src/Doc/Isar_Ref/Outer_Syntax.thy
author wenzelm
Mon May 30 14:15:44 2016 +0200 (2016-05-30)
changeset 63182 b065b4833092
parent 63140 0644c2e5a989
child 63183 4d04e14d7ab8
permissions -rw-r--r--
allow 'for' fixes for multi_specs;
     1 (*:maxLineLen=78:*)
     2 
     3 theory Outer_Syntax
     4 imports Base Main
     5 begin
     6 
     7 chapter \<open>Outer syntax --- the theory language \label{ch:outer-syntax}\<close>
     8 
     9 text \<open>
    10   The rather generic framework of Isabelle/Isar syntax emerges from three main
    11   syntactic categories: \<^emph>\<open>commands\<close> of the top-level Isar engine (covering
    12   theory and proof elements), \<^emph>\<open>methods\<close> for general goal refinements
    13   (analogous to traditional ``tactics''), and \<^emph>\<open>attributes\<close> for operations on
    14   facts (within a certain context). Subsequently we give a reference of basic
    15   syntactic entities underlying Isabelle/Isar syntax in a bottom-up manner.
    16   Concrete theory and proof language elements will be introduced later on.
    17 
    18   \<^medskip>
    19   In order to get started with writing well-formed Isabelle/Isar documents,
    20   the most important aspect to be noted is the difference of \<^emph>\<open>inner\<close> versus
    21   \<^emph>\<open>outer\<close> syntax. Inner syntax is that of Isabelle types and terms of the
    22   logic, while outer syntax is that of Isabelle/Isar theory sources
    23   (specifications and proofs). As a general rule, inner syntax entities may
    24   occur only as \<^emph>\<open>atomic entities\<close> within outer syntax. For example, the
    25   string \<^verbatim>\<open>"x + y"\<close> and identifier \<^verbatim>\<open>z\<close> are legal term specifications within a
    26   theory, while \<^verbatim>\<open>x + y\<close> without quotes is not.
    27 
    28   Printed theory documents usually omit quotes to gain readability (this is a
    29   matter of {\LaTeX} macro setup, say via \<^verbatim>\<open>\isabellestyle\<close>, see also @{cite
    30   "isabelle-system"}). Experienced users of Isabelle/Isar may easily
    31   reconstruct the lost technical information, while mere readers need not care
    32   about quotes at all.
    33 \<close>
    34 
    35 
    36 section \<open>Commands\<close>
    37 
    38 text \<open>
    39   \begin{matharray}{rcl}
    40     @{command_def "print_commands"}\<open>\<^sup>*\<close> & : & \<open>any \<rightarrow>\<close> \\
    41     @{command_def "help"}\<open>\<^sup>*\<close> & : & \<open>any \<rightarrow>\<close> \\
    42   \end{matharray}
    43 
    44   @{rail \<open>
    45     @@{command help} (@{syntax name} * )
    46   \<close>}
    47 
    48   \<^descr> @{command "print_commands"} prints all outer syntax keywords
    49   and commands.
    50 
    51   \<^descr> @{command "help"}~\<open>pats\<close> retrieves outer syntax
    52   commands according to the specified name patterns.
    53 \<close>
    54 
    55 
    56 subsubsection \<open>Examples\<close>
    57 
    58 text \<open>
    59   Some common diagnostic commands are retrieved like this (according to usual
    60   naming conventions):
    61 \<close>
    62 
    63 help "print"
    64 help "find"
    65 
    66 
    67 section \<open>Lexical matters \label{sec:outer-lex}\<close>
    68 
    69 text \<open>
    70   The outer lexical syntax consists of three main categories of syntax tokens:
    71 
    72     \<^enum> \<^emph>\<open>major keywords\<close> --- the command names that are available
    73     in the present logic session;
    74 
    75     \<^enum> \<^emph>\<open>minor keywords\<close> --- additional literal tokens required
    76     by the syntax of commands;
    77 
    78     \<^enum> \<^emph>\<open>named tokens\<close> --- various categories of identifiers etc.
    79 
    80   Major keywords and minor keywords are guaranteed to be disjoint. This helps
    81   user-interfaces to determine the overall structure of a theory text, without
    82   knowing the full details of command syntax. Internally, there is some
    83   additional information about the kind of major keywords, which approximates
    84   the command type (theory command, proof command etc.).
