenzelm@8515
   637
\item [$\ASSUME{a}{\vec\phi}$ and $\PRESUME{a}{\vec\phi}$] introduce local
wenzelm@8515
   638
  theorems $\vec\phi$ by assumption.  Subsequent results applied to an
wenzelm@8515
   639
  enclosing goal (e.g.\ by $\SHOWNAME$) are handled as follows: $\ASSUMENAME$
wenzelm@8515
   640
  expects to be able to unify with existing premises in the goal, while
wenzelm@8515
   641
  $\PRESUMENAME$ leaves $\vec\phi$ as new subgoals.
wenzelm@7335
   642
  
wenzelm@7335
   643
  Several lists of assumptions may be given (separated by
wenzelm@7895
   644
  $\isarkeyword{and}$); the resulting list of current facts consists of all of
wenzelm@7895
   645
  these concatenated.
wenzelm@7315
   646
\item [$\DEF{a}{x \equiv t}$] introduces a local (non-polymorphic) definition.
wenzelm@7315
   647
  In results exported from the context, $x$ is replaced by $t$.  Basically,
wenzelm@7987
   648
  $\DEF{}{x \equiv t}$ abbreviates $\FIX{x}~\ASSUME{}{x \equiv t}$, with the
wenzelm@7335
   649
  resulting hypothetical equation solved by reflexivity.
wenzelm@7431
   650
  
wenzelm@7431
   651
  The default name for the definitional equation is $x_def$.
wenzelm@7167
   652
\end{descr}
wenzelm@7167
   653
wenzelm@7895
   654
The special name $prems$\indexisarthm{prems} refers to all assumptions of the
wenzelm@7895
   655
current context as a list of theorems.
wenzelm@7315
   656
wenzelm@7167
   657
wenzelm@7167
   658
\subsection{Facts and forward chaining}
wenzelm@7167
   659
wenzelm@7167
   660
\indexisarcmd{note}\indexisarcmd{then}\indexisarcmd{from}\indexisarcmd{with}
wenzelm@7167
   661
\begin{matharray}{rcl}
wenzelm@7167
   662
  \isarcmd{note} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7167
   663
  \isarcmd{then} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm@7167
   664
  \isarcmd{from} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm@7167
   665
  \isarcmd{with} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm@7167
   666
\end{matharray}
wenzelm@7167
   667
wenzelm@7319
   668
New facts are established either by assumption or proof of local statements.
wenzelm@7335
   669
Any fact will usually be involved in further proofs, either as explicit
wenzelm@8547
   670
arguments of proof methods, or when forward chaining towards the next goal via
wenzelm@7335
   671
$\THEN$ (and variants).  Note that the special theorem name
wenzelm@7987
   672
$this$\indexisarthm{this} refers to the most recently established facts.
wenzelm@7167
   673
\begin{rail}
wenzelm@9199
   674
  'note' (thmdef? thmrefs comment? + 'and')
wenzelm@7167
   675
  ;
wenzelm@7167
   676
  'then' comment?
wenzelm@7167
   677
  ;
wenzelm@9199
   678
  ('from' | 'with') (thmrefs comment? + 'and')
wenzelm@7167
   679
  ;
wenzelm@7167
   680
\end{rail}
wenzelm@7167
   681
wenzelm@7167
   682
\begin{descr}
wenzelm@7175
   683
\item [$\NOTE{a}{\vec b}$] recalls existing facts $\vec b$, binding the result
wenzelm@7175
   684
  as $a$.  Note that attributes may be involved as well, both on the left and
wenzelm@7175
   685
  right hand sides.
wenzelm@7167
   686
\item [$\THEN$] indicates forward chaining by the current facts in order to
wenzelm@7895
   687
  establish the goal to be claimed next.  The initial proof method invoked to
wenzelm@7895
   688
  refine that will be offered the facts to do ``anything appropriate'' (cf.\ 
wenzelm@7895
   689
  also \S\ref{sec:proof-steps}).  For example, method $rule$ (see
wenzelm@8515
   690
  \S\ref{sec:pure-meth-att}) would typically do an elimination rather than an
wenzelm@7895
   691
  introduction.  Automatic methods usually insert the facts into the goal
wenzelm@8547
   692
  state before operation.  This provides a simple scheme to control relevance
wenzelm@8547
   693
  of facts in automated proof search.
wenzelm@7335
   694
\item [$\FROM{\vec b}$] abbreviates $\NOTE{}{\vec b}~\THEN$; thus $\THEN$ is
wenzelm@7458
   695
  equivalent to $\FROM{this}$.
wenzelm@10858
   696
\item [$\WITH{\vec b}$] abbreviates $\FROM{\vec b~this}$; thus the forward
wenzelm@7175
   697
  chaining is from earlier facts together with the current ones.
wenzelm@7167
   698
\end{descr}
wenzelm@7167
   699
wenzelm@8515
   700
Basic proof methods (such as $rule$, see \S\ref{sec:pure-meth-att}) expect
wenzelm@7895
   701
multiple facts to be given in their proper order, corresponding to a prefix of
wenzelm@7895
   702
the premises of the rule involved.  Note that positions may be easily skipped
wenzelm@9695
   703
using something like $\FROM{\Text{\texttt{_}}~a~b}$, for example.  This
wenzelm@8547
   704
involves the trivial rule $\PROP\psi \Imp \PROP\psi$, which happens to be
wenzelm@8547
   705
bound in Isabelle/Pure as ``\texttt{_}''
wenzelm@8547
   706
(underscore).\indexisarthm{_@\texttt{_}}
wenzelm@7389
   707
wenzelm@9238
   708
Forward chaining with an empty list of theorems is the same as not chaining.
wenzelm@9238
   709
Thus $\FROM{nothing}$ has no effect apart from entering $prove(chain)$ mode,
wenzelm@9238
   710
since $nothing$\indexisarthm{nothing} is bound to the empty list of facts.
wenzelm@9238
   711
wenzelm@7167
   712
wenzelm@7167
   713
\subsection{Goal statements}
wenzelm@7167
   714
wenzelm@7167
   715
\indexisarcmd{theorem}\indexisarcmd{lemma}
wenzelm@7167
   716
\indexisarcmd{have}\indexisarcmd{show}\indexisarcmd{hence}\indexisarcmd{thus}
wenzelm@7167
   717
\begin{matharray}{rcl}
wenzelm@7167
   718
  \isarcmd{theorem} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@7167
   719
  \isarcmd{lemma} & : & \isartrans{theory}{proof(prove)} \\
wenzelm@7987
   720
  \isarcmd{have} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\
wenzelm@7987
   721
  \isarcmd{show} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\
wenzelm@7167
   722
  \isarcmd{hence} & : & \isartrans{proof(state)}{proof(prove)} \\
wenzelm@7167
   723
  \isarcmd{thus} & : & \isartrans{proof(state)}{proof(prove)} \\
wenzelm@7167
   724
\end{matharray}
wenzelm@7167
   725
wenzelm@7175
   726
Proof mode is entered from theory mode by initial goal commands $\THEOREMNAME$
wenzelm@7895
   727
and $\LEMMANAME$.  New local goals may be claimed within proof mode as well.
