doc-src/IsarRef/pure.tex
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\chapter{Basic 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 in most object logics.  Chapter~\ref{ch:logics}
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refers to object-logic specific elements (mainly for HOL and ZF).
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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 emulate old-style tactical theorem 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{context}\indexisarcmd{end}
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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 ``real'' command of any theory has to be $\THEORY$, which starts a
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new theory based on the merge of existing ones.  Just preceding $\THEORY$,
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there may be an optional $\isarkeyword{header}$ declaration, which is relevant
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to document preparation only; it acts very much like a special pre-theory
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markup command (cf.\ \S\ref{sec:markup-thy} and \S\ref{sec:markup-thy}).  The
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$\END$ commands concludes a theory development; it has to be the very last
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command of any theory file to loaded in batch-mode.  The theory context may be
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also changed interactively by $\CONTEXT$ without creating a new theory.
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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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  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 [$\THEORY~A = B@1 + \cdots + B@n\colon$] starts a new theory $A$ based
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  on the merge of existing theories $B@1, \dots, B@n$.
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  Due to inclusion of several ancestors, the overall theory structure emerging
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  in an Isabelle session forms a directed acyclic graph (DAG).  Isabelle's
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  theory loader ensures that the sources contributing to the development graph
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  are always up-to-date.  Changed files are automatically reloaded when
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  processing theory headers interactively; batch-mode explicitly distinguishes
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  \verb,update_thy, from \verb,use_thy,, see also \cite{isabelle-ref}.
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  The optional $\isarkeyword{files}$ specification declares additional
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  dependencies on ML files.  Files will be loaded immediately, unless the name
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  is put in parentheses, which merely documents the dependency to be resolved
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  later in the text (typically via explicit $\isarcmd{use}$ in the body text,
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  see \S\ref{sec:ML}).  In reminiscence of the old-style theory system of
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  Isabelle, \texttt{$A$.thy} may be also accompanied by an additional file
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  \texttt{$A$.ML} consisting of ML code that is executed in the context of the
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  \emph{finished} theory $A$.  That file should not be included in the
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  $\isarkeyword{files}$ dependency declaration, 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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  This command is occasionally useful for quick interactive experiments;
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  normally one should always commence a new context via $\THEORY$.
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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{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 (see also \S\ref{sec:antiq} on ``antiquotations'').
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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.
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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}{rcll}
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  \isarcmd{classes} & : & \isartrans{theory}{theory} \\
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  \isarcmd{classrel} & : & \isartrans{theory}{theory} & (axiomatic!) \\
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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 +)
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  ;
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  'classrel' nameref ('<' | subseteq) nameref
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  ;
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  'defaultsort' sort
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  ;
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{classes}~c \subseteq \vec c$] declares class $c$ to be a
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  subclass of existing classes $\vec c$.  Cyclic class structures are ruled
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  out.
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\item [$\isarkeyword{classrel}~c@1 \subseteq c@2$] states a subclass relation
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  between 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 a new object-logic.
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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}{rcll}
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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} & (axiomatic!) \\
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\end{matharray}
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\begin{rail}
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  'types' (typespec '=' type infix? +)
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  ;
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  'typedecl' typespec infix?
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  ;
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  'nonterminals' (name +)
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  ;
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  'arities' (nameref '::' arity +)
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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 +)
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  ;
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  'constdefs' (constdecl prop +)
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  ;
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  constdecl: name '::' type mixfix?
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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 [$\CONSTDEFS~c::\sigma~eqn$] combines declarations and definitions of
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  constants, using the canonical name $c_def$ for the 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 +)
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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
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  $\isarkeyword{output}$ indicator is given, all productions are added both to
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  the input and output grammar.
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\item [$\isarkeyword{translations}~rules$] specifies syntactic translation
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  rules (i.e.\ macros): parse~/ print rules (\isasymrightleftharpoons), parse
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  rules (\isasymrightharpoonup), or print rules (\isasymleftharpoondown).
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  Translation patterns may be prefixed by the syntactic category to be used
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  for parsing; the default is $logic$.
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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{lemmas}\indexisarcmd{theorems}
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\begin{matharray}{rcll}
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  \isarcmd{axioms} & : & \isartrans{theory}{theory} & (axiomatic!) \\
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  \isarcmd{lemmas} & : & \isartrans{theory}{theory} \\
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  \isarcmd{theorems} & : & \isartrans{theory}{theory} \\
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\end{matharray}
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\begin{rail}
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  'axioms' (axmdecl prop +)
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  ;
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  ('lemmas' | 'theorems') locale? (thmdef? thmrefs + 'and')
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  ;
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\end{rail}
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\begin{descr}
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\item [$\isarkeyword{axioms}~a: \phi$] introduces arbitrary statements as
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  axioms of the meta-logic.  In fact, axioms are ``axiomatic theorems'', and
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  may be referred later just as any other theorem.
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  Axioms are usually only introduced when declaring new logical systems.
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  Everyday work is typically done the hard way, with proper definitions and
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  actual proven theorems.
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\item [$\isarkeyword{lemmas}~a = \vec b$] retrieves and stores existing facts
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  in the theory context, or the specified locale (see also
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  \S\ref{sec:locale}).  Typical applications would also involve attributes, to
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  declare Simplifier rules, for example.
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\item [$\isarkeyword{theorems}$] is essentially the same as
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  $\isarkeyword{lemmas}$, but marks the result as a different kind of facts.
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\end{descr}
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\subsection{Name spaces}
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\indexisarcmd{global}\indexisarcmd{local}\indexisarcmd{hide}
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\begin{matharray}{rcl}
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   352
  \isarcmd{global} & : & \isartrans{theory}{theory} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   353
  \isarcmd{local} & : & \isartrans{theory}{theory} \\
8726
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   354
  \isarcmd{hide} & : & \isartrans{theory}{theory} \\
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   355
\end{matharray}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   356
8726
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   357
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
   358
  'hide' name (nameref + )
8726
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   359
  ;
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   360
\end{rail}
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   361
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   362
Isabelle organizes any kind of name declarations (of types, constants,
8547
wenzelm
parents: 8533
diff changeset
   363
theorems etc.) by separate hierarchically structured name spaces.  Normally
8726
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   364
the user does not have to control the behavior of name spaces by hand, yet the
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   365
following commands provide some way to do so.
7175
wenzelm
parents: 7167
diff changeset
   366
7167
wenzelm
parents: 7141
diff changeset
   367
\begin{descr}
wenzelm
parents: 7141
diff changeset
   368
\item [$\isarkeyword{global}$ and $\isarkeyword{local}$] change the current
wenzelm
parents: 7141
diff changeset
   369
  name declaration mode.  Initially, theories start in $\isarkeyword{local}$
wenzelm
parents: 7141
diff changeset
   370
  mode, causing all names to be automatically qualified by the theory name.
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   371
  Changing this to $\isarkeyword{global}$ causes all names to be declared
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   372
  without the theory prefix, until $\isarkeyword{local}$ is declared again.
8726
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   373
  
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   374
  Note that global names are prone to get hidden accidently later, when
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   375
  qualified names of the same base name are introduced.
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   376
  
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   377
\item [$\isarkeyword{hide}~space~names$] removes declarations from a given
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   378
  name space (which may be $class$, $type$, or $const$).  Hidden objects
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   379
  remain valid within the logic, but are inaccessible from user input.  In
7b15f4bdd72f 'global' / 'local': comment;
wenzelm
parents: 8696
diff changeset
   380
  output, the special qualifier ``$\mathord?\mathord?$'' is prefixed to the
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   381
  full internal name.  Unqualified (global) names may not be hidden.
7167
wenzelm
parents: 7141
diff changeset
   382
\end{descr}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   383
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   384
7167
wenzelm
parents: 7141
diff changeset
   385
\subsection{Incorporating ML code}\label{sec:ML}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   386
8682
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   387
\indexisarcmd{use}\indexisarcmd{ML}\indexisarcmd{ML-command}
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   388
\indexisarcmd{ML-setup}\indexisarcmd{setup}
9199
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   389
\indexisarcmd{method-setup}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   390
\begin{matharray}{rcl}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   391
  \isarcmd{use} & : & \isartrans{\cdot}{\cdot} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   392
  \isarcmd{ML} & : & \isartrans{\cdot}{\cdot} \\
8682
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   393
  \isarcmd{ML_command} & : & \isartrans{\cdot}{\cdot} \\
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   394
  \isarcmd{ML_setup} & : & \isartrans{theory}{theory} \\
7175
wenzelm
parents: 7167
diff changeset
   395
  \isarcmd{setup} & : & \isartrans{theory}{theory} \\
9199
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   396
  \isarcmd{method_setup} & : & \isartrans{theory}{theory} \\
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   397
\end{matharray}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   398
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   399
\railalias{MLsetup}{ML\_setup}
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   400
\railterm{MLsetup}
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   401
9199
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   402
\railalias{methodsetup}{method\_setup}
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   403
\railterm{methodsetup}
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   404
8682
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   405
\railalias{MLcommand}{ML\_command}
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   406
\railterm{MLcommand}
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   407
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   408
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
   409
  'use' name
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   410
  ;
12879
wenzelm
parents: 12621
diff changeset
   411
  ('ML' | MLcommand | MLsetup | 'setup') text
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   412
  ;
12879
wenzelm
parents: 12621
diff changeset
   413
  methodsetup name '=' text text
9199
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   414
  ;
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   415
\end{rail}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   416
7167
wenzelm
parents: 7141
diff changeset
   417
\begin{descr}
7175
wenzelm
parents: 7167
diff changeset
   418
\item [$\isarkeyword{use}~file$] reads and executes ML commands from $file$.
7466
7df66ce6508a updated;
wenzelm
parents: 7458
diff changeset
   419
  The current theory context (if present) is passed down to the ML session,
7981
wenzelm
parents: 7974
diff changeset
   420
  but may not be modified.  Furthermore, the file name is checked with the
7466
7df66ce6508a updated;
wenzelm
parents: 7458
diff changeset
   421
  $\isarkeyword{files}$ dependency declaration given in the theory header (see
7df66ce6508a updated;
wenzelm
parents: 7458
diff changeset
   422
  also \S\ref{sec:begin-thy}).
7df66ce6508a updated;
wenzelm
parents: 7458
diff changeset
   423
  