    85 
    86   Keywords override named tokens. For example, the presence of a command
    87   called \<^verbatim>\<open>term\<close> inhibits the identifier \<^verbatim>\<open>term\<close>, but the string \<^verbatim>\<open>"term"\<close> can
    88   be used instead. By convention, the outer syntax always allows quoted
    89   strings in addition to identifiers, wherever a named entity is expected.
    90 
    91   When tokenizing a given input sequence, the lexer repeatedly takes the
    92   longest prefix of the input that forms a valid token. Spaces, tabs, newlines
    93   and formfeeds between tokens serve as explicit separators.
    94 
    95   \<^medskip>
    96   The categories for named tokens are defined once and for all as follows.
    97 
    98   \begin{center}
    99   \begin{supertabular}{rcl}
   100     @{syntax_def short_ident} & = & \<open>letter (subscript\<^sup>? quasiletter)\<^sup>*\<close> \\
   101     @{syntax_def long_ident} & = & \<open>short_ident(\<close>\<^verbatim>\<open>.\<close>\<open>short_ident)\<^sup>+\<close> \\
   102     @{syntax_def sym_ident} & = & \<open>sym\<^sup>+  |\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>short_ident\<close>\<^verbatim>\<open>>\<close> \\
   103     @{syntax_def nat} & = & \<open>digit\<^sup>+\<close> \\
   104     @{syntax_def float} & = & @{syntax_ref nat}\<^verbatim>\<open>.\<close>@{syntax_ref nat}~~\<open>|\<close>~~\<^verbatim>\<open>-\<close>@{syntax_ref nat}\<^verbatim>\<open>.\<close>@{syntax_ref nat} \\
   105     @{syntax_def term_var} & = & \<^verbatim>\<open>?\<close>\<open>short_ident  |\<close>~~\<^verbatim>\<open>?\<close>\<open>short_ident\<close>\<^verbatim>\<open>.\<close>\<open>nat\<close> \\
   106     @{syntax_def type_ident} & = & \<^verbatim>\<open>'\<close>\<open>short_ident\<close> \\
   107     @{syntax_def type_var} & = & \<^verbatim>\<open>?\<close>\<open>type_ident  |\<close>~~\<^verbatim>\<open>?\<close>\<open>type_ident\<close>\<^verbatim>\<open>.\<close>\<open>nat\<close> \\
   108     @{syntax_def string} & = & \<^verbatim>\<open>"\<close> \<open>\<dots>\<close> \<^verbatim>\<open>"\<close> \\
   109     @{syntax_def altstring} & = & \<^verbatim>\<open>`\<close> \<open>\<dots>\<close> \<^verbatim>\<open>`\<close> \\
   110     @{syntax_def cartouche} & = & @{verbatim "\<open>"} \<open>\<dots>\<close> @{verbatim "\<close>"} \\
   111     @{syntax_def verbatim} & = & \<^verbatim>\<open>{*\<close> \<open>\<dots>\<close> \<^verbatim>\<open>*}\<close> \\[1ex]
   112 
   113     \<open>letter\<close> & = & \<open>latin  |\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>latin\<close>\<^verbatim>\<open>>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\\<close>\<^verbatim>\<open><\<close>\<open>latin latin\<close>\<^verbatim>\<open>>\<close>~~\<open>|  greek  |\<close> \\
   114     \<open>subscript\<close> & = & \<^verbatim>\<open>\<^sub>\<close> \\
   115     \<open>quasiletter\<close> & = & \<open>letter  |  digit  |\<close>~~\<^verbatim>\<open>_\<close>~~\<open>|\<close>~~\<^verbatim>\<open>'\<close> \\
   116     \<open>latin\<close> & = & \<^verbatim>\<open>a\<close>~~\<open>| \<dots> |\<close>~~\<^verbatim>\<open>z\<close>~~\<open>|\<close>~~\<^verbatim>\<open>A\<close>~~\<open>|  \<dots> |\<close>~~\<^verbatim>\<open>Z\<close> \\
   117     \<open>digit\<close> & = & \<^verbatim>\<open>0\<close>~~\<open>|  \<dots> |\<close>~~\<^verbatim>\<open>9\<close> \\
   118     \<open>sym\<close> & = & \<^verbatim>\<open>!\<close>~~\<open>|\<close>~~\<^verbatim>\<open>#\<close>~~\<open>|\<close>~~\<^verbatim>\<open>$\<close>~~\<open>|\<close>~~\<^verbatim>\<open>%\<close>~~\<open>|\<close>~~\<^verbatim>\<open>&\<close>~~\<open>|\<close>~~\<^verbatim>\<open>*\<close>~~\<open>|\<close>~~\<^verbatim>\<open>+\<close>~~\<open>|\<close>~~\<^verbatim>\<open>-\<close>~~\<open>|\<close>~~\<^verbatim>\<open>/\<close>~~\<open>|\<close> \\
   119     & & \<^verbatim>\<open><\<close>~~\<open>|\<close>~~\<^verbatim>\<open>=\<close>~~\<open>|\<close>~~\<^verbatim>\<open>>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>?\<close>~~\<open>|\<close>~~\<^verbatim>\<open>@\<close>~~\<open>|\<close>~~\<^verbatim>\<open>^\<close>~~\<open>|\<close>~~\<^verbatim>\<open>_\<close>~~\<open>|\<close>~~\<^verbatim>\<open>|\<close>~~\<open>|\<close>~~\<^verbatim>\<open>~\<close> \\