wenzelm@7895
   728
Four variants are available, indicating whether the result is meant to solve
wenzelm@8547
   729
some pending goal or whether forward chaining is indicated.
wenzelm@7175
   730
wenzelm@7167
   731
\begin{rail}
wenzelm@7167
   732
  ('theorem' | 'lemma') goal
wenzelm@7167
   733
  ;
wenzelm@7167
   734
  ('have' | 'show' | 'hence' | 'thus') goal
wenzelm@7167
   735
  ;
wenzelm@7167
   736
wenzelm@8632
   737
  goal: thmdecl? prop proppat? comment?
wenzelm@7167
   738
  ;
wenzelm@7167
   739
\end{rail}
wenzelm@7167
   740
wenzelm@7167
   741
\begin{descr}
wenzelm@7335
   742
\item [$\THEOREM{a}{\phi}$] enters proof mode with $\phi$ as main goal,
wenzelm@8547
   743
  eventually resulting in some theorem $\turn \phi$ to be put back into the
wenzelm@8547
   744
  theory.
wenzelm@7987
   745
\item [$\LEMMA{a}{\phi}$] is similar to $\THEOREMNAME$, but tags the result as
wenzelm@7167
   746
  ``lemma''.
wenzelm@7335
   747
\item [$\HAVE{a}{\phi}$] claims a local goal, eventually resulting in a
wenzelm@7167
   748
  theorem with the current assumption context as hypotheses.
wenzelm@7335
   749
\item [$\SHOW{a}{\phi}$] is similar to $\HAVE{a}{\phi}$, but solves some
wenzelm@7895
   750
  pending goal with the result \emph{exported} into the corresponding context
wenzelm@7895
   751
  (cf.\ \S\ref{sec:proof-context}).
wenzelm@7895
   752
\item [$\HENCENAME$] abbreviates $\THEN~\HAVENAME$, i.e.\ claims a local goal
wenzelm@7895
   753
  to be proven by forward chaining the current facts.  Note that $\HENCENAME$
wenzelm@7895
   754
  is also equivalent to $\FROM{this}~\HAVENAME$.
wenzelm@7895
   755
\item [$\THUSNAME$] abbreviates $\THEN~\SHOWNAME$.  Note that $\THUSNAME$ is
wenzelm@7895
   756
  also equivalent to $\FROM{this}~\SHOWNAME$.
wenzelm@7167
   757
\end{descr}
wenzelm@7167
   758
wenzelm@10550
   759
Any goal statement causes some term abbreviations (such as $\Var{thesis}$,
wenzelm@10550
   760
$\dots$) to be bound automatically, see also \S\ref{sec:term-abbrev}.
wenzelm@10550
   761
Furthermore, the local context of a (non-atomic) goal is provided via the case
wenzelm@10550
   762
name $antecedent$\indexisarcase{antecedent}, see also \S\ref{sec:cases}.
wenzelm@10550
   763
wenzelm@10550
   764
\medskip
wenzelm@10550
   765
wenzelm@10550
   766
\begin{warn}
wenzelm@10550
   767
  Isabelle/Isar suffers theory-level goal statements to contain \emph{unbound
wenzelm@10550
   768
    schematic variables}, although this does not conform to the aim of
wenzelm@10550
   769
  human-readable proof documents!  The main problem with schematic goals is
wenzelm@10550
   770
  that the actual outcome is usually hard to predict, depending on the
wenzelm@10550
   771
  behavior of the actual proof methods applied during the reasoning.  Note
wenzelm@10550
   772
  that most semi-automated methods heavily depend on several kinds of implicit
wenzelm@10550
   773
  rule declarations within the current theory context.  As this would also
wenzelm@10550
   774
  result in non-compositional checking of sub-proofs, \emph{local goals} are
wenzelm@10550
   775
  not allowed to be schematic at all.
wenzelm@10550
   776
  
wenzelm@10550
   777
  Nevertheless, schematic goals do have their use in Prolog-style interactive
wenzelm@10550
   778
  synthesis of proven results, usually by stepwise refinement via emulation of
wenzelm@10550
   779
  traditional Isabelle tactic scripts (see also \S\ref{sec:tactic-commands}).
wenzelm@10550
   780
  In any case, users should know what they are doing!
wenzelm@10550
   781
\end{warn}
wenzelm@8991
   782
wenzelm@7167
   783
wenzelm@7167
   784
\subsection{Initial and terminal proof steps}\label{sec:proof-steps}
wenzelm@7167
   785
wenzelm@7175
   786
\indexisarcmd{proof}\indexisarcmd{qed}\indexisarcmd{by}
wenzelm@7175
   787
\indexisarcmd{.}\indexisarcmd{..}\indexisarcmd{sorry}
wenzelm@7175
   788
\begin{matharray}{rcl}
wenzelm@7175
   789
  \isarcmd{proof} & : & \isartrans{proof(prove)}{proof(state)} \\
wenzelm@7175
   790
  \isarcmd{qed} & : & \isartrans{proof(state)}{proof(state) ~|~ theory} \\
wenzelm@7175
   791
  \isarcmd{by} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   792
  \isarcmd{.\,.} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   793
  \isarcmd{.} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   794
  \isarcmd{sorry} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm@7175
   795
\end{matharray}
wenzelm@7175
   796
wenzelm@8547
   797
Arbitrary goal refinement via tactics is considered harmful.  Properly, the
wenzelm@7335
   798
Isar framework admits proof methods to be invoked in two places only.
wenzelm@7167
   799
\begin{enumerate}
wenzelm@7175
   800
\item An \emph{initial} refinement step $\PROOF{m@1}$ reduces a newly stated
wenzelm@7335
   801
  goal to a number of sub-goals that are to be solved later.  Facts are passed
wenzelm@7895
   802
  to $m@1$ for forward chaining, if so indicated by $proof(chain)$ mode.
wenzelm@7167
   803
  
wenzelm@7987
   804
\item A \emph{terminal} conclusion step $\QED{m@2}$ is intended to solve
wenzelm@7987
   805
  remaining goals.  No facts are passed to $m@2$.
wenzelm@7167
   806
\end{enumerate}
wenzelm@7167
   807
wenzelm@8547
   808
The only other proper way to affect pending goals is by $\SHOWNAME$, which
wenzelm@8547
   809
involves an explicit statement of what is to be solved.
wenzelm@7167
   810
wenzelm@7175
   811
\medskip
wenzelm@7175
   812
wenzelm@7167
   813
Also note that initial proof methods should either solve the goal completely,
wenzelm@7895
   814
or constitute some well-understood reduction to new sub-goals.  Arbitrary
wenzelm@7895
   815
automatic proof tools that are prone leave a large number of badly structured
wenzelm@7895
   816
sub-goals are no help in continuing the proof document in any intelligible
wenzelm@7987
   817
way.