8682
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   424
\item [$\isarkeyword{ML}~text$ and $\isarkeyword{ML_command}~text$] execute ML
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   425
  commands from $text$.  The theory context is passed in the same way as for
10858
wenzelm
parents: 10686
diff changeset
   426
  $\isarkeyword{use}$, but may not be changed.  Note that the output of
8682
82ebf8618e6b added 'ML_command';
wenzelm
parents: 8664
diff changeset
   427
  $\isarkeyword{ML_command}$ is less verbose than plain $\isarkeyword{ML}$.
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   428
  
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   429
\item [$\isarkeyword{ML_setup}~text$] executes ML commands from $text$.  The
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   430
  theory context is passed down to the ML session, and fetched back
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   431
  afterwards.  Thus $text$ may actually change the theory as a side effect.
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   432
  
7167
wenzelm
parents: 7141
diff changeset
   433
\item [$\isarkeyword{setup}~text$] changes the current theory context by
8379
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   434
  applying $text$, which refers to an ML expression of type
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   435
  \texttt{(theory~->~theory)~list}.  The $\isarkeyword{setup}$ command is the
8547
wenzelm
parents: 8533
diff changeset
   436
  canonical way to initialize any object-logic specific tools and packages
wenzelm
parents: 8533
diff changeset
   437
  written in ML.
9199
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   438
  
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   439
\item [$\isarkeyword{method_setup}~name = text~description$] defines a proof
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   440
  method in the current theory.  The given $text$ has to be an ML expression
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   441
  of type \texttt{Args.src -> Proof.context -> Proof.method}.  Parsing
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   442
  concrete method syntax from \texttt{Args.src} input can be quite tedious in
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   443
  general.  The following simple examples are for methods without any explicit
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   444
  arguments, or a list of theorems, respectively.
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   445
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   446
{\footnotesize
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   447
\begin{verbatim}
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
   448
 Method.no_args (Method.METHOD (fn facts => foobar_tac))
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
   449
 Method.thms_args (fn thms => Method.METHOD (fn facts => foobar_tac))
10899
5de31ddf9c03 more method_setup examples;
wenzelm
parents: 10858
diff changeset
   450
 Method.ctxt_args (fn ctxt => Method.METHOD (fn facts => foobar_tac))
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   451
 Method.thms_ctxt_args (fn thms => fn ctxt =>
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   452
    Method.METHOD (fn facts => foobar_tac))
9199
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   453
\end{verbatim}
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   454
}
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   455
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   456
Note that mere tactic emulations may ignore the \texttt{facts} parameter
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   457
above.  Proper proof methods would do something ``appropriate'' with the list
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   458
of current facts, though.  Single-rule methods usually do strict
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   459
forward-chaining (e.g.\ by using \texttt{Method.multi_resolves}), while
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   460
automatic ones just insert the facts using \texttt{Method.insert_tac} before
7a1a856f0571 facts: support multiple lists of arguments;
wenzelm
parents: 9030
diff changeset
   461
applying the main tactic.
7167
wenzelm
parents: 7141
diff changeset
   462
\end{descr}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   463
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   464
8250
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   465
\subsection{Syntax translation functions}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   466
8250
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   467
\indexisarcmd{parse-ast-translation}\indexisarcmd{parse-translation}
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   468
\indexisarcmd{print-translation}\indexisarcmd{typed-print-translation}
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   469
\indexisarcmd{print-ast-translation}\indexisarcmd{token-translation}
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   470
\begin{matharray}{rcl}
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   471
  \isarcmd{parse_ast_translation} & : & \isartrans{theory}{theory} \\
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   472
  \isarcmd{parse_translation} & : & \isartrans{theory}{theory} \\
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   473
  \isarcmd{print_translation} & : & \isartrans{theory}{theory} \\
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   474
  \isarcmd{typed_print_translation} & : & \isartrans{theory}{theory} \\
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   475
  \isarcmd{print_ast_translation} & : & \isartrans{theory}{theory} \\
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   476
  \isarcmd{token_translation} & : & \isartrans{theory}{theory} \\
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   477
\end{matharray}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   478
9273
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   479
\railalias{parseasttranslation}{parse\_ast\_translation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   480
\railterm{parseasttranslation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   481
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   482
\railalias{parsetranslation}{parse\_translation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   483
\railterm{parsetranslation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   484
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   485
\railalias{printtranslation}{print\_translation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   486
\railterm{printtranslation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   487
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   488
\railalias{typedprinttranslation}{typed\_print\_translation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   489
\railterm{typedprinttranslation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   490
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   491
\railalias{printasttranslation}{print\_ast\_translation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   492
\railterm{printasttranslation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   493
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   494
\railalias{tokentranslation}{token\_translation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   495
\railterm{tokentranslation}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   496
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   497
\begin{rail}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   498
  ( parseasttranslation | parsetranslation | printtranslation | typedprinttranslation |
12879
wenzelm
parents: 12621
diff changeset
   499
  printasttranslation | tokentranslation ) text
9273
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   500
\end{rail}
798673f65f02 allow comment in more commands;
wenzelm
parents: 9238
diff changeset
   501
8250
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   502
Syntax translation functions written in ML admit almost arbitrary
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   503
manipulations of Isabelle's inner syntax.  Any of the above commands have a
f4029c34adef Syntax translation functions;
wenzelm
parents: 8207
diff changeset
   504
single \railqtoken{text} argument that refers to an ML expression of
8379
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   505
appropriate type.
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   506
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   507
\begin{ttbox}
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   508
val parse_ast_translation   : (string * (ast list -> ast)) list
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   509
val parse_translation       : (string * (term list -> term)) list
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   510
val print_translation       : (string * (term list -> term)) list
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   511
val typed_print_translation :
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   512
  (string * (bool -> typ -> term list -> term)) list
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   513
val print_ast_translation   : (string * (ast list -> ast)) list
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   514
val token_translation       :
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   515
  (string * string * (string -> string * real)) list
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   516
\end{ttbox}
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   517
See \cite[\S8]{isabelle-ref} for more information on syntax transformations.
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   518
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   519
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   520
\subsection{Oracles}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   521
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   522
\indexisarcmd{oracle}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   523
\begin{matharray}{rcl}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   524
  \isarcmd{oracle} & : & \isartrans{theory}{theory} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   525
\end{matharray}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   526
7175
wenzelm
parents: 7167
diff changeset
   527
Oracles provide an interface to external reasoning systems, without giving up
wenzelm
parents: 7167
diff changeset
   528
control completely --- each theorem carries a derivation object recording any
wenzelm
parents: 7167
diff changeset
   529
oracle invocation.  See \cite[\S6]{isabelle-ref} for more information.
wenzelm
parents: 7167
diff changeset
   530
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   531
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
   532
  'oracle' name '=' text
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   533
  ;
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   534
\end{rail}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   535
7167
wenzelm
parents: 7141
diff changeset
   536
\begin{descr}
7175
wenzelm
parents: 7167
diff changeset
   537
\item [$\isarkeyword{oracle}~name=text$] declares oracle $name$ to be ML