   120     \<open>greek\<close> & = & \<^verbatim>\<open>\<alpha>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<beta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<gamma>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<delta>\<close>~~\<open>|\<close> \\
   121           &   & \<^verbatim>\<open>\<epsilon>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<zeta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<eta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<theta>\<close>~~\<open>|\<close> \\
   122           &   & \<^verbatim>\<open>\<iota>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<kappa>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<mu>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<nu>\<close>~~\<open>|\<close> \\
   123           &   & \<^verbatim>\<open>\<xi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<pi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<rho>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<sigma>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<tau>\<close>~~\<open>|\<close> \\
   124           &   & \<^verbatim>\<open>\<upsilon>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<phi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<chi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<psi>\<close>~~\<open>|\<close> \\
   125           &   & \<^verbatim>\<open>\<omega>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Gamma>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Delta>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Theta>\<close>~~\<open>|\<close> \\
   126           &   & \<^verbatim>\<open>\<Lambda>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Xi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Pi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Sigma>\<close>~~\<open>|\<close> \\
   127           &   & \<^verbatim>\<open>\<Upsilon>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Phi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Psi>\<close>~~\<open>|\<close>~~\<^verbatim>\<open>\<Omega>\<close> \\
   128   \end{supertabular}
   129   \end{center}
   130 
   131   A @{syntax_ref term_var} or @{syntax_ref type_var} describes an unknown,
   132   which is internally a pair of base name and index (ML type @{ML_type
   133   indexname}). These components are either separated by a dot as in \<open>?x.1\<close> or
   134   \<open>?x7.3\<close> or run together as in \<open>?x1\<close>. The latter form is possible if the base
   135   name does not end with digits. If the index is 0, it may be dropped
   136   altogether: \<open>?x\<close> and \<open>?x0\<close> and \<open>?x.0\<close> all refer to the same unknown, with
   137   basename \<open>x\<close> and index 0.
   138 
   139   The syntax of @{syntax_ref string} admits any characters, including
   140   newlines; ``\<^verbatim>\<open>"\<close>'' (double-quote) and ``\<^verbatim>\<open>\\<close>'' (backslash) need to be
   141   escaped by a backslash; arbitrary character codes may be specified as
   142   ``\<^verbatim>\<open>\\<close>\<open>ddd\<close>'', with three decimal digits. Alternative strings according to
   143   @{syntax_ref altstring} are analogous, using single back-quotes instead.
   144 
   145   The body of @{syntax_ref verbatim} may consist of any text not containing
   146   ``\<^verbatim>\<open>*}\<close>''; this allows to include quotes without further escapes, but there
   147   is no way to escape ``\<^verbatim>\<open>*}\<close>''. Cartouches do not have this limitation.
   148 
   149   A @{syntax_ref cartouche} consists of arbitrary text, with properly balanced
   150   blocks of ``@{verbatim "\<open>"}~\<open>\<dots>\<close>~@{verbatim "\<close>"}''. Note that the rendering
   151   of cartouche delimiters is usually like this: ``\<open>\<open> \<dots> \<close>\<close>''.
   152 
   153   Source comments take the form \<^verbatim>\<open>(*\<close>~\<open>\<dots>\<close>~\<^verbatim>\<open>*)\<close> and may be nested, although
   154   the user-interface might prevent this. Note that this form indicates source
   155   comments only, which are stripped after lexical analysis of the input. The
   156   Isar syntax also provides proper \<^emph>\<open>document comments\<close> that are considered as
   157   part of the text (see \secref{sec:comments}).