wenzelm@7167
   818
wenzelm@7175
   819
\medskip
wenzelm@7175
   820
wenzelm@8547
   821
Unless given explicitly by the user, the default initial method is ``$rule$'',
wenzelm@8547
   822
which applies a single standard elimination or introduction rule according to
wenzelm@8547
   823
the topmost symbol involved.  There is no separate default terminal method.
wenzelm@8547
   824
Any remaining goals are always solved by assumption in the very last step.
wenzelm@7167
   825
wenzelm@7167
   826
\begin{rail}
wenzelm@7167
   827
  'proof' interest? meth? comment?
wenzelm@7167
   828
  ;
wenzelm@7167
   829
  'qed' meth? comment?
wenzelm@7167
   830
  ;
wenzelm@7167
   831
  'by' meth meth? comment?
wenzelm@7167
   832
  ;
wenzelm@7167
   833
  ('.' | '..' | 'sorry') comment?
wenzelm@7167
   834
  ;
wenzelm@7167
   835
wenzelm@7167
   836
  meth: method interest?
wenzelm@7167
   837
  ;
wenzelm@7167
   838
\end{rail}
wenzelm@7167
   839
wenzelm@7167
   840
\begin{descr}
wenzelm@7335
   841
\item [$\PROOF{m@1}$] refines the goal by proof method $m@1$; facts for
wenzelm@7335
   842
  forward chaining are passed if so indicated by $proof(chain)$ mode.
wenzelm@7335
   843
\item [$\QED{m@2}$] refines any remaining goals by proof method $m@2$ and
wenzelm@7895
   844
  concludes the sub-proof by assumption.  If the goal had been $\SHOWNAME$ (or
wenzelm@7895
   845
  $\THUSNAME$), some pending sub-goal is solved as well by the rule resulting
wenzelm@7895
   846
  from the result \emph{exported} into the enclosing goal context.  Thus
wenzelm@7895
   847
  $\QEDNAME$ may fail for two reasons: either $m@2$ fails, or the resulting
wenzelm@7895
   848
  rule does not fit to any pending goal\footnote{This includes any additional
wenzelm@7895
   849
    ``strong'' assumptions as introduced by $\ASSUMENAME$.} of the enclosing
wenzelm@7895
   850
  context.  Debugging such a situation might involve temporarily changing
wenzelm@7895
   851
  $\SHOWNAME$ into $\HAVENAME$, or weakening the local context by replacing
wenzelm@7895
   852
  some occurrences of $\ASSUMENAME$ by $\PRESUMENAME$.
wenzelm@7895
   853
\item [$\BYY{m@1}{m@2}$] is a \emph{terminal proof}\index{proof!terminal}; it
wenzelm@7987
   854
  abbreviates $\PROOF{m@1}~\QED{m@2}$, with backtracking across both methods,
wenzelm@7987
   855
  though.  Debugging an unsuccessful $\BYY{m@1}{m@2}$ commands might be done
wenzelm@7895
   856
  by expanding its definition; in many cases $\PROOF{m@1}$ is already
wenzelm@7175
   857
  sufficient to see what is going wrong.
wenzelm@7895
   858
\item [``$\DDOT$''] is a \emph{default proof}\index{proof!default}; it
wenzelm@8515
   859
  abbreviates $\BY{rule}$.
wenzelm@7895
   860
\item [``$\DOT$''] is a \emph{trivial proof}\index{proof!trivial}; it
wenzelm@8195
   861
  abbreviates $\BY{this}$.
wenzelm@8379
   862
\item [$\SORRY$] is a \emph{fake proof}\index{proof!fake}; provided that the
wenzelm@8379
   863
  \texttt{quick_and_dirty} flag is enabled, $\SORRY$ pretends to solve the
wenzelm@8515
   864
  goal without further ado.  Of course, the result would be a fake theorem
wenzelm@8515
   865
  only, involving some oracle in its internal derivation object (this is
wenzelm@8515
   866
  indicated as ``$[!]$'' in the printed result).  The main application of
wenzelm@8515
   867
  $\SORRY$ is to support experimentation and top-down proof development.
wenzelm@8515
   868
\end{descr}
wenzelm@8515
   869
wenzelm@8515
   870
wenzelm@8515
   871
\subsection{Fundamental methods and attributes}\label{sec:pure-meth-att}
wenzelm@8515
   872
wenzelm@8547
   873
The following proof methods and attributes refer to basic logical operations
wenzelm@8547
   874
of Isar.  Further methods and attributes are provided by several generic and
wenzelm@8547
   875
object-logic specific tools and packages (see chapters \ref{ch:gen-tools} and
wenzelm@8547
   876
\ref{ch:hol-tools}).
wenzelm@8515
   877
wenzelm@8515
   878
\indexisarmeth{assumption}\indexisarmeth{this}\indexisarmeth{rule}\indexisarmeth{$-$}
wenzelm@9936
   879
\indexisaratt{intro}\indexisaratt{elim}\indexisaratt{dest}\indexisaratt{rule}
wenzelm@8515
   880
\indexisaratt{OF}\indexisaratt{of}
wenzelm@8515
   881
\begin{matharray}{rcl}
wenzelm@8515
   882
  assumption & : & \isarmeth \\
wenzelm@8515
   883
  this & : & \isarmeth \\
wenzelm@8515
   884
  rule & : & \isarmeth \\
wenzelm@8515
   885
  - & : & \isarmeth \\
wenzelm@8515
   886
  OF & : & \isaratt \\
wenzelm@8515
   887
  of & : & \isaratt \\
wenzelm@8515
   888
  intro & : & \isaratt \\
wenzelm@8515
   889
  elim & : & \isaratt \\
wenzelm@8515
   890
  dest & : & \isaratt \\
wenzelm@9936
   891
  rule & : & \isaratt \\
wenzelm@8515
   892
\end{matharray}
wenzelm@8515
   893
wenzelm@8515
   894
\begin{rail}
wenzelm@8547
   895
  'rule' thmrefs?
wenzelm@8515
   896
  ;
wenzelm@8515
   897
  'OF' thmrefs
wenzelm@8515
   898
  ;
wenzelm@8693
   899
  'of' insts ('concl' ':' insts)?
wenzelm@8515
   900
  ;
wenzelm@9936
   901
  'rule' 'del'
wenzelm@9936
   902
  ;
wenzelm@8515
   903
\end{rail}
wenzelm@8515
   904
wenzelm@8515
   905
\begin{descr}
wenzelm@8515
   906
\item [$assumption$] solves some goal by a single assumption step.  Any facts
wenzelm@8515
   907
  given (${} \le 1$) are guaranteed to participate in the refinement.  Recall
wenzelm@8515
   908
  that $\QEDNAME$ (see \S\ref{sec:proof-steps}) already concludes any
wenzelm@8515
   909
  remaining sub-goals by assumption.
wenzelm@8515
   910
\item [$this$] applies all of the current facts directly as rules.  Recall
wenzelm@8515
   911
  that ``$\DOT$'' (dot) abbreviates $\BY{this}$.