8379
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   538
  function $text$, which has to be of type
4c7659e98eb9 tuned ML types;
wenzelm
parents: 8250
diff changeset
   539
  \texttt{Sign.sg~*~Object.T~->~term}.
7167
wenzelm
parents: 7141
diff changeset
   540
\end{descr}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   541
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   542
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   543
\section{Proof commands}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   544
7987
wenzelm
parents: 7981
diff changeset
   545
Proof commands perform transitions of Isar/VM machine configurations, which
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   546
are block-structured, consisting of a stack of nodes with three main
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   547
components: logical proof context, current facts, and open goals.  Isar/VM
8547
wenzelm
parents: 8533
diff changeset
   548
transitions are \emph{typed} according to the following three different modes
wenzelm
parents: 8533
diff changeset
   549
of operation:
7167
wenzelm
parents: 7141
diff changeset
   550
\begin{descr}
wenzelm
parents: 7141
diff changeset
   551
\item [$proof(prove)$] means that a new goal has just been stated that is now
8547
wenzelm
parents: 8533
diff changeset
   552
  to be \emph{proven}; the next command may refine it by some proof method,
wenzelm
parents: 8533
diff changeset
   553
  and enter a sub-proof to establish the actual result.
10858
wenzelm
parents: 10686
diff changeset
   554
\item [$proof(state)$] is like a nested theory mode: the context may be
7987
wenzelm
parents: 7981
diff changeset
   555
  augmented by \emph{stating} additional assumptions, intermediate results
wenzelm
parents: 7981
diff changeset
   556
  etc.
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   557
\item [$proof(chain)$] is intermediate between $proof(state)$ and
7987
wenzelm
parents: 7981
diff changeset
   558
  $proof(prove)$: existing facts (i.e.\ the contents of the special ``$this$''
wenzelm
parents: 7981
diff changeset
   559
  register) have been just picked up in order to be used when refining the
wenzelm
parents: 7981
diff changeset
   560
  goal claimed next.
7167
wenzelm
parents: 7141
diff changeset
   561
\end{descr}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   562
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   563
The proof mode indicator may be read as a verb telling the writer what kind of
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   564
operation may be performed next.  The corresponding typings of proof commands
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   565
restricts the shape of well-formed proof texts to particular command
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   566
sequences.  So dynamic arrangements of commands eventually turn out as static
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   567
texts.  Appendix~\ref{ap:refcard} gives a simplified grammar of the overall
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   568
(extensible) language emerging that way.
7167
wenzelm
parents: 7141
diff changeset
   569
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   570
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   571
\subsection{Markup commands}\label{sec:markup-prf}
7167
wenzelm
parents: 7141
diff changeset
   572
7987
wenzelm
parents: 7981
diff changeset
   573
\indexisarcmd{sect}\indexisarcmd{subsect}\indexisarcmd{subsubsect}
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   574
\indexisarcmd{txt}\indexisarcmd{txt-raw}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   575
\begin{matharray}{rcl}
8101
ae555dd9585b proof markup: any mode;
wenzelm
parents: 7988
diff changeset
   576
  \isarcmd{sect} & : & \isartrans{proof}{proof} \\
ae555dd9585b proof markup: any mode;
wenzelm
parents: 7988
diff changeset
   577
  \isarcmd{subsect} & : & \isartrans{proof}{proof} \\
ae555dd9585b proof markup: any mode;
wenzelm
parents: 7988
diff changeset
   578
  \isarcmd{subsubsect} & : & \isartrans{proof}{proof} \\
ae555dd9585b proof markup: any mode;
wenzelm
parents: 7988
diff changeset
   579
  \isarcmd{txt} & : & \isartrans{proof}{proof} \\
ae555dd9585b proof markup: any mode;
wenzelm
parents: 7988
diff changeset
   580
  \isarcmd{txt_raw} & : & \isartrans{proof}{proof} \\
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   581
\end{matharray}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   582
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   583
These markup commands for proof mode closely correspond to the ones of theory
8684
dfe444b748aa improved document preparation;
wenzelm
parents: 8682
diff changeset
   584
mode (see \S\ref{sec:markup-thy}).
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   585
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   586
\railalias{txtraw}{txt\_raw}
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   587
\railterm{txtraw}
7175
wenzelm
parents: 7167
diff changeset
   588
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   589
\begin{rail}
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   590
  ('sect' | 'subsect' | 'subsubsect' | 'txt' | txtraw) text
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   591
  ;
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   592
\end{rail}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   593
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   594
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   595
\subsection{Context elements}\label{sec:proof-context}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   596
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   597
\indexisarcmd{fix}\indexisarcmd{assume}\indexisarcmd{presume}\indexisarcmd{def}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   598
\begin{matharray}{rcl}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   599
  \isarcmd{fix} & : & \isartrans{proof(state)}{proof(state)} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   600
  \isarcmd{assume} & : & \isartrans{proof(state)}{proof(state)} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   601
  \isarcmd{presume} & : & \isartrans{proof(state)}{proof(state)} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   602
  \isarcmd{def} & : & \isartrans{proof(state)}{proof(state)} \\
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   603
\end{matharray}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   604
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   605
The logical proof context consists of fixed variables and assumptions.  The
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   606
former closely correspond to Skolem constants, or meta-level universal
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   607
quantification as provided by the Isabelle/Pure logical framework.
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   608
Introducing some \emph{arbitrary, but fixed} variable via $\FIX x$ results in
7987
wenzelm
parents: 7981
diff changeset
   609
a local value that may be used in the subsequent proof as any other variable
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   610
or constant.  Furthermore, any result $\edrv \phi[x]$ exported from the
7987
wenzelm
parents: 7981
diff changeset
   611
context will be universally closed wrt.\ $x$ at the outermost level: $\edrv
wenzelm
parents: 7981
diff changeset
   612
\All x \phi$ (this is expressed using Isabelle's meta-variables).
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   613
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   614
Similarly, introducing some assumption $\chi$ has two effects.  On the one
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   615
hand, a local theorem is created that may be used as a fact in subsequent
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   616
proof steps.  On the other hand, any result $\chi \drv \phi$ exported from the
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   617
context becomes conditional wrt.\ the assumption: $\edrv \chi \Imp \phi$.
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   618
Thus, solving an enclosing goal using such a result would basically introduce
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   619
a new subgoal stemming from the assumption.  How this situation is handled
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   620
depends on the actual version of assumption command used: while $\ASSUMENAME$
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   621
insists on solving the subgoal by unification with some premise of the goal,
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   622
$\PRESUMENAME$ leaves the subgoal unchanged in order to be proved later by the
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   623
user.
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   624
7319
wenzelm
parents: 7315
diff changeset
   625
Local definitions, introduced by $\DEF{}{x \equiv t}$, are achieved by
7987
wenzelm
parents: 7981
diff changeset
   626
combining $\FIX x$ with another version of assumption that causes any
wenzelm
parents: 7981
diff changeset
   627
hypothetical equation $x \equiv t$ to be eliminated by the reflexivity rule.
wenzelm
parents: 7981
diff changeset
   628
Thus, exporting some result $x \equiv t \drv \phi[x]$ yields $\edrv \phi[t]$.
7175
wenzelm
parents: 7167
diff changeset
   629
10686
60c795d6bd9e 'def': equiv;
wenzelm
parents: 10640
diff changeset
   630
\railalias{equiv}{\isasymequiv}
60c795d6bd9e 'def': equiv;
wenzelm
parents: 10640
diff changeset
   631
\railterm{equiv}
60c795d6bd9e 'def': equiv;
wenzelm
parents: 10640
diff changeset
   632
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   633
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
   634
  'fix' (vars + 'and')
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   635
  ;
12879
wenzelm
parents: 12621
diff changeset
   636
  ('assume' | 'presume') (props + 'and')
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   637
  ;
12879
wenzelm
parents: 12621
diff changeset
   638
  'def' thmdecl? \\ name ('==' | equiv) term termpat?
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   639
  ;
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   640
\end{rail}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
   641
7167
wenzelm
parents: 7141
diff changeset
   642
\begin{descr}
8547
wenzelm
parents: 8533
diff changeset
   643
\item [$\FIX{\vec x}$] introduces local \emph{arbitrary, but fixed} variables
wenzelm
parents: 8533
diff changeset
   644
  $\vec x$.
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   645
\item [$\ASSUME{a}{\vec\phi}$ and $\PRESUME{a}{\vec\phi}$] introduce local
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   646
  theorems $\vec\phi$ by assumption.  Subsequent results applied to an
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   647
  enclosing goal (e.g.\ by $\SHOWNAME$) are handled as follows: $\ASSUMENAME$
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   648
  expects to be able to unify with existing premises in the goal, while
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   649
  $\PRESUMENAME$ leaves $\vec\phi$ as new subgoals.
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   650
  