   158 
   159   Common mathematical symbols such as \<open>\<forall>\<close> are represented in Isabelle as \<^verbatim>\<open>\<forall>\<close>.
   160   There are infinitely many Isabelle symbols like this, although proper
   161   presentation is left to front-end tools such as {\LaTeX} or Isabelle/jEdit.
   162   A list of predefined Isabelle symbols that work well with these tools is
   163   given in \appref{app:symbols}. Note that \<^verbatim>\<open>\<lambda>\<close> does not belong to the
   164   \<open>letter\<close> category, since it is already used differently in the Pure term
   165   language.
   166 \<close>
   167 
   168 
   169 section \<open>Common syntax entities\<close>
   170 
   171 text \<open>
   172   We now introduce several basic syntactic entities, such as names, terms, and
   173   theorem specifications, which are factored out of the actual Isar language
   174   elements to be described later.
   175 \<close>
   176 
   177 
   178 subsection \<open>Names\<close>
   179 
   180 text \<open>
   181   Entity @{syntax name} usually refers to any name of types, constants,
   182   theorems etc.\ Quoted strings provide an escape for non-identifier names or
   183   those ruled out by outer syntax keywords (e.g.\ quoted \<^verbatim>\<open>"let"\<close>).
   184 
   185   @{rail \<open>
   186     @{syntax_def name}: @{syntax short_ident} | @{syntax long_ident} |
   187       @{syntax sym_ident} | @{syntax nat} | @{syntax string}
   188     ;
   189     @{syntax_def par_name}: '(' @{syntax name} ')'
   190   \<close>}
   191 \<close>
   192 
   193 
   194 subsection \<open>Numbers\<close>
   195 
   196 text \<open>
   197   The outer lexical syntax (\secref{sec:outer-lex}) admits natural numbers and
   198   floating point numbers. These are combined as @{syntax int} and @{syntax
   199   real} as follows.
   200 
   201   @{rail \<open>
   202     @{syntax_def int}: @{syntax nat} | '-' @{syntax nat}
   203     ;
   204     @{syntax_def real}: @{syntax float} | @{syntax int}
   205   \<close>}
   206 
   207   Note that there is an overlap with the category @{syntax name}, which also
   208   includes @{syntax nat}.
   209 \<close>
   210 
   211 
   212 subsection \<open>Embedded content\<close>
   213 
   214 text \<open>
   215   Entity @{syntax embedded} refers to content of other languages: cartouches
   216   allow arbitrary nesting of sub-languages that respect the recursive
   217   balancing of cartouche delimiters. Quoted strings are possible as well, but
   218   require escaped quotes when nested. As a shortcut, tokens that appear as
   219   plain identifiers in the outer language may be used as inner language
   220   content without delimiters.
   221 
   222   @{rail \<open>
   223     @{syntax_def embedded}: @{syntax cartouche} | @{syntax string} |
   224       @{syntax short_ident} | @{syntax long_ident} | @{syntax sym_ident} |
   225       @{syntax term_var} | @{syntax type_ident} | @{syntax type_var} | @{syntax nat}
   226   \<close>}
   227 \<close>
   228 
   229 
   230 subsection \<open>Comments \label{sec:comments}\<close>
   231 
   232 text \<open>
   233   Large chunks of plain @{syntax text} are usually given @{syntax verbatim},
   234   i.e.\ enclosed in \<^verbatim>\<open>{*\<close>~\<open>\<dots>\<close>~\<^verbatim>\<open>*}\<close>, or as @{syntax cartouche} \<open>\<open>\<dots>\<close>\<close>. For
   235   convenience, any of the smaller text units conforming to @{syntax name} are
   236   admitted as well. A marginal @{syntax comment} is of the form \<^verbatim>\<open>--\<close>~@{syntax
   237   text} or \<^verbatim>\<open>\<comment>\<close>~@{syntax text}. Any number of these may occur within
   238   Isabelle/Isar commands.
   239 
   240   @{rail \<open>
   241     @{syntax_def text}: @{syntax embedded} | @{syntax verbatim}
   242     ;
   243     @{syntax_def comment}: ('--' | @'\<comment>') @{syntax text}
   244   \<close>}
   245 \<close>
   246 
   247 
   248 subsection \<open>Type classes, sorts and arities\<close>
   249 
   250 text \<open>
   251   Classes are specified by plain names. Sorts have a very simple inner syntax,
   252   which is either a single class name \<open>c\<close> or a list \<open>{c\<^sub>1, \<dots>, c\<^sub>n}\<close> referring
   253   to the intersection of these classes. The syntax of type arities is given
   254   directly at the outer level.