wenzelm@8547
   912
\item [$rule~\vec a$] applies some rule given as argument in backward manner;
wenzelm@8515
   913
  facts are used to reduce the rule before applying it to the goal.  Thus
wenzelm@8515
   914
  $rule$ without facts is plain \emph{introduction}, while with facts it
wenzelm@8515
   915
  becomes \emph{elimination}.
wenzelm@8515
   916
  
wenzelm@8547
   917
  When no arguments are given, the $rule$ method tries to pick appropriate
wenzelm@8547
   918
  rules automatically, as declared in the current context using the $intro$,
wenzelm@8547
   919
  $elim$, $dest$ attributes (see below).  This is the default behavior of
wenzelm@8547
   920
  $\PROOFNAME$ and ``$\DDOT$'' (double-dot) steps (see
wenzelm@8515
   921
  \S\ref{sec:proof-steps}).
wenzelm@8515
   922
\item [``$-$''] does nothing but insert the forward chaining facts as premises
wenzelm@8515
   923
  into the goal.  Note that command $\PROOFNAME$ without any method actually
wenzelm@8515
   924
  performs a single reduction step using the $rule$ method; thus a plain
wenzelm@8515
   925
  \emph{do-nothing} proof step would be $\PROOF{-}$ rather than $\PROOFNAME$
wenzelm@8515
   926
  alone.
wenzelm@8547
   927
\item [$OF~\vec a$] applies some theorem to given rules $\vec a$ (in
wenzelm@8547
   928
  parallel).  This corresponds to the \texttt{MRS} operator in ML
wenzelm@8547
   929
  \cite[\S5]{isabelle-ref}, but note the reversed order.  Positions may be
wenzelm@8547
   930
  skipped by including ``$\_$'' (underscore) as argument.
wenzelm@8547
   931
\item [$of~\vec t$] performs positional instantiation.  The terms $\vec t$ are
wenzelm@8515
   932
  substituted for any schematic variables occurring in a theorem from left to
wenzelm@8515
   933
  right; ``\texttt{_}'' (underscore) indicates to skip a position.  Arguments
wenzelm@8515
   934
  following a ``$concl\colon$'' specification refer to positions of the
wenzelm@8515
   935
  conclusion of a rule.
wenzelm@8515
   936
\item [$intro$, $elim$, and $dest$] declare introduction, elimination, and
wenzelm@8515
   937
  destruct rules, respectively.  Note that the classical reasoner (see
wenzelm@8515
   938
  \S\ref{sec:classical-basic}) introduces different versions of these
wenzelm@8515
   939
  attributes, and the $rule$ method, too.  In object-logics with classical
wenzelm@8515
   940
  reasoning enabled, the latter version should be used all the time to avoid
wenzelm@8515
   941
  confusion!
wenzelm@9936
   942
\item [$rule~del$] undeclares introduction, elimination, or destruct rules.
wenzelm@7315
   943
\end{descr}
wenzelm@7315
   944
wenzelm@7315
   945
wenzelm@7315
   946
\subsection{Term abbreviations}\label{sec:term-abbrev}
wenzelm@7315
   947
wenzelm@7315
   948
\indexisarcmd{let}
wenzelm@7315
   949
\begin{matharray}{rcl}
wenzelm@7315
   950
  \isarcmd{let} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7315
   951
  \isarkeyword{is} & : & syntax \\
wenzelm@7315
   952
\end{matharray}
wenzelm@7315
   953
wenzelm@7315
   954
Abbreviations may be either bound by explicit $\LET{p \equiv t}$ statements,
wenzelm@7987
   955
or by annotating assumptions or goal statements with a list of patterns
wenzelm@7987
   956
$\ISS{p@1\;\dots}{p@n}$.  In both cases, higher-order matching is invoked to
wenzelm@7987
   957
bind extra-logical term variables, which may be either named schematic
wenzelm@7987
   958
variables of the form $\Var{x}$, or nameless dummies ``\texttt{_}''
wenzelm@7987
   959
(underscore).\indexisarvar{_@\texttt{_}} Note that in the $\LETNAME$ form the
wenzelm@7987
   960
patterns occur on the left-hand side, while the $\ISNAME$ patterns are in
wenzelm@7987
   961
postfix position.
wenzelm@7315
   962
wenzelm@8620
   963
Polymorphism of term bindings is handled in Hindley-Milner style, as in ML.
wenzelm@8620
   964
Type variables referring to local assumptions or open goal statements are
wenzelm@8620
   965
\emph{fixed}, while those of finished results or bound by $\LETNAME$ may occur
wenzelm@8620
   966
in \emph{arbitrary} instances later.  Even though actual polymorphism should
wenzelm@8620
   967
be rarely used in practice, this mechanism is essential to achieve proper
wenzelm@8620
   968
incremental type-inference, as the user proceeds to build up the Isar proof
wenzelm@8620
   969
text.
wenzelm@8620
   970
wenzelm@8620
   971
\medskip
wenzelm@8620
   972
wenzelm@7319
   973
Term abbreviations are quite different from actual local definitions as
wenzelm@7319
   974
introduced via $\DEFNAME$ (see \S\ref{sec:proof-context}).  The latter are
wenzelm@7315
   975
visible within the logic as actual equations, while abbreviations disappear
wenzelm@8620
   976
during the input process just after type checking.  Also note that $\DEFNAME$
wenzelm@8620
   977
does not support polymorphism.
wenzelm@7315
   978
wenzelm@7315
   979
\begin{rail}
wenzelm@8664
   980
  'let' ((term + 'and') '=' term comment? + 'and')
wenzelm@7315
   981
  ;  
wenzelm@7315
   982
\end{rail}
wenzelm@7315
   983
wenzelm@7315
   984
The syntax of $\ISNAME$ patterns follows \railnonterm{termpat} or
wenzelm@7315
   985
\railnonterm{proppat} (see \S\ref{sec:term-pats}).
wenzelm@7315
   986
wenzelm@7315
   987
\begin{descr}
wenzelm@7315
   988
\item [$\LET{\vec p = \vec t}$] binds any text variables in patters $\vec p$
wenzelm@7315
   989
  by simultaneous higher-order matching against terms $\vec t$.
wenzelm@7315
   990
\item [$\IS{\vec p}$] resembles $\LETNAME$, but matches $\vec p$ against the
wenzelm@7315
   991
  preceding statement.  Also note that $\ISNAME$ is not a separate command,
wenzelm@7315
   992
  but part of others (such as $\ASSUMENAME$, $\HAVENAME$ etc.).
wenzelm@7315
   993
\end{descr}
wenzelm@7315
   994
wenzelm@10160
   995
Some \emph{automatic} term abbreviations\index{term abbreviations} for goals
wenzelm@7988
   996
and facts are available as well.  For any open goal,
wenzelm@10160
   997
$\Var{thesis}$\indexisarvar{thesis} refers to its object-level statement,
wenzelm@10160
   998
abstracted over any meta-level parameters (if present).  Likewise,
wenzelm@10160
   999
$\Var{this}$\indexisarvar{this} is bound for fact statements resulting from
wenzelm@10160
  1000
assumptions or finished goals.  In case $\Var{this}$ refers to an object-logic
wenzelm@10160
  1001
statement that is an application $f(t)$, then $t$ is bound to the special text
wenzelm@10160
  1002
variable ``$\dots$''\indexisarvar{\dots} (three dots).  The canonical
wenzelm@10160
  1003
application of the latter are calculational proofs (see
wenzelm@10160
  1004
\S\ref{sec:calculation}).