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   651
  Several lists of assumptions may be given (separated by
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   652
  $\isarkeyword{and}$); the resulting list of current facts consists of all of
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   653
  these concatenated.
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   654
\item [$\DEF{a}{x \equiv t}$] introduces a local (non-polymorphic) definition.
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   655
  In results exported from the context, $x$ is replaced by $t$.  Basically,
7987
wenzelm
parents: 7981
diff changeset
   656
  $\DEF{}{x \equiv t}$ abbreviates $\FIX{x}~\ASSUME{}{x \equiv t}$, with the
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   657
  resulting hypothetical equation solved by reflexivity.
7431
83e60a678c3a fix: vars;
wenzelm
parents: 7397
diff changeset
   658
  
83e60a678c3a fix: vars;
wenzelm
parents: 7397
diff changeset
   659
  The default name for the definitional equation is $x_def$.
7167
wenzelm
parents: 7141
diff changeset
   660
\end{descr}
wenzelm
parents: 7141
diff changeset
   661
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   662
The special name $prems$\indexisarthm{prems} refers to all assumptions of the
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   663
current context as a list of theorems.
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
   664
7167
wenzelm
parents: 7141
diff changeset
   665
wenzelm
parents: 7141
diff changeset
   666
\subsection{Facts and forward chaining}
wenzelm
parents: 7141
diff changeset
   667
wenzelm
parents: 7141
diff changeset
   668
\indexisarcmd{note}\indexisarcmd{then}\indexisarcmd{from}\indexisarcmd{with}
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   669
\indexisarcmd{using}
7167
wenzelm
parents: 7141
diff changeset
   670
\begin{matharray}{rcl}
wenzelm
parents: 7141
diff changeset
   671
  \isarcmd{note} & : & \isartrans{proof(state)}{proof(state)} \\
wenzelm
parents: 7141
diff changeset
   672
  \isarcmd{then} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm
parents: 7141
diff changeset
   673
  \isarcmd{from} & : & \isartrans{proof(state)}{proof(chain)} \\
wenzelm
parents: 7141
diff changeset
   674
  \isarcmd{with} & : & \isartrans{proof(state)}{proof(chain)} \\
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   675
  \isarcmd{using} & : & \isartrans{proof(prove)}{proof(prove)} \\
7167
wenzelm
parents: 7141
diff changeset
   676
\end{matharray}
wenzelm
parents: 7141
diff changeset
   677
7319
wenzelm
parents: 7315
diff changeset
   678
New facts are established either by assumption or proof of local statements.
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   679
Any fact will usually be involved in further proofs, either as explicit
8547
wenzelm
parents: 8533
diff changeset
   680
arguments of proof methods, or when forward chaining towards the next goal via
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   681
$\THEN$ (and variants); $\FROMNAME$ and $\WITHNAME$ are composite forms
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   682
involving $\NOTE$.  The $\USINGNAME$ elements allows to augment the collection
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   683
of used facts \emph{after} a goal has been stated.  Note that the special
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   684
theorem name $this$\indexisarthm{this} refers to the most recently established
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   685
facts, but only \emph{before} issuing a follow-up claim.
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   686
7167
wenzelm
parents: 7141
diff changeset
   687
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
   688
  'note' (thmdef? thmrefs + 'and')
7167
wenzelm
parents: 7141
diff changeset
   689
  ;
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   690
  ('from' | 'with' | 'using') (thmrefs + 'and')
7167
wenzelm
parents: 7141
diff changeset
   691
  ;
wenzelm
parents: 7141
diff changeset
   692
\end{rail}
wenzelm
parents: 7141
diff changeset
   693
wenzelm
parents: 7141
diff changeset
   694
\begin{descr}
7175
wenzelm
parents: 7167
diff changeset
   695
\item [$\NOTE{a}{\vec b}$] recalls existing facts $\vec b$, binding the result
wenzelm
parents: 7167
diff changeset
   696
  as $a$.  Note that attributes may be involved as well, both on the left and
wenzelm
parents: 7167
diff changeset
   697
  right hand sides.
7167
wenzelm
parents: 7141
diff changeset
   698
\item [$\THEN$] indicates forward chaining by the current facts in order to
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   699
  establish the goal to be claimed next.  The initial proof method invoked to
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   700
  refine that will be offered the facts to do ``anything appropriate'' (cf.\ 
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   701
  also \S\ref{sec:proof-steps}).  For example, method $rule$ (see
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   702
  \S\ref{sec:pure-meth-att}) would typically do an elimination rather than an
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   703
  introduction.  Automatic methods usually insert the facts into the goal
8547
wenzelm
parents: 8533
diff changeset
   704
  state before operation.  This provides a simple scheme to control relevance
wenzelm
parents: 8533
diff changeset
   705
  of facts in automated proof search.
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   706
\item [$\FROM{\vec b}$] abbreviates $\NOTE{}{\vec b}~\THEN$; thus $\THEN$ is
7458
bb282845ca77 updated;
wenzelm
parents: 7431
diff changeset
   707
  equivalent to $\FROM{this}$.
10858
wenzelm
parents: 10686
diff changeset
   708
\item [$\WITH{\vec b}$] abbreviates $\FROM{\vec b~this}$; thus the forward
7175
wenzelm
parents: 7167
diff changeset
   709
  chaining is from earlier facts together with the current ones.
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   710
\item [$\USING{\vec b}$] augments the facts being currently indicated for use
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   711
  in a subsequent refinement step (such as $\APPLYNAME$ or $\PROOFNAME$).
7167
wenzelm
parents: 7141
diff changeset
   712
\end{descr}
wenzelm
parents: 7141
diff changeset
   713
9238
ad37b21c0dc6 added "nothing" (empty list of theorems);
wenzelm
parents: 9233
diff changeset
   714
Forward chaining with an empty list of theorems is the same as not chaining.
ad37b21c0dc6 added "nothing" (empty list of theorems);
wenzelm
parents: 9233
diff changeset
   715
Thus $\FROM{nothing}$ has no effect apart from entering $prove(chain)$ mode,
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   716
since $nothing$\indexisarthm{nothing} is bound to the empty list of theorems.
9238
ad37b21c0dc6 added "nothing" (empty list of theorems);
wenzelm
parents: 9233
diff changeset
   717
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   718
Basic proof methods (such as $rule$) expect multiple facts to be given in
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   719
their proper order, corresponding to a prefix of the premises of the rule
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   720
involved.  Note that positions may be easily skipped using something like
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   721
$\FROM{\Text{\texttt{_}}~a~b}$, for example.  This involves the trivial rule
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   722
$\PROP\psi \Imp \PROP\psi$, which happens to be bound in Isabelle/Pure as
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   723
``\texttt{_}'' (underscore).\indexisarthm{_@\texttt{_}}
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   724
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   725
Automated methods (such as $simp$ or $auto$) just insert any given facts
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   726
before their usual operation.  Depending on the kind of procedure involved,
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   727
the order of facts is less significant here.
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   728
7167
wenzelm
parents: 7141
diff changeset
   729
12976
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
   730
\subsection{Goal statements}\label{sec:goals}
7167
wenzelm
parents: 7141
diff changeset
   731
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   732
\indexisarcmd{lemma}\indexisarcmd{theorem}\indexisarcmd{corollary}
7167
wenzelm
parents: 7141
diff changeset
   733
\indexisarcmd{have}\indexisarcmd{show}\indexisarcmd{hence}\indexisarcmd{thus}
wenzelm
parents: 7141
diff changeset
   734
\begin{matharray}{rcl}
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   735
  \isarcmd{lemma} & : & \isartrans{theory}{proof(prove)} \\
7167
wenzelm
parents: 7141
diff changeset
   736
  \isarcmd{theorem} & : & \isartrans{theory}{proof(prove)} \\
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   737
  \isarcmd{corollary} & : & \isartrans{theory}{proof(prove)} \\
7987
wenzelm
parents: 7981
diff changeset
   738
  \isarcmd{have} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\
wenzelm
parents: 7981
diff changeset
   739
  \isarcmd{show} & : & \isartrans{proof(state) ~|~ proof(chain)}{proof(prove)} \\
7167
wenzelm
parents: 7141
diff changeset
   740
  \isarcmd{hence} & : & \isartrans{proof(state)}{proof(prove)} \\
wenzelm
parents: 7141
diff changeset
   741
  \isarcmd{thus} & : & \isartrans{proof(state)}{proof(prove)} \\
wenzelm
parents: 7141
diff changeset
   742
\end{matharray}
wenzelm
parents: 7141
diff changeset
   743
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   744
From a theory context, proof mode is entered by an initial goal command such
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   745
as $\LEMMANAME$, $\THEOREMNAME$, $\COROLLARYNAME$.  Within a proof, new claims
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   746
may be introduced locally as well; four variants are available here to
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   747
indicate whether forward chaining of facts should be performed initially (via
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   748
$\THEN$), and whether the emerging result is meant to solve some pending goal.
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   749
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   750
Goals may consist of multiple statements, resulting in a list of facts
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   751
eventually.  A pending multi-goal is internally represented as a meta-level
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   752
conjunction (printed as \verb,&&,), which is automatically split into the
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   753
corresponding number of sub-goals prior to any initial method application, via
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   754
$\PROOFNAME$ (\S\ref{sec:proof-steps}) or $\APPLYNAME$
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   755
(\S\ref{sec:tactic-commands}).\footnote{The $induct$ method covered in
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   756
  \S\ref{sec:cases-induct-meth} acts on multiple claims simultaneously.}
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   757
13016
wenzelm
parents: 12976
diff changeset
   758
Claims at the theory level may be either in short or long form.  A short goal
wenzelm
parents: 12976
diff changeset
   759
merely consists of several simultaneous propositions (often just one).  A long
wenzelm
parents: 12976
diff changeset
   760
goal includes an explicit context specification for the subsequent
wenzelm
parents: 12976
diff changeset
   761
conclusions, involving local parameters; here the role of each part of the
wenzelm
parents: 12976
diff changeset
   762
statement is explicitly marked by separate keywords (see also
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   763
\S\ref{sec:locale}).
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   764
7167
wenzelm
parents: 7141
diff changeset
   765
\begin{rail}
13016
wenzelm
parents: 12976
diff changeset
   766
  ('lemma' | 'theorem' | 'corollary') locale? (goal | longgoal)
7167
wenzelm
parents: 7141
diff changeset
   767
  ;
13016
wenzelm
parents: 12976
diff changeset
   768
  ('have' | 'show' | 'hence' | 'thus') goal
7167
wenzelm
parents: 7141
diff changeset
   769
  ;
12966
6373b4d09325 'using' command;
wenzelm
parents: 12879
diff changeset
   770
  
13016
wenzelm
parents: 12976
diff changeset
   771
  goal: (props + 'and')
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   772
  ;
13016
wenzelm
parents: 12976
diff changeset
   773
  longgoal: thmdecl? (contextelem *) 'shows' goal
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   774
  ;
7167
wenzelm
parents: 7141
diff changeset
   775
\end{rail}
wenzelm
parents: 7141
diff changeset
   776
wenzelm
parents: 7141
diff changeset
   777
\begin{descr}
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   778
\item [$\LEMMA{a}{\vec\phi}$] enters proof mode with $\vec\phi$ as main goal,
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   779
  eventually resulting in some fact $\turn \vec\phi$ to be put back into the
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   780
  theory context, and optionally into the specified locale, cf.\ 
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   781
  \S\ref{sec:locale}.  An additional \railnonterm{context} specification may
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   782
  build an initial proof context for the subsequent claim; this may include
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   783
  local definitions and syntax as well, see the definition of $contextelem$ in
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   784
  \S\ref{sec:locale}.
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   785
  
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   786
\item [$\THEOREM{a}{\vec\phi}$ and $\COROLLARY{a}{\vec\phi}$] are essentially
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   787
  the same as $\LEMMA{a}{\vec\phi}$, but the facts are internally marked as
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   788
  being of a different kind.  This discrimination acts like a formal comment.
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   789
  
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   790
\item [$\HAVE{a}{\vec\phi}$] claims a local goal, eventually resulting in a
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   791
  fact within the current logical context.  This operation is completely
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   792
  independent of any pending sub-goals of an enclosing goal statements, so
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   793
  $\HAVENAME$ may be freely used for experimental exploration of potential
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   794
  results within a proof body.
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   795
  