   255 
   256   @{rail \<open>
   257     @{syntax_def classdecl}: @{syntax name} (('<' | '\<subseteq>') (@{syntax name} + ','))?
   258     ;
   259     @{syntax_def sort}: @{syntax embedded}
   260     ;
   261     @{syntax_def arity}: ('(' (@{syntax sort} + ',') ')')? @{syntax sort}
   262   \<close>}
   263 \<close>
   264 
   265 
   266 subsection \<open>Types and terms \label{sec:types-terms}\<close>
   267 
   268 text \<open>
   269   The actual inner Isabelle syntax, that of types and terms of the logic, is
   270   far too sophisticated in order to be modelled explicitly at the outer theory
   271   level. Basically, any such entity has to be quoted to turn it into a single
   272   token (the parsing and type-checking is performed internally later). For
   273   convenience, a slightly more liberal convention is adopted: quotes may be
   274   omitted for any type or term that is already atomic at the outer level. For
   275   example, one may just write \<^verbatim>\<open>x\<close> instead of quoted \<^verbatim>\<open>"x"\<close>. Note that
   276   symbolic identifiers (e.g.\ \<^verbatim>\<open>++\<close> or \<open>\<forall>\<close> are available as well, provided
   277   these have not been superseded by commands or other keywords already (such
   278   as \<^verbatim>\<open>=\<close> or \<^verbatim>\<open>+\<close>).
   279 
   280   @{rail \<open>
   281     @{syntax_def type}: @{syntax embedded}
   282     ;
   283     @{syntax_def term}: @{syntax embedded}
   284     ;
   285     @{syntax_def prop}: @{syntax embedded}
   286   \<close>}
   287 
   288   Positional instantiations are specified as a sequence of terms, or the
   289   placeholder ``\<open>_\<close>'' (underscore), which means to skip a position.
   290 
   291   @{rail \<open>
   292     @{syntax_def inst}: '_' | @{syntax term}
   293     ;
   294     @{syntax_def insts}: (@{syntax inst} *)
   295   \<close>}
   296 
   297   Named instantiations are specified as pairs of assignments \<open>v = t\<close>, which
   298   refer to schematic variables in some theorem that is instantiated. Both type
   299   and terms instantiations are admitted, and distinguished by the usual syntax
   300   of variable names.
   301 
   302   @{rail \<open>
   303     @{syntax_def named_inst}: variable '=' (type | term)
   304     ;
   305     @{syntax_def named_insts}: (named_inst @'and' +)
   306     ;
   307     variable: @{syntax name} | @{syntax term_var} | @{syntax type_ident} | @{syntax type_var}
   308   \<close>}
   309 
   310   Type declarations and definitions usually refer to @{syntax typespec} on the
   311   left-hand side. This models basic type constructor application at the outer
   312   syntax level. Note that only plain postfix notation is available here, but
   313   no infixes.
   314 
   315   @{rail \<open>
   316     @{syntax_def typespec}:
   317       (() | @{syntax type_ident} | '(' ( @{syntax type_ident} + ',' ) ')') @{syntax name}
   318     ;
   319     @{syntax_def typespec_sorts}:
   320       (() | (@{syntax type_ident} ('::' @{syntax sort})?) |
   321         '(' ( (@{syntax type_ident} ('::' @{syntax sort})?) + ',' ) ')') @{syntax name}
   322   \<close>}
   323 \<close>
   324 
   325 
   326 subsection \<open>Term patterns and declarations \label{sec:term-decls}\<close>
   327 
   328 text \<open>
   329   Wherever explicit propositions (or term fragments) occur in a proof text,
   330   casual binding of schematic term variables may be given specified via
   331   patterns of the form ``\<^theory_text>\<open>(is p\<^sub>1 \<dots> p\<^sub>n)\<close>''. This works both for @{syntax
   332   term} and @{syntax prop}.
   333 
   334   @{rail \<open>
   335     @{syntax_def term_pat}: '(' (@'is' @{syntax term} +) ')'
   336     ;
   337     @{syntax_def prop_pat}: '(' (@'is' @{syntax prop} +) ')'
   338   \<close>}
   339 
   340   \<^medskip>
   341   Declarations of local variables \<open>x :: \<tau>\<close> and logical propositions \<open>a : \<phi>\<close>
   342   represent different views on the same principle of introducing a local
   343   scope. In practice, one may usually omit the typing of @{syntax vars} (due
   344   to type-inference), and the naming of propositions (due to implicit
   345   references of current facts). In any case, Isar proof elements usually admit
   346   to introduce multiple such items simultaneously.