wenzelm@10160
  1005
wenzelm@10160
  1006
%FIXME !?
wenzelm@7315
  1007
wenzelm@10160
  1008
% A few \emph{automatic} term abbreviations\index{term abbreviations} for goals
wenzelm@10160
  1009
% and facts are available as well.  For any open goal,
wenzelm@10160
  1010
% $\Var{thesis_prop}$\indexisarvar{thesis-prop} refers to the full proposition
wenzelm@10160
  1011
% (which may be a rule), $\Var{thesis_concl}$\indexisarvar{thesis-concl} to its
wenzelm@10160
  1012
% (atomic) conclusion, and $\Var{thesis}$\indexisarvar{thesis} to its
wenzelm@10160
  1013
% object-level statement.  The latter two abstract over any meta-level
wenzelm@10160
  1014
% parameters.
wenzelm@10160
  1015
wenzelm@10160
  1016
% Fact statements resulting from assumptions or finished goals are bound as
wenzelm@10160
  1017
% $\Var{this_prop}$\indexisarvar{this-prop},
wenzelm@10160
  1018
% $\Var{this_concl}$\indexisarvar{this-concl}, and
wenzelm@10160
  1019
% $\Var{this}$\indexisarvar{this}, similar to $\Var{thesis}$ above.  In case
wenzelm@10160
  1020
% $\Var{this}$ refers to an object-logic statement that is an application
wenzelm@10160
  1021
% $f(t)$, then $t$ is bound to the special text variable
wenzelm@10160
  1022
% ``$\dots$''\indexisarvar{\dots} (three dots).  The canonical application of
wenzelm@10160
  1023
% the latter are calculational proofs (see \S\ref{sec:calculation}).
wenzelm@7315
  1024
wenzelm@7315
  1025
wenzelm@7134
  1026
\subsection{Block structure}
wenzelm@7134
  1027
wenzelm@8896
  1028
\indexisarcmd{next}\indexisarcmd{\{}\indexisarcmd{\}}
wenzelm@7397
  1029
\begin{matharray}{rcl}
wenzelm@8448
  1030
  \NEXT & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7974
  1031
  \BG & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7974
  1032
  \EN & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@7397
  1033
\end{matharray}
wenzelm@7397
  1034
wenzelm@9030
  1035
\railalias{lbrace}{\ttlbrace}
wenzelm@9030
  1036
\railterm{lbrace}
wenzelm@9030
  1037
wenzelm@9030
  1038
\railalias{rbrace}{\ttrbrace}
wenzelm@9030
  1039
\railterm{rbrace}
wenzelm@9030
  1040
wenzelm@9030
  1041
\begin{rail}
wenzelm@9030
  1042
  'next' comment?
wenzelm@9030
  1043
  ;
wenzelm@9030
  1044
  lbrace comment?
wenzelm@9030
  1045
  ;
wenzelm@9030
  1046
  rbrace comment?
wenzelm@9030
  1047
  ;
wenzelm@9030
  1048
\end{rail}
wenzelm@9030
  1049
wenzelm@7167
  1050
While Isar is inherently block-structured, opening and closing blocks is
wenzelm@7167
  1051
mostly handled rather casually, with little explicit user-intervention.  Any
wenzelm@7167
  1052
local goal statement automatically opens \emph{two} blocks, which are closed
wenzelm@7167
  1053
again when concluding the sub-proof (by $\QEDNAME$ etc.).  Sections of
wenzelm@8448
  1054
different context within a sub-proof may be switched via $\NEXT$, which is
wenzelm@8448
  1055
just a single block-close followed by block-open again.  Thus the effect of
wenzelm@8448
  1056
$\NEXT$ to reset the local proof context. There is no goal focus involved
wenzelm@8448
  1057
here!
wenzelm@7167
  1058
wenzelm@7175
  1059
For slightly more advanced applications, there are explicit block parentheses
wenzelm@7895
  1060
as well.  These typically achieve a stronger forward style of reasoning.
wenzelm@7167
  1061
wenzelm@7167
  1062
\begin{descr}
wenzelm@8448
  1063
\item [$\NEXT$] switches to a fresh block within a sub-proof, resetting the
wenzelm@8448
  1064
  local context to the initial one.
wenzelm@8896
  1065
\item [$\BG$ and $\EN$] explicitly open and close blocks.  Any current facts
wenzelm@8896
  1066
  pass through ``$\BG$'' unchanged, while ``$\EN$'' causes any result to be
wenzelm@7895
  1067
  \emph{exported} into the enclosing context.  Thus fixed variables are
wenzelm@7895
  1068
  generalized, assumptions discharged, and local definitions unfolded (cf.\ 
wenzelm@7895
  1069
  \S\ref{sec:proof-context}).  There is no difference of $\ASSUMENAME$ and
wenzelm@7895
  1070
  $\PRESUMENAME$ in this mode of forward reasoning --- in contrast to plain
wenzelm@7895
  1071
  backward reasoning with the result exported at $\SHOWNAME$ time.
wenzelm@7167
  1072
\end{descr}
wenzelm@7134
  1073
wenzelm@7134
  1074
wenzelm@9605
  1075
\subsection{Emulating tactic scripts}\label{sec:tactic-commands}
wenzelm@8515
  1076
wenzelm@9605
  1077
The Isar provides separate commands to accommodate tactic-style proof scripts
wenzelm@9605
  1078
within the same system.  While being outside the orthodox Isar proof language,
wenzelm@9605
  1079
these might come in handy for interactive exploration and debugging, or even
wenzelm@9605
  1080
actual tactical proof within new-style theories (to benefit from document
wenzelm@9605
  1081
preparation, for example).  See also \S\ref{sec:tactics} for actual tactics,
wenzelm@9605
  1082
that have been encapsulated as proof methods.  Proper proof methods may be
wenzelm@9605
  1083
used in scripts, too.