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   796
\item [$\SHOW{a}{\vec\phi}$] is like $\HAVE{a}{\vec\phi}$ plus a second stage
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   797
  to refine some pending sub-goal for each one of the finished result, after
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   798
  having been exported into the corresponding context (at the head of the
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   799
  sub-proof that the $\SHOWNAME$ command belongs to).
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   800
  
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   801
  To accommodate interactive debugging, resulting rules are printed before
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   802
  being applied internally.  Even more, interactive execution of $\SHOWNAME$
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   803
  predicts potential failure after finishing its proof, and displays the
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   804
  resulting error message as a warning beforehand, adding this header:
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   805
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   806
  \begin{ttbox}
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   807
  Problem! Local statement will fail to solve any pending goal
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   808
  \end{ttbox}
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   809
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   810
\item [$\HENCENAME$] abbreviates $\THEN~\HAVENAME$, i.e.\ claims a local goal
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   811
  to be proven by forward chaining the current facts.  Note that $\HENCENAME$
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   812
  is also equivalent to $\FROM{this}~\HAVENAME$.
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   813
\item [$\THUSNAME$] abbreviates $\THEN~\SHOWNAME$.  Note that $\THUSNAME$ is
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   814
  also equivalent to $\FROM{this}~\SHOWNAME$.
7167
wenzelm
parents: 7141
diff changeset
   815
\end{descr}
wenzelm
parents: 7141
diff changeset
   816
10550
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   817
Any goal statement causes some term abbreviations (such as $\Var{thesis}$,
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   818
$\dots$) to be bound automatically, see also \S\ref{sec:term-abbrev}.
11549
e7265e70fd7c renamed "antecedent" case to "rule_context";
wenzelm
parents: 11100
diff changeset
   819
Furthermore, the local context of a (non-atomic) goal is provided via the
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   820
$rule_context$\indexisarcase{rule-context} case, see also
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   821
\S\ref{sec:rule-cases}.
10550
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   822
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   823
\medskip
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   824
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   825
\begin{warn}
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   826
  Isabelle/Isar suffers theory-level goal statements to contain \emph{unbound
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   827
    schematic variables}, although this does not conform to the aim of
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   828
  human-readable proof documents!  The main problem with schematic goals is
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   829
  that the actual outcome is usually hard to predict, depending on the
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   830
  behavior of the actual proof methods applied during the reasoning.  Note
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   831
  that most semi-automated methods heavily depend on several kinds of implicit
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   832
  rule declarations within the current theory context.  As this would also
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   833
  result in non-compositional checking of sub-proofs, \emph{local goals} are
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   834
  not allowed to be schematic at all.  Nevertheless, schematic goals do have
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   835
  their use in Prolog-style interactive synthesis of proven results, usually
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   836
  by stepwise refinement via emulation of traditional Isabelle tactic scripts
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   837
  (see also \S\ref{sec:tactic-commands}).  In any case, users should know what
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   838
  they are doing.
10550
93ca45370c59 schematic goals;
wenzelm
parents: 10223
diff changeset
   839
\end{warn}
8991
dc70b797827f case 'antecedent';
wenzelm
parents: 8947
diff changeset
   840
7167
wenzelm
parents: 7141
diff changeset
   841
wenzelm
parents: 7141
diff changeset
   842
\subsection{Initial and terminal proof steps}\label{sec:proof-steps}
wenzelm
parents: 7141
diff changeset
   843
7175
wenzelm
parents: 7167
diff changeset
   844
\indexisarcmd{proof}\indexisarcmd{qed}\indexisarcmd{by}
wenzelm
parents: 7167
diff changeset
   845
\indexisarcmd{.}\indexisarcmd{..}\indexisarcmd{sorry}
wenzelm
parents: 7167
diff changeset
   846
\begin{matharray}{rcl}
wenzelm
parents: 7167
diff changeset
   847
  \isarcmd{proof} & : & \isartrans{proof(prove)}{proof(state)} \\
wenzelm
parents: 7167
diff changeset
   848
  \isarcmd{qed} & : & \isartrans{proof(state)}{proof(state) ~|~ theory} \\
wenzelm
parents: 7167
diff changeset
   849
  \isarcmd{by} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm
parents: 7167
diff changeset
   850
  \isarcmd{.\,.} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm
parents: 7167
diff changeset
   851
  \isarcmd{.} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm
parents: 7167
diff changeset
   852
  \isarcmd{sorry} & : & \isartrans{proof(prove)}{proof(state) ~|~ theory} \\
wenzelm
parents: 7167
diff changeset
   853
\end{matharray}
wenzelm
parents: 7167
diff changeset
   854
8547
wenzelm
parents: 8533
diff changeset
   855
Arbitrary goal refinement via tactics is considered harmful.  Properly, the
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   856
Isar framework admits proof methods to be invoked in two places only.
7167
wenzelm
parents: 7141
diff changeset
   857
\begin{enumerate}
7175
wenzelm
parents: 7167
diff changeset
   858
\item An \emph{initial} refinement step $\PROOF{m@1}$ reduces a newly stated
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   859
  goal to a number of sub-goals that are to be solved later.  Facts are passed
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   860
  to $m@1$ for forward chaining, if so indicated by $proof(chain)$ mode.
7167
wenzelm
parents: 7141
diff changeset
   861
  
7987
wenzelm
parents: 7981
diff changeset
   862
\item A \emph{terminal} conclusion step $\QED{m@2}$ is intended to solve
wenzelm
parents: 7981
diff changeset
   863
  remaining goals.  No facts are passed to $m@2$.
7167
wenzelm
parents: 7141
diff changeset
   864
\end{enumerate}
wenzelm
parents: 7141
diff changeset
   865
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   866
The only other proper way to affect pending goals in a proof body is by
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   867
$\SHOWNAME$, which involves an explicit statement of what is to be solved
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   868
eventually.  Thus we avoid the fundamental problem of unstructured tactic
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   869
scripts that consist of numerous consecutive goal transformations, with
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   870
invisible effects.
7167
wenzelm
parents: 7141
diff changeset
   871
7175
wenzelm
parents: 7167
diff changeset
   872
\medskip
wenzelm
parents: 7167
diff changeset
   873
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   874
As a general rule of thumb for good proof style, initial proof methods should
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   875
either solve the goal completely, or constitute some well-understood reduction
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   876
to new sub-goals.  Arbitrary automatic proof tools that are prone leave a
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   877
large number of badly structured sub-goals are no help in continuing the proof
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   878
document in any intelligible way.
7175
wenzelm
parents: 7167
diff changeset
   879
8547
wenzelm
parents: 8533
diff changeset
   880
Unless given explicitly by the user, the default initial method is ``$rule$'',
wenzelm
parents: 8533
diff changeset
   881
which applies a single standard elimination or introduction rule according to
wenzelm
parents: 8533
diff changeset
   882
the topmost symbol involved.  There is no separate default terminal method.
wenzelm
parents: 8533
diff changeset
   883
Any remaining goals are always solved by assumption in the very last step.
7167
wenzelm
parents: 7141
diff changeset
   884
wenzelm
parents: 7141
diff changeset
   885
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
   886
  'proof' method?
7167
wenzelm
parents: 7141
diff changeset
   887
  ;
12879
wenzelm
parents: 12621
diff changeset
   888
  'qed' method?
7167
wenzelm
parents: 7141
diff changeset
   889
  ;
12879
wenzelm
parents: 12621
diff changeset
   890
  'by' method method?
7167
wenzelm
parents: 7141
diff changeset
   891
  ;
12879
wenzelm
parents: 12621
diff changeset
   892
  ('.' | '..' | 'sorry')
7167
wenzelm
parents: 7141
diff changeset
   893
  ;
wenzelm
parents: 7141
diff changeset
   894
\end{rail}
wenzelm
parents: 7141
diff changeset
   895
wenzelm
parents: 7141
diff changeset
   896
\begin{descr}
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   897
\item [$\PROOF{m@1}$] refines the goal by proof method $m@1$; facts for
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   898
  forward chaining are passed if so indicated by $proof(chain)$ mode.
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
   899
\item [$\QED{m@2}$] refines any remaining goals by proof method $m@2$ and
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   900
  concludes the sub-proof by assumption.  If the goal had been $\SHOWNAME$ (or
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   901
  $\THUSNAME$), some pending sub-goal is solved as well by the rule resulting
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   902
  from the result \emph{exported} into the enclosing goal context.  Thus
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   903
  $\QEDNAME$ may fail for two reasons: either $m@2$ fails, or the resulting
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   904
  rule does not fit to any pending goal\footnote{This includes any additional
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   905
    ``strong'' assumptions as introduced by $\ASSUMENAME$.} of the enclosing
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   906
  context.  Debugging such a situation might involve temporarily changing
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   907
  $\SHOWNAME$ into $\HAVENAME$, or weakening the local context by replacing
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   908
  some occurrences of $\ASSUMENAME$ by $\PRESUMENAME$.
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   909
\item [$\BYY{m@1}{m@2}$] is a \emph{terminal proof}\index{proof!terminal}; it
7987
wenzelm
parents: 7981
diff changeset
   910
  abbreviates $\PROOF{m@1}~\QED{m@2}$, with backtracking across both methods,
wenzelm
parents: 7981
diff changeset
   911
  though.  Debugging an unsuccessful $\BYY{m@1}{m@2}$ commands might be done
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   912
  by expanding its definition; in many cases $\PROOF{m@1}$ is already
7175
wenzelm
parents: 7167
diff changeset
   913
  sufficient to see what is going wrong.
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   914
\item [``$\DDOT$''] is a \emph{default proof}\index{proof!default}; it
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   915
  abbreviates $\BY{rule}$.
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
   916
\item [``$\DOT$''] is a \emph{trivial proof}\index{proof!trivial}; it
8195
af2575a5c5ae '.' == by this;
wenzelm
parents: 8101
diff changeset
   917
  abbreviates $\BY{this}$.
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   918
\item [$\SORRY$] is a \emph{fake proof}\index{proof!fake} pretending to solve
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   919
  the pending claim without further ado.  This only works in interactive
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   920
  development, or if the \texttt{quick_and_dirty} flag is enabled.  Certainly,
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   921
  any facts emerging from fake proofs are not the real thing.  Internally,
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   922
  each theorem container is tainted by an oracle invocation, which is
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   923
  indicated as ``$[!]$'' in the printed result.
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   924
  