   347 
   348   @{rail \<open>
   349     @{syntax_def vars}: (@{syntax name} +) ('::' @{syntax type})?
   350     ;
   351     @{syntax_def props}: @{syntax thmdecl}? (@{syntax prop} @{syntax prop_pat}? +)
   352     ;
   353     @{syntax_def props'}: (@{syntax prop} @{syntax prop_pat}? +)
   354   \<close>}
   355 
   356   The treatment of multiple declarations corresponds to the complementary
   357   focus of @{syntax vars} versus @{syntax props}. In ``\<open>x\<^sub>1 \<dots> x\<^sub>n :: \<tau>\<close>'' the
   358   typing refers to all variables, while in \<open>a: \<phi>\<^sub>1 \<dots> \<phi>\<^sub>n\<close> the naming refers to
   359   all propositions collectively. Isar language elements that refer to @{syntax
   360   vars} or @{syntax props} typically admit separate typings or namings via
   361   another level of iteration, with explicit @{keyword_ref "and"} separators;
   362   e.g.\ see @{command "fix"} and @{command "assume"} in
   363   \secref{sec:proof-context}.
   364 
   365   @{rail \<open>
   366     @{syntax_def "fixes"}:
   367       ((@{syntax name} ('::' @{syntax type})? @{syntax mixfix}? | @{syntax vars}) + @'and')
   368     ;
   369     @{syntax_def "for_fixes"}: (@'for' @{syntax "fixes"})?
   370   \<close>}
   371 
   372   The category @{syntax "fixes"} is a richer variant of @{syntax vars}: it
   373   admits specification of mixfix syntax for the entities that are introduced
   374   into the context. An optional suffix ``@{keyword "for"}~\<open>fixes\<close>'' is
   375   admitted in many situations to indicate a so-called ``eigen-context'' of a
   376   formal element: the result will be exported and thus generalized over the
   377   given variables.
   378 \<close>
   379 
   380 
   381 subsection \<open>Attributes and theorems \label{sec:syn-att}\<close>
   382 
   383 text \<open>
   384   Attributes have their own ``semi-inner'' syntax, in the sense that input
   385   conforming to @{syntax args} below is parsed by the attribute a second time.
   386   The attribute argument specifications may be any sequence of atomic entities
   387   (identifiers, strings etc.), or properly bracketed argument lists. Below
   388   @{syntax atom} refers to any atomic entity, including any @{syntax keyword}
   389   conforming to @{syntax sym_ident}.
   390 
   391   @{rail \<open>
   392     @{syntax_def atom}: @{syntax name} | @{syntax type_ident} |
   393       @{syntax type_var} | @{syntax term_var} | @{syntax nat} | @{syntax float} |
   394       @{syntax keyword} | @{syntax cartouche}
   395     ;
   396     arg: @{syntax atom} | '(' @{syntax args} ')' | '[' @{syntax args} ']'
   397     ;
   398     @{syntax_def args}: arg *
   399     ;
   400     @{syntax_def attributes}: '[' (@{syntax name} @{syntax args} * ',') ']'
   401   \<close>}
   402 
   403   Theorem specifications come in several flavors: @{syntax axmdecl} and
   404   @{syntax thmdecl} usually refer to axioms, assumptions or results of goal
   405   statements, while @{syntax thmdef} collects lists of existing theorems.
   406   Existing theorems are given by @{syntax thm} and @{syntax thms}, the
   407   former requires an actual singleton result.
   408 
   409   There are three forms of theorem references:
   410 
   411     \<^enum> named facts \<open>a\<close>,
   412 
   413     \<^enum> selections from named facts \<open>a(i)\<close> or \<open>a(j - k)\<close>,
   414 
   415     \<^enum> literal fact propositions using token syntax @{syntax_ref altstring}
   416     \<^verbatim>\<open>`\<close>\<open>\<phi>\<close>\<^verbatim>\<open>`\<close> or @{syntax_ref cartouche}
   417     \<open>\<open>\<phi>\<close>\<close> (see also method @{method_ref fact}).
   418 
   419   Any kind of theorem specification may include lists of attributes both on
   420   the left and right hand sides; attributes are applied to any immediately
   421   preceding fact. If names are omitted, the theorems are not stored within the
   422   theorem database of the theory or proof context, but any given attributes
   423   are applied nonetheless.
   424 
   425   An extra pair of brackets around attributes (like ``\<open>[[simproc a]]\<close>'')
   426   abbreviates a theorem reference involving an internal dummy fact, which will
   427   be ignored later on. So only the effect of the attribute on the background
   428   context will persist. This form of in-place declarations is particularly
   429   useful with commands like @{command "declare"} and @{command "using"}.
   430 
   431   @{rail \<open>
   432     @{syntax_def axmdecl}: @{syntax name} @{syntax attributes}? ':'
   433     ;
   434     @{syntax_def thmbind}:
   435       @{syntax name} @{syntax attributes} | @{syntax name} | @{syntax attributes}
   436     ;
   437     @{syntax_def thmdecl}: thmbind ':'
   438     ;
   439     @{syntax_def thmdef}: thmbind '='
   440     ;
   441     @{syntax_def thm}:
   442       (@{syntax name} selection? | @{syntax altstring} | @{syntax cartouche})
   443         @{syntax attributes}? |
   444       '[' @{syntax attributes} ']'
   445     ;
   446     @{syntax_def thms}: @{syntax thm} +
   447     ;
   448     selection: '(' ((@{syntax nat} | @{syntax nat} '-' @{syntax nat}?) + ',') ')'
   449   \<close>}
   450 \<close>
   451 
   452 
   453 subsection \<open>Structured specifications\<close>
   454 
   455 text \<open>
   456   Structured specifications use propositions with explicit notation for the
   457   ``eigen-context'' to describe rule structure: \<open>\<And>x. A x \<Longrightarrow> \<dots> \<Longrightarrow> B x\<close> is
   458   expressed as \<^theory_text>\<open>B x if A x and \<dots> for x\<close>. It is also possible to use dummy
   459   terms ``\<open>_\<close>'' (underscore) to refer to locally fixed variables anonymously.
   460 
   461   Multiple specifications are delimited by ``\<open>|\<close>'' to emphasize separate
   462   cases: each with its own scope of inferred types for free variables.
   463 
   464 
   465   @{rail \<open>
   466     @{syntax_def multi_specs}: (@{syntax structured_spec} + '|')
   467     ;
   468     @{syntax_def structured_spec}:
   469       @{syntax thmdecl}? @{syntax prop} @{syntax spec_prems} @{syntax for_fixes}
   470     ;
   471     @{syntax_def spec_prems}: (@'if' ((@{syntax prop}+) + @'and'))?
   472   \<close>}
   473 \<close>
   474 
   475 
   476 section \<open>Diagnostic commands\<close>
   477 
   478 text \<open>
   479   \begin{matharray}{rcl}
   480     @{command_def "print_theory"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   481     @{command_def "print_definitions"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   482     @{command_def "print_methods"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   483     @{command_def "print_attributes"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   484     @{command_def "print_theorems"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   485     @{command_def "find_theorems"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   486     @{command_def "find_consts"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   487     @{command_def "thm_deps"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   488     @{command_def "unused_thms"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   489     @{command_def "print_facts"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   490     @{command_def "print_term_bindings"}\<open>\<^sup>*\<close> & : & \<open>context \<rightarrow>\<close> \\
   491   \end{matharray}
   492 
   493   @{rail \<open>
   494     (@@{command print_theory} |
   495       @@{command print_definitions} |
   496       @@{command print_methods} |
   497       @@{command print_attributes} |
   498       @@{command print_theorems} |
   499       @@{command print_facts}) ('!'?)
   500     ;
   501     @@{command find_theorems} ('(' @{syntax nat}? 'with_dups'? ')')? \<newline> (thm_criterion*)
   502     ;
   503     thm_criterion: ('-'?) ('name' ':' @{syntax name} | 'intro' | 'elim' | 'dest' |
   504       'solves' | 'simp' ':' @{syntax term} | @{syntax term})
   505     ;
   506     @@{command find_consts} (const_criterion*)
   507     ;
   508     const_criterion: ('-'?)
   509       ('name' ':' @{syntax name} | 'strict' ':' @{syntax type} | @{syntax type})
   510     ;
   511     @@{command thm_deps} @{syntax thmrefs}
   512     ;
   513     @@{command unused_thms} ((@{syntax name} +) '-' (@{syntax name} * ))?
   514   \<close>}
   515 
   516   These commands print certain parts of the theory and proof context. Note
   517   that there are some further ones available, such as for the set of rules
   518   declared for simplifications.
   519 
   520   \<^descr> @{command "print_theory"} prints the main logical content of the
   521   background theory; the ``\<open>!\<close>'' option indicates extra verbosity.
   522 
   523   \<^descr> @{command "print_definitions"} prints dependencies of definitional
   524   specifications within the background theory, which may be constants
   525   (\secref{sec:term-definitions}, \secref{sec:overloading}) or types
   526   (\secref{sec:types-pure}, \secref{sec:hol-typedef}); the ``\<open>!\<close>'' option
   527   indicates extra verbosity.
   528 
   529   \<^descr> @{command "print_methods"} prints all proof methods available in the
   530   current theory context; the ``\<open>!\<close>'' option indicates extra verbosity.
   531 
   532   \<^descr> @{command "print_attributes"} prints all attributes available in the
   533   current theory context; the ``\<open>!\<close>'' option indicates extra verbosity.
   534 
   535   \<^descr> @{command "print_theorems"} prints theorems of the background theory
   536   resulting from the last command; the ``\<open>!\<close>'' option indicates extra
   537   verbosity.
   538 
   539   \<^descr> @{command "print_facts"} prints all local facts of the current context,
   540   both named and unnamed ones; the ``\<open>!\<close>'' option indicates extra verbosity.
   541 
   542   \<^descr> @{command "print_term_bindings"} prints all term bindings that are present
   543   in the context.
   544 
   545   \<^descr> @{command "find_theorems"}~\<open>criteria\<close> retrieves facts from the theory or
   546   proof context matching all of given search criteria. The criterion \<open>name: p\<close>
   547   selects all theorems whose fully qualified name matches pattern \<open>p\<close>, which
   548   may contain ``\<open>*\<close>'' wildcards. The criteria \<open>intro\<close>, \<open>elim\<close>, and \<open>dest\<close>
   549   select theorems that match the current goal as introduction, elimination or
   550   destruction rules, respectively. The criterion \<open>solves\<close> returns all rules
   551   that would directly solve the current goal. The criterion \<open>simp: t\<close> selects
   552   all rewrite rules whose left-hand side matches the given term. The criterion
   553   term \<open>t\<close> selects all theorems that contain the pattern \<open>t\<close> -- as usual,
   554   patterns may contain occurrences of the dummy ``\<open>_\<close>'', schematic variables,
   555   and type constraints.
   556 
   557   Criteria can be preceded by ``\<open>-\<close>'' to select theorems that do \<^emph>\<open>not\<close> match.
   558   Note that giving the empty list of criteria yields \<^emph>\<open>all\<close> currently known
   559   facts. An optional limit for the number of printed facts may be given; the
   560   default is 40. By default, duplicates are removed from the search result.
   561   Use \<open>with_dups\<close> to display duplicates.
   562 
   563   \<^descr> @{command "find_consts"}~\<open>criteria\<close> prints all constants whose type meets
   564   all of the given criteria. The criterion \<open>strict: ty\<close> is met by any type
   565   that matches the type pattern \<open>ty\<close>. Patterns may contain both the dummy type
   566   ``\<open>_\<close>'' and sort constraints. The criterion \<open>ty\<close> is similar, but it also
   567   matches against subtypes. The criterion \<open>name: p\<close> and the prefix ``\<open>-\<close>''
   568   function as described for @{command "find_theorems"}.
   569 
   570   \<^descr> @{command "thm_deps"}~\<open>a\<^sub>1 \<dots> a\<^sub>n\<close> visualizes dependencies of facts, using
   571   Isabelle's graph browser tool (see also @{cite "isabelle-system"}).
   572 
   573   \<^descr> @{command "unused_thms"}~\<open>A\<^sub>1 \<dots> A\<^sub>m - B\<^sub>1 \<dots> B\<^sub>n\<close> displays all theorems
   574   that are proved in theories \<open>B\<^sub>1 \<dots> B\<^sub>n\<close> or their parents but not in \<open>A\<^sub>1 \<dots>
   575   A\<^sub>m\<close> or their parents and that are never used. If \<open>n\<close> is \<open>0\<close>, the end of the
   576   range of theories defaults to the current theory. If no range is specified,
   577   only the unused theorems in the current theory are displayed.
   578 \<close>
   579 
   580 end