wenzelm@8515
  1084
wenzelm@9605
  1085
\indexisarcmd{apply}\indexisarcmd{apply-end}\indexisarcmd{done}
wenzelm@8515
  1086
\indexisarcmd{defer}\indexisarcmd{prefer}\indexisarcmd{back}
wenzelm@9605
  1087
\indexisarcmd{declare}
wenzelm@8515
  1088
\begin{matharray}{rcl}
wenzelm@8533
  1089
  \isarcmd{apply}^* & : & \isartrans{proof(prove)}{proof(prove)} \\
wenzelm@9605
  1090
  \isarcmd{apply_end}^* & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm@8946
  1091
  \isarcmd{done}^* & : & \isartrans{proof(prove)}{proof(state)} \\
wenzelm@8533
  1092
  \isarcmd{defer}^* & : & \isartrans{proof}{proof} \\
wenzelm@8533
  1093
  \isarcmd{prefer}^* & : & \isartrans{proof}{proof} \\
wenzelm@8533
  1094
  \isarcmd{back}^* & : & \isartrans{proof}{proof} \\
wenzelm@9605
  1095
  \isarcmd{declare}^* & : & \isartrans{theory}{theory} \\
wenzelm@8515
  1096
\end{matharray}
wenzelm@8515
  1097
wenzelm@8515
  1098
\railalias{applyend}{apply\_end}
wenzelm@8515
  1099
\railterm{applyend}
wenzelm@8515
  1100
wenzelm@8515
  1101
\begin{rail}
wenzelm@9605
  1102
  ( 'apply' | applyend ) method comment?
wenzelm@8515
  1103
  ;
wenzelm@8946
  1104
  'done' comment?
wenzelm@8946
  1105
  ;
wenzelm@8682
  1106
  'defer' nat? comment?
wenzelm@8515
  1107
  ;
wenzelm@8682
  1108
  'prefer' nat comment?
wenzelm@8515
  1109
  ;
wenzelm@9273
  1110
  'back' comment?
wenzelm@9273
  1111
  ;
wenzelm@9605
  1112
  'declare' thmrefs comment?
wenzelm@9605
  1113
  ;
wenzelm@8515
  1114
\end{rail}
wenzelm@8515
  1115
wenzelm@8515
  1116
\begin{descr}
wenzelm@10223
  1117
\item [$\APPLY{m}$] applies proof method $m$ in initial position, but unlike
wenzelm@10223
  1118
  $\PROOFNAME$ it retains ``$proof(prove)$'' mode.  Thus consecutive method
wenzelm@10223
  1119
  applications may be given just as in tactic scripts.
wenzelm@8515
  1120
  
wenzelm@8881
  1121
  Facts are passed to $m$ as indicated by the goal's forward-chain mode, and
wenzelm@10223
  1122
  are \emph{consumed} afterwards.  Thus any further $\APPLYNAME$ command would
wenzelm@10223
  1123
  always work in a purely backward manner.
wenzelm@8946
  1124
  
wenzelm@8515
  1125
\item [$\isarkeyword{apply_end}~(m)$] applies proof method $m$ as if in
wenzelm@8515
  1126
  terminal position.  Basically, this simulates a multi-step tactic script for
wenzelm@8515
  1127
  $\QEDNAME$, but may be given anywhere within the proof body.
wenzelm@8515
  1128
  
wenzelm@8515
  1129
  No facts are passed to $m$.  Furthermore, the static context is that of the
wenzelm@8515
  1130
  enclosing goal (as for actual $\QEDNAME$).  Thus the proof method may not
wenzelm@8515
  1131
  refer to any assumptions introduced in the current body, for example.
wenzelm@9605
  1132
wenzelm@9605
  1133
\item [$\isarkeyword{done}$] completes a proof script, provided that the
wenzelm@9605
  1134
  current goal state is already solved completely.  Note that actual
wenzelm@9605
  1135
  structured proof commands (e.g.\ ``$\DOT$'' or $\SORRY$) may be used to
wenzelm@9605
  1136
  conclude proof scripts as well.
wenzelm@9605
  1137
wenzelm@8515
  1138
\item [$\isarkeyword{defer}~n$ and $\isarkeyword{prefer}~n$] shuffle the list
wenzelm@8515
  1139
  of pending goals: $defer$ puts off goal $n$ to the end of the list ($n = 1$
wenzelm@8515
  1140
  by default), while $prefer$ brings goal $n$ to the top.
wenzelm@9605
  1141
wenzelm@8515
  1142
\item [$\isarkeyword{back}$] does back-tracking over the result sequence of
wenzelm@8515
  1143
  the latest proof command.\footnote{Unlike the ML function \texttt{back}
wenzelm@8515
  1144
    \cite{isabelle-ref}, the Isar command does not search upwards for further
wenzelm@8515
  1145
    branch points.} Basically, any proof command may return multiple results.
wenzelm@9605
  1146
  
wenzelm@9605
  1147
\item [$\isarkeyword{declare}~thms$] declares theorems to the current theory
wenzelm@9605
  1148
  context.  No theorem binding is involved here, unlike
wenzelm@9605
  1149
  $\isarkeyword{theorems}$ or $\isarkeyword{lemmas}$ (cf.\ 
wenzelm@9605
  1150
  \S\ref{sec:axms-thms}).  So $\isarkeyword{declare}$ only has the effect of
wenzelm@9605
  1151
  applying attributes as included in the theorem specification.
wenzelm@9006
  1152
\end{descr}
wenzelm@9006
  1153
wenzelm@9006
  1154
Any proper Isar proof method may be used with tactic script commands such as
wenzelm@10223
  1155
$\APPLYNAME$.  A few additional emulations of actual tactics are provided as
wenzelm@10223
  1156
well; these would be never used in actual structured proofs, of course.
wenzelm@9006
  1157
wenzelm@8515
  1158
wenzelm@8515
  1159
\subsection{Meta-linguistic features}
wenzelm@8515
  1160
wenzelm@8515
  1161
\indexisarcmd{oops}
wenzelm@8515
  1162
\begin{matharray}{rcl}
wenzelm@8515
  1163
  \isarcmd{oops} & : & \isartrans{proof}{theory} \\
wenzelm@8515
  1164
\end{matharray}
wenzelm@8515
  1165
wenzelm@8515
  1166
The $\OOPS$ command discontinues the current proof attempt, while considering
wenzelm@8515
  1167
the partial proof text as properly processed.  This is conceptually quite
wenzelm@8515
  1168
different from ``faking'' actual proofs via $\SORRY$ (see
wenzelm@8515
  1169
\S\ref{sec:proof-steps}): $\OOPS$ does not observe the proof structure at all,
wenzelm@8515
  1170
but goes back right to the theory level.  Furthermore, $\OOPS$ does not
wenzelm@8515
  1171
produce any result theorem --- there is no claim to be able to complete the
wenzelm@8515
  1172
proof anyhow.
wenzelm@8515
  1173
wenzelm@8515
  1174
A typical application of $\OOPS$ is to explain Isar proofs \emph{within} the
wenzelm@8515
  1175
system itself, in conjunction with the document preparation tools of Isabelle
wenzelm@8515
  1176
described in \cite{isabelle-sys}.  Thus partial or even wrong proof attempts
wenzelm@8515
  1177
can be discussed in a logically sound manner.  Note that the Isabelle {\LaTeX}
wenzelm@8515
  1178
macros can be easily adapted to print something like ``$\dots$'' instead of an
wenzelm@8515
  1179
``$\OOPS$'' keyword.
wenzelm@8515
  1180
wenzelm@8547
  1181
\medskip The $\OOPS$ command is undoable, unlike $\isarkeyword{kill}$ (see
wenzelm@8547
  1182
\S\ref{sec:history}).  The effect is to get back to the theory \emph{before}
wenzelm@8547
  1183
the opening of the proof.