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   925
  The most important application of $\SORRY$ is to support experimentation and
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
   926
  top-down proof development in a simple manner.
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   927
\end{descr}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   928
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   929
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   930
\subsection{Fundamental methods and attributes}\label{sec:pure-meth-att}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   931
8547
wenzelm
parents: 8533
diff changeset
   932
The following proof methods and attributes refer to basic logical operations
wenzelm
parents: 8533
diff changeset
   933
of Isar.  Further methods and attributes are provided by several generic and
wenzelm
parents: 8533
diff changeset
   934
object-logic specific tools and packages (see chapters \ref{ch:gen-tools} and
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   935
\ref{ch:logics}).
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   936
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   937
\indexisarmeth{$-$}\indexisarmeth{assumption}
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   938
\indexisarmeth{this}\indexisarmeth{rule}\indexisarmeth{rules}
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   939
\indexisarattof{Pure}{intro}\indexisarattof{Pure}{elim}
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
   940
\indexisarattof{Pure}{dest}\indexisarattof{Pure}{rule}
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   941
\indexisaratt{OF}\indexisaratt{of}
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   942
\begin{matharray}{rcl}
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   943
  - & : & \isarmeth \\
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   944
  assumption & : & \isarmeth \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   945
  this & : & \isarmeth \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   946
  rule & : & \isarmeth \\
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   947
  rules & : & \isarmeth \\[0.5ex]
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   948
  intro & : & \isaratt \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   949
  elim & : & \isaratt \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   950
  dest & : & \isaratt \\
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   951
  rule & : & \isaratt \\[0.5ex]
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   952
  OF & : & \isaratt \\
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   953
  of & : & \isaratt \\
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   954
\end{matharray}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   955
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   956
\begin{rail}
8547
wenzelm
parents: 8533
diff changeset
   957
  'rule' thmrefs?
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   958
  ;
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   959
  'rules' ('!' ?) (rulemod *)
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   960
  ;
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   961
  rulemod: ('intro' | 'elim' | 'dest') ((('!' | () | '?') nat?) | 'del') ':' thmrefs
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   962
  ;
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   963
  ('intro' | 'elim' | 'dest') ('!' | () | '?') nat?
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   964
  ;
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   965
  'rule' 'del'
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   966
  ;
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   967
  'OF' thmrefs
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   968
  ;
8693
feb1f9af3836 'insts' syntax;
wenzelm
parents: 8684
diff changeset
   969
  'of' insts ('concl' ':' insts)?
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   970
  ;
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   971
\end{rail}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   972
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   973
\begin{descr}
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   974
  
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   975
\item [``$-$''] does nothing but insert the forward chaining facts as premises
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   976
  into the goal.  Note that command $\PROOFNAME$ without any method actually
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   977
  performs a single reduction step using the $rule$ method; thus a plain
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   978
  \emph{do-nothing} proof step would be $\PROOF{-}$ rather than $\PROOFNAME$
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   979
  alone.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   980
  
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   981
\item [$assumption$] solves some goal by a single assumption step.  Any facts
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   982
  given (${} \le 1$) are guaranteed to participate in the refinement.  Recall
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   983
  that $\QEDNAME$ (see \S\ref{sec:proof-steps}) already concludes any
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   984
  remaining sub-goals by assumption, so structured proofs usually need not
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   985
  quote the $assumption$ method at all.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   986
  
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   987
\item [$this$] applies all of the current facts directly as rules.  Recall
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   988
  that ``$\DOT$'' (dot) abbreviates $\BY{this}$.
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
   989
  
8547
wenzelm
parents: 8533
diff changeset
   990
\item [$rule~\vec a$] applies some rule given as argument in backward manner;
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   991
  facts are used to reduce the rule before applying it to the goal.  Thus
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   992
  $rule$ without facts is plain \emph{introduction}, while with facts it
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   993
  becomes \emph{elimination}.
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   994
  
8547
wenzelm
parents: 8533
diff changeset
   995
  When no arguments are given, the $rule$ method tries to pick appropriate
wenzelm
parents: 8533
diff changeset
   996
  rules automatically, as declared in the current context using the $intro$,
wenzelm
parents: 8533
diff changeset
   997
  $elim$, $dest$ attributes (see below).  This is the default behavior of
wenzelm
parents: 8533
diff changeset
   998
  $\PROOFNAME$ and ``$\DDOT$'' (double-dot) steps (see
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
   999
  \S\ref{sec:proof-steps}).
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1000
  
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1001
\item [$rules$] performs intuitionistic proof search, depending on
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1002
  specifically declared rules from the context, or given as explicit
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1003
  arguments.  Chained facts are inserted into the goal before commencing proof
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1004
  search; $rules!$ means to include the current $prems$ as well.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1005
  
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1006
  Rules need to be classified as $intro$, $elim$, or $dest$; here the ``$!$''
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1007
  indicator refers to ``safe'' rules, which may be applied aggressively
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1008
  (without considering back-tracking later).  Rules declared with ``$?$'' are
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1009
  ignored in proof search (the single-step $rule$ method still observes
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1010
  these).  An explicit weight annotation may be given as well; otherwise the
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1011
  number of rule premises will be taken into account.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1012
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1013
\item [$intro$, $elim$, and $dest$] declare introduction, elimination, and
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1014
  destruct rules, to be used with the $rule$ and $rules$ methods.  Note that
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1015
  the latter will ignore rules declare with ``$?$'', while ``$!$'' are used
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1016
  most aggressively.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1017
  
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1018
  The classical reasoner (see \S\ref{sec:classical-basic}) introduces its own
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1019
  variants of these attributes; use qualified names to access the present
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1020
  versions of Isabelle/Pure, i.e.\ $Pure{\dtt}intro$ or $CPure{\dtt}intro$.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1021
  
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1022
\item [$rule~del$] undeclares introduction, elimination, or destruct rules.
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1023
  
8547
wenzelm
parents: 8533
diff changeset
  1024
\item [$OF~\vec a$] applies some theorem to given rules $\vec a$ (in
wenzelm
parents: 8533
diff changeset
  1025
  parallel).  This corresponds to the \texttt{MRS} operator in ML
wenzelm
parents: 8533
diff changeset
  1026
  \cite[\S5]{isabelle-ref}, but note the reversed order.  Positions may be
wenzelm
parents: 8533
diff changeset
  1027
  skipped by including ``$\_$'' (underscore) as argument.
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1028
  
8547
wenzelm
parents: 8533
diff changeset
  1029
\item [$of~\vec t$] performs positional instantiation.  The terms $\vec t$ are
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1030
  substituted for any schematic variables occurring in a theorem from left to
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1031
  right; ``\texttt{_}'' (underscore) indicates to skip a position.  Arguments
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1032
  following a ``$concl\colon$'' specification refer to positions of the
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1033
  conclusion of a rule.
13024
0461b281c2b5 more stuff;
wenzelm
parents: 13016
diff changeset
  1034
  