wenzelm@8515
  1184
wenzelm@8515
  1185
wenzelm@7134
  1186
\section{Other commands}
wenzelm@7134
  1187
wenzelm@9605
  1188
\subsection{Diagnostics}
wenzelm@7134
  1189
wenzelm@10858
  1190
\indexisarcmd{pr}\indexisarcmd{thm}\indexisarcmd{term}
wenzelm@10858
  1191
\indexisarcmd{prop}\indexisarcmd{typ}
wenzelm@7134
  1192
\begin{matharray}{rcl}
wenzelm@8515
  1193
  \isarcmd{pr}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1194
  \isarcmd{thm}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1195
  \isarcmd{term}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1196
  \isarcmd{prop}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@8515
  1197
  \isarcmd{typ}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@7134
  1198
\end{matharray}
wenzelm@7134
  1199
wenzelm@9605
  1200
These diagnostic commands assist interactive development.  Note that $undo$
wenzelm@9605
  1201
does not apply here, the theory or proof configuration is not changed.
wenzelm@7335
  1202
wenzelm@7134
  1203
\begin{rail}
wenzelm@9727
  1204
  'pr' modes? nat? (',' nat)?
wenzelm@7134
  1205
  ;
wenzelm@10584
  1206
  'thm' modes? thmrefs comment?
wenzelm@8485
  1207
  ;
wenzelm@10584
  1208
  'term' modes? term comment?
wenzelm@7134
  1209
  ;
wenzelm@10584
  1210
  'prop' modes? prop comment?
wenzelm@7134
  1211
  ;
wenzelm@10584
  1212
  'typ' modes? type comment?
wenzelm@8485
  1213
  ;
wenzelm@8485
  1214
wenzelm@8485
  1215
  modes: '(' (name + ) ')'
wenzelm@7134
  1216
  ;
wenzelm@7134
  1217
\end{rail}
wenzelm@7134
  1218
wenzelm@7167
  1219
\begin{descr}
wenzelm@9727
  1220
\item [$\isarkeyword{pr}~goals, prems$] prints the current proof state (if
wenzelm@9727
  1221
  present), including the proof context, current facts and goals.  The
wenzelm@9727
  1222
  optional limit arguments affect the number of goals and premises to be
wenzelm@9727
  1223
  displayed, which is initially 10 for both.  Omitting limit values leaves the
wenzelm@9727
  1224
  current setting unchanged.
wenzelm@8547
  1225
\item [$\isarkeyword{thm}~\vec a$] retrieves theorems from the current theory
wenzelm@8547
  1226
  or proof context.  Note that any attributes included in the theorem
wenzelm@7974
  1227
  specifications are applied to a temporary context derived from the current
wenzelm@8547
  1228
  theory or proof; the result is discarded, i.e.\ attributes involved in $\vec
wenzelm@8547
  1229
  a$ do not have any permanent effect.
wenzelm@9727
  1230
\item [$\isarkeyword{term}~t$ and $\isarkeyword{prop}~\phi$] read, type-check
wenzelm@9727
  1231
  and print terms or propositions according to the current theory or proof
wenzelm@7895
  1232
  context; the inferred type of $t$ is output as well.  Note that these
wenzelm@7895
  1233
  commands are also useful in inspecting the current environment of term
wenzelm@7895
  1234
  abbreviations.
wenzelm@7974
  1235
\item [$\isarkeyword{typ}~\tau$] reads and prints types of the meta-logic
wenzelm@7974
  1236
  according to the current theory or proof context.
wenzelm@9605
  1237
\end{descr}
wenzelm@9605
  1238
wenzelm@9605
  1239
All of the diagnostic commands above admit a list of $modes$ to be specified,
wenzelm@9605
  1240
which is appended to the current print mode (see also \cite{isabelle-ref}).
wenzelm@9605
  1241
Thus the output behavior may be modified according particular print mode
wenzelm@9605
  1242
features.  For example, $\isarkeyword{pr}~(latex~xsymbols~symbols)$ would
wenzelm@9605
  1243
print the current proof state with mathematical symbols and special characters
wenzelm@9605
  1244
represented in {\LaTeX} source, according to the Isabelle style
wenzelm@9605
  1245
\cite{isabelle-sys}.
wenzelm@9605
  1246
wenzelm@9605
  1247
Note that antiquotations (cf.\ \S\ref{sec:antiq}) provide a more systematic
wenzelm@9605
  1248
way to include formal items into the printed text document.
wenzelm@9605
  1249
wenzelm@9605
  1250
wenzelm@9605
  1251
\subsection{Inspecting the context}
wenzelm@9605
  1252
wenzelm@9605
  1253
\indexisarcmd{print-facts}\indexisarcmd{print-binds}
wenzelm@9605
  1254
\indexisarcmd{print-commands}\indexisarcmd{print-syntax}
wenzelm@9605
  1255
\indexisarcmd{print-methods}\indexisarcmd{print-attributes}
wenzelm@10858
  1256
\indexisarcmd{thms-containing}\indexisarcmd{thm-deps}
wenzelm@10858
  1257
\indexisarcmd{print-theorems}
wenzelm@9605
  1258
\begin{matharray}{rcl}
wenzelm@9605
  1259
  \isarcmd{print_commands}^* & : & \isarkeep{\cdot} \\
wenzelm@9605
  1260
  \isarcmd{print_syntax}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@9605
  1261
  \isarcmd{print_methods}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@9605
  1262
  \isarcmd{print_attributes}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@10858
  1263
  \isarcmd{print_theorems}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@10858
  1264
  \isarcmd{thms_containing}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@10858
  1265
  \isarcmd{thms_deps}^* & : & \isarkeep{theory~|~proof} \\
wenzelm@9605
  1266
  \isarcmd{print_facts}^* & : & \isarkeep{proof} \\
wenzelm@9605
  1267
  \isarcmd{print_binds}^* & : & \isarkeep{proof} \\
wenzelm@9605
  1268
\end{matharray}
wenzelm@9605
  1269
wenzelm@10858
  1270
\railalias{thmscontaining}{thms\_containing}
wenzelm@10858
  1271
\railterm{thmscontaining}
wenzelm@10858
  1272
wenzelm@10858
  1273
\railalias{thmdeps}{thm\_deps}
wenzelm@10858
  1274
\railterm{thmdeps}
wenzelm@10858
  1275
wenzelm@10858
  1276
\begin{rail}
wenzelm@10858
  1277
  thmscontaining (name * )
wenzelm@10858
  1278
  ;
wenzelm@10858
  1279
  thmdeps thmrefs
wenzelm@10858
  1280
  ;
wenzelm@10858
  1281
\end{rail}
wenzelm@10858
  1282
wenzelm@10858
  1283
These commands print certain parts of the theory and proof context.  Note that
wenzelm@10858
  1284
there are some further ones available, such as for the set of rules declared
wenzelm@10858
  1285
for simplifications.