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1035
\end{descr}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1036
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1037
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1038
\subsection{Term abbreviations}\label{sec:term-abbrev}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1039
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1040
\indexisarcmd{let}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1041
\begin{matharray}{rcl}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1042
  \isarcmd{let} & : & \isartrans{proof(state)}{proof(state)} \\
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1043
  \isarkeyword{is} & : & syntax \\
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1044
\end{matharray}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1045
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1046
Abbreviations may be either bound by explicit $\LET{p \equiv t}$ statements,
7987
wenzelm
parents: 7981
diff changeset
  1047
or by annotating assumptions or goal statements with a list of patterns
wenzelm
parents: 7981
diff changeset
  1048
$\ISS{p@1\;\dots}{p@n}$.  In both cases, higher-order matching is invoked to
wenzelm
parents: 7981
diff changeset
  1049
bind extra-logical term variables, which may be either named schematic
wenzelm
parents: 7981
diff changeset
  1050
variables of the form $\Var{x}$, or nameless dummies ``\texttt{_}''
wenzelm
parents: 7981
diff changeset
  1051
(underscore).\indexisarvar{_@\texttt{_}} Note that in the $\LETNAME$ form the
wenzelm
parents: 7981
diff changeset
  1052
patterns occur on the left-hand side, while the $\ISNAME$ patterns are in
wenzelm
parents: 7981
diff changeset
  1053
postfix position.
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1054
12621
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
  1055
Polymorphism of term bindings is handled in Hindley-Milner style, similar to
48cafea0684b next round of updates;
wenzelm
parents: 12618
diff changeset
  1056
ML.  Type variables referring to local assumptions or open goal statements are
8620
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1057
\emph{fixed}, while those of finished results or bound by $\LETNAME$ may occur
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1058
in \emph{arbitrary} instances later.  Even though actual polymorphism should
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1059
be rarely used in practice, this mechanism is essential to achieve proper
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1060
incremental type-inference, as the user proceeds to build up the Isar proof
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1061
text.
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1062
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1063
\medskip
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1064
7319
wenzelm
parents: 7315
diff changeset
  1065
Term abbreviations are quite different from actual local definitions as
wenzelm
parents: 7315
diff changeset
  1066
introduced via $\DEFNAME$ (see \S\ref{sec:proof-context}).  The latter are
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1067
visible within the logic as actual equations, while abbreviations disappear
8620
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1068
during the input process just after type checking.  Also note that $\DEFNAME$
3786d47f5570 support Hindley-Milner polymorphisms in results and bindings;
wenzelm
parents: 8547
diff changeset
  1069
does not support polymorphism.
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1070
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1071
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
  1072
  'let' ((term + 'and') '=' term + 'and')
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1073
  ;  
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1074
\end{rail}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1075
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1076
The syntax of $\ISNAME$ patterns follows \railnonterm{termpat} or
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
  1077
\railnonterm{proppat} (see \S\ref{sec:term-decls}).
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1078
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1079
\begin{descr}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1080
\item [$\LET{\vec p = \vec t}$] binds any text variables in patters $\vec p$
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1081
  by simultaneous higher-order matching against terms $\vec t$.
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1082
\item [$\IS{\vec p}$] resembles $\LETNAME$, but matches $\vec p$ against the
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1083
  preceding statement.  Also note that $\ISNAME$ is not a separate command,
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1084
  but part of others (such as $\ASSUMENAME$, $\HAVENAME$ etc.).
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1085
\end{descr}
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1086
10160
wenzelm
parents: 9936
diff changeset
  1087
Some \emph{automatic} term abbreviations\index{term abbreviations} for goals
7988
wenzelm
parents: 7987
diff changeset
  1088
and facts are available as well.  For any open goal,
10160
wenzelm
parents: 9936
diff changeset
  1089
$\Var{thesis}$\indexisarvar{thesis} refers to its object-level statement,
wenzelm
parents: 9936
diff changeset
  1090
abstracted over any meta-level parameters (if present).  Likewise,
wenzelm
parents: 9936
diff changeset
  1091
$\Var{this}$\indexisarvar{this} is bound for fact statements resulting from
wenzelm
parents: 9936
diff changeset
  1092
assumptions or finished goals.  In case $\Var{this}$ refers to an object-logic
wenzelm
parents: 9936
diff changeset
  1093
statement that is an application $f(t)$, then $t$ is bound to the special text
wenzelm
parents: 9936
diff changeset
  1094
variable ``$\dots$''\indexisarvar{\dots} (three dots).  The canonical
wenzelm
parents: 9936
diff changeset
  1095
application of the latter are calculational proofs (see
wenzelm
parents: 9936
diff changeset
  1096
\S\ref{sec:calculation}).
wenzelm
parents: 9936
diff changeset
  1097
7315
76a39a3784b5 checkpoint;
wenzelm
parents: 7175
diff changeset
  1098
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1099
\subsection{Block structure}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1100
8896
c80aba8c1d5e replaced {{ }} by { };
wenzelm
parents: 8883
diff changeset
  1101
\indexisarcmd{next}\indexisarcmd{\{}\indexisarcmd{\}}
7397
wenzelm
parents: 7389
diff changeset
  1102
\begin{matharray}{rcl}
8448
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1103
  \NEXT & : & \isartrans{proof(state)}{proof(state)} \\
7974
34245feb6e82 improved;
wenzelm
parents: 7895
diff changeset
  1104
  \BG & : & \isartrans{proof(state)}{proof(state)} \\
34245feb6e82 improved;
wenzelm
parents: 7895
diff changeset
  1105
  \EN & : & \isartrans{proof(state)}{proof(state)} \\
7397
wenzelm
parents: 7389
diff changeset
  1106
\end{matharray}
wenzelm
parents: 7389
diff changeset
  1107
7167
wenzelm
parents: 7141
diff changeset
  1108
While Isar is inherently block-structured, opening and closing blocks is
wenzelm
parents: 7141
diff changeset
  1109
mostly handled rather casually, with little explicit user-intervention.  Any
wenzelm
parents: 7141
diff changeset
  1110
local goal statement automatically opens \emph{two} blocks, which are closed
wenzelm
parents: 7141
diff changeset
  1111
again when concluding the sub-proof (by $\QEDNAME$ etc.).  Sections of
8448
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1112
different context within a sub-proof may be switched via $\NEXT$, which is
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1113
just a single block-close followed by block-open again.  Thus the effect of
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1114
$\NEXT$ to reset the local proof context. There is no goal focus involved
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1115
here!
7167
wenzelm
parents: 7141
diff changeset
  1116
7175
wenzelm
parents: 7167
diff changeset
  1117
For slightly more advanced applications, there are explicit block parentheses
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1118
as well.  These typically achieve a stronger forward style of reasoning.
7167
wenzelm
parents: 7141
diff changeset
  1119
wenzelm
parents: 7141
diff changeset
  1120
\begin{descr}
8448
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1121
\item [$\NEXT$] switches to a fresh block within a sub-proof, resetting the
e7df316491d4 tuned 'case';
wenzelm
parents: 8379
diff changeset
  1122
  local context to the initial one.
8896
c80aba8c1d5e replaced {{ }} by { };
wenzelm
parents: 8883
diff changeset
  1123
\item [$\BG$ and $\EN$] explicitly open and close blocks.  Any current facts
c80aba8c1d5e replaced {{ }} by { };
wenzelm
parents: 8883
diff changeset
  1124
  pass through ``$\BG$'' unchanged, while ``$\EN$'' causes any result to be
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1125
  \emph{exported} into the enclosing context.  Thus fixed variables are
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1126
  generalized, assumptions discharged, and local definitions unfolded (cf.\ 
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1127
  \S\ref{sec:proof-context}).  There is no difference of $\ASSUMENAME$ and
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1128
  $\PRESUMENAME$ in this mode of forward reasoning --- in contrast to plain
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1129
  backward reasoning with the result exported at $\SHOWNAME$ time.
7167
wenzelm
parents: 7141
diff changeset
  1130
\end{descr}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1131
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1132
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1133
\subsection{Emulating tactic scripts}\label{sec:tactic-commands}
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1134
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1135
The Isar provides separate commands to accommodate tactic-style proof scripts
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1136
within the same system.  While being outside the orthodox Isar proof language,
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1137
these might come in handy for interactive exploration and debugging, or even
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1138
actual tactical proof within new-style theories (to benefit from document
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1139
preparation, for example).  See also \S\ref{sec:tactics} for actual tactics,
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1140
that have been encapsulated as proof methods.  Proper proof methods may be
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1141
used in scripts, too.
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1142
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1143
\indexisarcmd{apply}\indexisarcmd{apply-end}\indexisarcmd{done}
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1144
\indexisarcmd{defer}\indexisarcmd{prefer}\indexisarcmd{back}
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1145
\indexisarcmd{declare}
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1146
\begin{matharray}{rcl}
8533
d534ddf14076 res_inst_tac etc.;
wenzelm
parents: 8515
diff changeset
  1147
  \isarcmd{apply}^* & : & \isartrans{proof(prove)}{proof(prove)} \\
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1148
  \isarcmd{apply_end}^* & : & \isartrans{proof(state)}{proof(state)} \\
8946
40e06237934c "done" command;
wenzelm
parents: 8896
diff changeset
  1149
  \isarcmd{done}^* & : & \isartrans{proof(prove)}{proof(state)} \\
8533
d534ddf14076 res_inst_tac etc.;
wenzelm
parents: 8515
diff changeset
  1150
  \isarcmd{defer}^* & : & \isartrans{proof}{proof} \\
d534ddf14076 res_inst_tac etc.;
wenzelm
parents: 8515
diff changeset
  1151
  \isarcmd{prefer}^* & : & \isartrans{proof}{proof} \\
d534ddf14076 res_inst_tac etc.;
wenzelm
parents: 8515
diff changeset
  1152
  \isarcmd{back}^* & : & \isartrans{proof}{proof} \\
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1153
  \isarcmd{declare}^* & : & \isartrans{theory}{theory} \\
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1154
\end{matharray}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1155
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1156
\railalias{applyend}{apply\_end}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1157
\railterm{applyend}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1158
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1159
\begin{rail}
12879
wenzelm
parents: 12621
diff changeset
  1160
  ( 'apply' | applyend ) method
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1161
  ;
12879
wenzelm
parents: 12621
diff changeset
  1162
  'defer' nat?
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1163
  ;
12879
wenzelm
parents: 12621
diff changeset
  1164
  'prefer' nat
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1165
  ;
12976
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
  1166
  'declare' locale? (thmrefs + 'and')
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1167
  ;
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1168
\end{rail}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1169
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1170
\begin{descr}
10223
wenzelm
parents: 10160
diff changeset
  1171
\item [$\APPLY{m}$] applies proof method $m$ in initial position, but unlike
wenzelm
parents: 10160
diff changeset
  1172
  $\PROOFNAME$ it retains ``$proof(prove)$'' mode.  Thus consecutive method
wenzelm
parents: 10160
diff changeset
  1173
  applications may be given just as in tactic scripts.
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1174
  
8881
0467dd0d66ff 'apply' consumes facts;
wenzelm
parents: 8726
diff changeset
  1175
  Facts are passed to $m$ as indicated by the goal's forward-chain mode, and
10223
wenzelm
parents: 10160
diff changeset
  1176
  are \emph{consumed} afterwards.  Thus any further $\APPLYNAME$ command would
wenzelm
parents: 10160
diff changeset
  1177
  always work in a purely backward manner.
8946
40e06237934c "done" command;
wenzelm
parents: 8896
diff changeset
  1178
  
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1179
\item [$\isarkeyword{apply_end}~(m)$] applies proof method $m$ as if in
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1180
  terminal position.  Basically, this simulates a multi-step tactic script for
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1181
  $\QEDNAME$, but may be given anywhere within the proof body.
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1182
  
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1183
  No facts are passed to $m$.  Furthermore, the static context is that of the
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1184
  enclosing goal (as for actual $\QEDNAME$).  Thus the proof method may not
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1185
  refer to any assumptions introduced in the current body, for example.
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1186
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1187
\item [$\isarkeyword{done}$] completes a proof script, provided that the
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1188
  current goal state is already solved completely.  Note that actual
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1189
  structured proof commands (e.g.\ ``$\DOT$'' or $\SORRY$) may be used to
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1190
  conclude proof scripts as well.
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1191
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1192
\item [$\isarkeyword{defer}~n$ and $\isarkeyword{prefer}~n$] shuffle the list
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1193
  of pending goals: $defer$ puts off goal $n$ to the end of the list ($n = 1$
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1194
  by default), while $prefer$ brings goal $n$ to the top.
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1195
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1196
\item [$\isarkeyword{back}$] does back-tracking over the result sequence of
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1197
  the latest proof command.\footnote{Unlike the ML function \texttt{back}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1198
    \cite{isabelle-ref}, the Isar command does not search upwards for further
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1199
    branch points.} Basically, any proof command may return multiple results.
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1200
  
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1201
\item [$\isarkeyword{declare}~thms$] declares theorems to the current theory
12976
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
  1202
  context (or the specified locale, see also \S\ref{sec:locale}).  No theorem
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
  1203
  binding is involved here, unlike $\isarkeyword{theorems}$ or
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
  1204
  $\isarkeyword{lemmas}$ (cf.\ \S\ref{sec:axms-thms}), so
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
  1205
  $\isarkeyword{declare}$ only has the effect of applying attributes as
5cfe2941a5db contexts, locales, sym(metric);
wenzelm
parents: 12966
diff changeset
  1206
  included in the theorem specification.
9006
3832cc6f4a43 tuned tactic emulation;
wenzelm
parents: 8991
diff changeset
  1207
\end{descr}
3832cc6f4a43 tuned tactic emulation;
wenzelm
parents: 8991
diff changeset
  1208
3832cc6f4a43 tuned tactic emulation;
wenzelm
parents: 8991
diff changeset
  1209
Any proper Isar proof method may be used with tactic script commands such as
10223
wenzelm
parents: 10160
diff changeset
  1210
$\APPLYNAME$.  A few additional emulations of actual tactics are provided as
wenzelm
parents: 10160
diff changeset
  1211
well; these would be never used in actual structured proofs, of course.
9006
3832cc6f4a43 tuned tactic emulation;
wenzelm
parents: 8991
diff changeset
  1212
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1213
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1214
\subsection{Meta-linguistic features}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1215
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1216
\indexisarcmd{oops}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1217
\begin{matharray}{rcl}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1218
  \isarcmd{oops} & : & \isartrans{proof}{theory} \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1219
\end{matharray}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1220
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1221
The $\OOPS$ command discontinues the current proof attempt, while considering
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1222
the partial proof text as properly processed.  This is conceptually quite
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1223
different from ``faking'' actual proofs via $\SORRY$ (see
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1224
\S\ref{sec:proof-steps}): $\OOPS$ does not observe the proof structure at all,
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1225
but goes back right to the theory level.  Furthermore, $\OOPS$ does not
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1226
produce any result theorem --- there is no claim to be able to complete the
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1227
proof anyhow.
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1228
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1229
A typical application of $\OOPS$ is to explain Isar proofs \emph{within} the
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1230
system itself, in conjunction with the document preparation tools of Isabelle
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1231
described in \cite{isabelle-sys}.  Thus partial or even wrong proof attempts
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1232
can be discussed in a logically sound manner.  Note that the Isabelle {\LaTeX}
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1233
macros can be easily adapted to print something like ``$\dots$'' instead of an
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1234
``$\OOPS$'' keyword.
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1235
12618
43a97a2155d0 first stage of major update;
wenzelm
parents: 11549
diff changeset
  1236
\medskip The $\OOPS$ command is undo-able, unlike $\isarkeyword{kill}$ (see
8547
wenzelm
parents: 8533
diff changeset
  1237
\S\ref{sec:history}).  The effect is to get back to the theory \emph{before}
wenzelm
parents: 8533
diff changeset
  1238
the opening of the proof.
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1239
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1240
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1241
\section{Other commands}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1242
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1243
\subsection{Diagnostics}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1244
10858
wenzelm
parents: 10686
diff changeset
  1245
\indexisarcmd{pr}\indexisarcmd{thm}\indexisarcmd{term}
wenzelm
parents: 10686
diff changeset
  1246
\indexisarcmd{prop}\indexisarcmd{typ}
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1247
\begin{matharray}{rcl}
8515
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1248
  \isarcmd{pr}^* & : & \isarkeep{\cdot} \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1249
  \isarcmd{thm}^* & : & \isarkeep{theory~|~proof} \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1250
  \isarcmd{term}^* & : & \isarkeep{theory~|~proof} \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1251
  \isarcmd{prop}^* & : & \isarkeep{theory~|~proof} \\
160739e1f443 pure methods / atts moved here;
wenzelm
parents: 8510
diff changeset
  1252
  \isarcmd{typ}^* & : & \isarkeep{theory~|~proof} \\
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1253
\end{matharray}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1254
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1255
These diagnostic commands assist interactive development.  Note that $undo$
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1256
does not apply here, the theory or proof configuration is not changed.
7335
abba35b98892 draft release;
wenzelm
parents: 7321
diff changeset
  1257
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1258
\begin{rail}
9727
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1259
  'pr' modes? nat? (',' nat)?
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1260
  ;
12879
wenzelm
parents: 12621
diff changeset
  1261
  'thm' modes? thmrefs
8485
80ddf678e533 moved "cases" to generic.tex;
wenzelm
parents: 8448
diff changeset
  1262
  ;
12879
wenzelm
parents: 12621
diff changeset
  1263
  'term' modes? term
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1264
  ;
12879
wenzelm
parents: 12621
diff changeset
  1265
  'prop' modes? prop
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1266
  ;
12879
wenzelm
parents: 12621
diff changeset
  1267
  'typ' modes? type
8485
80ddf678e533 moved "cases" to generic.tex;
wenzelm
parents: 8448
diff changeset
  1268
  ;
80ddf678e533 moved "cases" to generic.tex;
wenzelm
parents: 8448
diff changeset
  1269
80ddf678e533 moved "cases" to generic.tex;
wenzelm
parents: 8448
diff changeset
  1270
  modes: '(' (name + ) ')'
7134
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1271
  ;
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1272
\end{rail}
320b412e5800 more stuff;
wenzelm
parents: 7046
diff changeset
  1273
7167
wenzelm
parents: 7141
diff changeset
  1274
\begin{descr}
9727
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1275
\item [$\isarkeyword{pr}~goals, prems$] prints the current proof state (if
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1276
  present), including the proof context, current facts and goals.  The
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1277
  optional limit arguments affect the number of goals and premises to be
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1278
  displayed, which is initially 10 for both.  Omitting limit values leaves the
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1279
  current setting unchanged.
8547
wenzelm
parents: 8533
diff changeset
  1280
\item [$\isarkeyword{thm}~\vec a$] retrieves theorems from the current theory
wenzelm
parents: 8533
diff changeset
  1281
  or proof context.  Note that any attributes included in the theorem
7974
34245feb6e82 improved;
wenzelm
parents: 7895
diff changeset
  1282
  specifications are applied to a temporary context derived from the current
8547
wenzelm
parents: 8533
diff changeset
  1283
  theory or proof; the result is discarded, i.e.\ attributes involved in $\vec
wenzelm
parents: 8533
diff changeset
  1284
  a$ do not have any permanent effect.
9727
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1285
\item [$\isarkeyword{term}~t$ and $\isarkeyword{prop}~\phi$] read, type-check
5e18de753e0f 'syntax': improved mode spec;
wenzelm
parents: 9695
diff changeset
  1286
  and print terms or propositions according to the current theory or proof
7895
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1287
  context; the inferred type of $t$ is output as well.  Note that these
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1288
  commands are also useful in inspecting the current environment of term
7c492d8bc8e3 updated;
wenzelm
parents: 7608
diff changeset
  1289
  abbreviations.
7974
34245feb6e82 improved;
wenzelm
parents: 7895
diff changeset
  1290
\item [$\isarkeyword{typ}~\tau$] reads and prints types of the meta-logic
34245feb6e82 improved;
wenzelm
parents: 7895
diff changeset
  1291
  according to the current theory or proof context.
9605
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1292
\end{descr}
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1293
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1294
All of the diagnostic commands above admit a list of $modes$ to be specified,
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1295
which is appended to the current print mode (see also \cite{isabelle-ref}).
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1296
Thus the output behavior may be modified according particular print mode
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1297
features.  For example, $\isarkeyword{pr}~(latex~xsymbols~symbols)$ would
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1298
print the current proof state with mathematical symbols and special characters
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1299
represented in {\LaTeX} source, according to the Isabelle style
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1300
\cite{isabelle-sys}.
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1301
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1302
Note that antiquotations (cf.\ \S\ref{sec:antiq}) provide a more systematic
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1303
way to include formal items into the printed text document.
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1304
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1305
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1306
\subsection{Inspecting the context}
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1307
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
diff changeset
  1308
\indexisarcmd{print-facts}\indexisarcmd{print-binds}
60d8c954390f added 'declare' command;
wenzelm
parents: 9471
di