wenzelm@9605
  1286
wenzelm@9605
  1287
\begin{descr}
wenzelm@9605
  1288
\item [$\isarkeyword{print_commands}$] prints Isabelle's outer theory syntax,
wenzelm@9605
  1289
  including keywords and command.
wenzelm@9605
  1290
\item [$\isarkeyword{print_syntax}$] prints the inner syntax of types and
wenzelm@9605
  1291
  terms, depending on the current context.  The output can be very verbose,
wenzelm@9605
  1292
  including grammar tables and syntax translation rules.  See \cite[\S7,
wenzelm@9605
  1293
  \S8]{isabelle-ref} for further information on Isabelle's inner syntax.
wenzelm@10858
  1294
\item [$\isarkeyword{print_methods}$] prints all proof methods available in
wenzelm@10858
  1295
  the current theory context.
wenzelm@10858
  1296
\item [$\isarkeyword{print_attributes}$] prints all attributes available in
wenzelm@10858
  1297
  the current theory context.
wenzelm@10858
  1298
\item [$\isarkeyword{print_theorems}$] prints theorems available in the
wenzelm@10858
  1299
  current theory context.  In interactive mode this actually refers to the
wenzelm@10858
  1300
  theorems left by the last transaction; this allows to inspect the result of
wenzelm@10858
  1301
  advanced definitional packages, such as $\isarkeyword{datatype}$.
wenzelm@10858
  1302
\item [$\isarkeyword{thms_containing}~\vec c$] retrieves theorems from the
wenzelm@10858
  1303
  theory context containing all of the constants $\vec c$.  Note that giving
wenzelm@10858
  1304
  the empty list yields \emph{all} theorems of the current theory.
wenzelm@10858
  1305
\item [$\isarkeyword{thm_deps}~\vec a$] visualizes dependencies of theorems
wenzelm@10858
  1306
  and lemmas, using Isabelle's graph browser tool (see also
wenzelm@10858
  1307
  \cite{isabelle-sys}).
wenzelm@8379
  1308
\item [$\isarkeyword{print_facts}$] prints any named facts of the current
wenzelm@8379
  1309
  context, including assumptions and local results.
wenzelm@8379
  1310
\item [$\isarkeyword{print_binds}$] prints all term abbreviations present in
wenzelm@8379
  1311
  the context.
wenzelm@8485
  1312
\end{descr}
wenzelm@8485
  1313
wenzelm@8485
  1314
wenzelm@8485
  1315
\subsection{History commands}\label{sec:history}
wenzelm@8485
  1316
wenzelm@8485
  1317
\indexisarcmd{undo}\indexisarcmd{redo}\indexisarcmd{kill}
wenzelm@8485
  1318
\begin{matharray}{rcl}
wenzelm@8485
  1319
  \isarcmd{undo}^{{*}{*}} & : & \isarkeep{\cdot} \\
wenzelm@8485
  1320
  \isarcmd{redo}^{{*}{*}} & : & \isarkeep{\cdot} \\
wenzelm@8485
  1321
  \isarcmd{kill}^{{*}{*}} & : & \isarkeep{\cdot} \\
wenzelm@8485
  1322
\end{matharray}
wenzelm@8485
  1323
wenzelm@8485
  1324
The Isabelle/Isar top-level maintains a two-stage history, for theory and
wenzelm@8485
  1325
proof state transformation.  Basically, any command can be undone using
wenzelm@8485
  1326
$\isarkeyword{undo}$, excluding mere diagnostic elements.  Its effect may be
wenzelm@10858
  1327
revoked via $\isarkeyword{redo}$, unless the corresponding
wenzelm@8485
  1328
$\isarkeyword{undo}$ step has crossed the beginning of a proof or theory.  The
wenzelm@8485
  1329
$\isarkeyword{kill}$ command aborts the current history node altogether,
wenzelm@8485
  1330
discontinuing a proof or even the whole theory.  This operation is \emph{not}
wenzelm@8485
  1331
undoable.
wenzelm@8485
  1332
wenzelm@8485
  1333
\begin{warn}
wenzelm@8547
  1334
  History commands should never be used with user interfaces such as
wenzelm@8547
  1335
  Proof~General \cite{proofgeneral,Aspinall:TACAS:2000}, which takes care of
wenzelm@8547
  1336
  stepping forth and back itself.  Interfering by manual $\isarkeyword{undo}$,
wenzelm@8510
  1337
  $\isarkeyword{redo}$, or even $\isarkeyword{kill}$ commands would quickly
wenzelm@8510
  1338
  result in utter confusion.
wenzelm@8485
  1339
\end{warn}
wenzelm@8485
  1340
wenzelm@8379
  1341
wenzelm@7134
  1342
\subsection{System operations}
wenzelm@7134
  1343
wenzelm@7167
  1344
\indexisarcmd{cd}\indexisarcmd{pwd}\indexisarcmd{use-thy}\indexisarcmd{use-thy-only}
wenzelm@7167
  1345
\indexisarcmd{update-thy}\indexisarcmd{update-thy-only}
wenzelm@7134
  1346
\begin{matharray}{rcl}
wenzelm@8515
  1347
  \isarcmd{cd}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1348
  \isarcmd{pwd}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1349
  \isarcmd{use_thy}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1350
  \isarcmd{use_thy_only}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1351
  \isarcmd{update_thy}^* & : & \isarkeep{\cdot} \\
wenzelm@8515
  1352
  \isarcmd{update_thy_only}^* & : & \isarkeep{\cdot} \\
wenzelm@7134
  1353
\end{matharray}
wenzelm@7134
  1354
wenzelm@7167
  1355
\begin{descr}
wenzelm@7134
  1356
\item [$\isarkeyword{cd}~name$] changes the current directory of the Isabelle
wenzelm@7134
  1357
  process.
wenzelm@7134
  1358
\item [$\isarkeyword{pwd}~$] prints the current working directory.
wenzelm@7175
  1359
\item [$\isarkeyword{use_thy}$, $\isarkeyword{use_thy_only}$,
wenzelm@7987
  1360
  $\isarkeyword{update_thy}$, $\isarkeyword{update_thy_only}$] load some
wenzelm@7895
  1361
  theory given as $name$ argument.  These commands are basically the same as
wenzelm@7987
  1362
  the corresponding ML functions\footnote{The ML versions also change the
wenzelm@7987
  1363
    implicit theory context to that of the theory loaded.}  (see also
wenzelm@7987
  1364
  \cite[\S1,\S6]{isabelle-ref}).  Note that both the ML and Isar versions may
wenzelm@7987
  1365
  load new- and old-style theories alike.
wenzelm@7167
  1366
\end{descr}
wenzelm@7134
  1367
wenzelm@7987
  1368
These system commands are scarcely used when working with the Proof~General
wenzelm@7987
  1369
interface, since loading of theories is done fully transparently.
wenzelm@7134
  1370
wenzelm@8379
  1371
wenzelm@7046
  1372
%%% Local Variables: 
wenzelm@7046
  1373
%%% mode: latex
wenzelm@7046
  1374
%%% TeX-master: "isar-ref"
wenzelm@7046
  1375
%%% End: