doc-src/IsarRef/Inner_Syntax.thy

+theory Inner_Syntax
+imports Base Main
+begin
+
+chapter {* Inner syntax --- the term language \label{ch:inner-syntax} *}
+
+text {* The inner syntax of Isabelle provides concrete notation for
+  the main entities of the logical framework, notably @{text
+  "\<lambda>"}-terms with types and type classes.  Applications may either
+  extend existing syntactic categories by additional notation, or
+  define new sub-languages that are linked to the standard term
+  language via some explicit markers.  For example @{verbatim
+  FOO}~@{text "foo"} could embed the syntax corresponding for some
+  user-defined nonterminal @{text "foo"} --- within the bounds of the
+  given lexical syntax of Isabelle/Pure.
+
+  The most basic way to specify concrete syntax for logical entities
+  works via mixfix annotations (\secref{sec:mixfix}), which may be
+  usually given as part of the original declaration or via explicit
+  notation commands later on (\secref{sec:notation}).  This already
+  covers many needs of concrete syntax without having to understand
+  the full complexity of inner syntax layers.
+
+  Further details of the syntax engine involves the classical
+  distinction of lexical language versus context-free grammar (see
+  \secref{sec:pure-syntax}), and various mechanisms for \emph{syntax
+  transformations} (see \secref{sec:syntax-transformations}).
+*}
+
+
+section {* Printing logical entities *}
+
+subsection {* Diagnostic commands \label{sec:print-diag} *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def "typ"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+    @{command_def "term"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+    @{command_def "prop"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+    @{command_def "thm"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+    @{command_def "prf"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+    @{command_def "full_prf"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+    @{command_def "pr"}@{text "\<^sup>*"} & : & @{text "any \<rightarrow>"} \\
+  \end{matharray}
+
+  These diagnostic commands assist interactive development by printing
+  internal logical entities in a human-readable fashion.
+
+  @{rail "
+    @@{command typ} @{syntax modes}? @{syntax type} ('::' @{syntax sort})?
+    ;
+    @@{command term} @{syntax modes}? @{syntax term}
+    ;
+    @@{command prop} @{syntax modes}? @{syntax prop}
+    ;
+    @@{command thm} @{syntax modes}? @{syntax thmrefs}
+    ;
+    ( @@{command prf} | @@{command full_prf} ) @{syntax modes}? @{syntax thmrefs}?
+    ;
+    @@{command pr} @{syntax modes}? @{syntax nat}?
+    ;
+
+    @{syntax_def modes}: '(' (@{syntax name} + ) ')'
+  "}
+
+  \begin{description}
+
+  \item @{command "typ"}~@{text \<tau>} reads and prints a type expression
+  according to the current context.
+
+  \item @{command "typ"}~@{text "\<tau> :: s"} uses type-inference to
+  determine the most general way to make @{text "\<tau>"} conform to sort
+  @{text "s"}.  For concrete @{text "\<tau>"} this checks if the type
+  belongs to that sort.  Dummy type parameters ``@{text "_"}''
+  (underscore) are assigned to fresh type variables with most general
+  sorts, according the the principles of type-inference.
+
+  \item @{command "term"}~@{text t} and @{command "prop"}~@{text \<phi>}
+  read, type-check and print terms or propositions according to the
+  current theory or proof context; the inferred type of @{text t} is
+  output as well.  Note that these commands are also useful in
+  inspecting the current environment of term abbreviations.
+
+  \item @{command "thm"}~@{text "a\<^sub>1 \<dots> a\<^sub>n"} retrieves
+  theorems from the current theory or proof context.  Note that any
+  attributes included in the theorem specifications are applied to a
+  temporary context derived from the current theory or proof; the
+  result is discarded, i.e.\ attributes involved in @{text "a\<^sub>1,
+  \<dots>, a\<^sub>n"} do not have any permanent effect.
+
+  \item @{command "prf"} displays the (compact) proof term of the
+  current proof state (if present), or of the given theorems. Note
+  that this requires proof terms to be switched on for the current
+  object logic (see the ``Proof terms'' section of the Isabelle
+  reference manual for information on how to do this).
+
+  \item @{command "full_prf"} is like @{command "prf"}, but displays
+  the full proof term, i.e.\ also displays information omitted in the
+  compact proof term, which is denoted by ``@{text _}'' placeholders
+  there.
+
+  \item @{command "pr"}~@{text "goals"} prints the current proof state
+  (if present), including current facts and goals.  The optional limit
+  arguments affect the number of goals to be displayed, which is
+  initially 10.  Omitting limit value leaves the current setting
+  unchanged.
+
+  \end{description}
+
+  All of the diagnostic commands above admit a list of @{text modes}
+  to be specified, which is appended to the current print mode; see
+  also \secref{sec:print-modes}.  Thus the output behavior may be
+  modified according particular print mode features.  For example,
+  @{command "pr"}~@{text "(latex xsymbols)"} would print the current
+  proof state with mathematical symbols and special characters
+  represented in {\LaTeX} source, according to the Isabelle style
+  \cite{isabelle-sys}.
+
+  Note that antiquotations (cf.\ \secref{sec:antiq}) provide a more
+  systematic way to include formal items into the printed text
+  document.
+*}
+
+
+subsection {* Details of printed content *}
+
+text {*
+  \begin{tabular}{rcll}
+    @{attribute_def show_types} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def show_sorts} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def show_consts} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def show_abbrevs} & : & @{text attribute} & default @{text true} \\
+    @{attribute_def show_brackets} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def names_long} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def names_short} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def names_unique} & : & @{text attribute} & default @{text true} \\
+    @{attribute_def eta_contract} & : & @{text attribute} & default @{text true} \\
+    @{attribute_def goals_limit} & : & @{text attribute} & default @{text 10} \\
+    @{attribute_def show_main_goal} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def show_hyps} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def show_tags} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def show_question_marks} & : & @{text attribute} & default @{text true} \\
+  \end{tabular}
+  \medskip
+
+  These configuration options control the detail of information that
+  is displayed for types, terms, theorems, goals etc.  See also
+  \secref{sec:config}.
+
+  \begin{description}
+
+  \item @{attribute show_types} and @{attribute show_sorts} control
+  printing of type constraints for term variables, and sort
+  constraints for type variables.  By default, neither of these are
+  shown in output.  If @{attribute show_sorts} is enabled, types are
+  always shown as well.
+
+  Note that displaying types and sorts may explain why a polymorphic
+  inference rule fails to resolve with some goal, or why a rewrite
+  rule does not apply as expected.
+
+  \item @{attribute show_consts} controls printing of types of
+  constants when displaying a goal state.
+
+  Note that the output can be enormous, because polymorphic constants
+  often occur at several different type instances.
+
+  \item @{attribute show_abbrevs} controls folding of constant
+  abbreviations.
+
+  \item @{attribute show_brackets} controls bracketing in pretty
+  printed output.  If enabled, all sub-expressions of the pretty
+  printing tree will be parenthesized, even if this produces malformed
+  term syntax!  This crude way of showing the internal structure of
+  pretty printed entities may occasionally help to diagnose problems
+  with operator priorities, for example.
+
+  \item @{attribute names_long}, @{attribute names_short}, and
+  @{attribute names_unique} control the way of printing fully
+  qualified internal names in external form.  See also
+  \secref{sec:antiq} for the document antiquotation options of the
+  same names.
+
+  \item @{attribute eta_contract} controls @{text "\<eta>"}-contracted
+  printing of terms.
+
+  The @{text \<eta>}-contraction law asserts @{prop "(\<lambda>x. f x) \<equiv> f"},
+  provided @{text x} is not free in @{text f}.  It asserts
+  \emph{extensionality} of functions: @{prop "f \<equiv> g"} if @{prop "f x \<equiv>
+  g x"} for all @{text x}.  Higher-order unification frequently puts
+  terms into a fully @{text \<eta>}-expanded form.  For example, if @{text
+  F} has type @{text "(\<tau> \<Rightarrow> \<tau>) \<Rightarrow> \<tau>"} then its expanded form is @{term
+  "\<lambda>h. F (\<lambda>x. h x)"}.
+
+  Enabling @{attribute eta_contract} makes Isabelle perform @{text
+  \<eta>}-contractions before printing, so that @{term "\<lambda>h. F (\<lambda>x. h x)"}
+  appears simply as @{text F}.
+
+  Note that the distinction between a term and its @{text \<eta>}-expanded
+  form occasionally matters.  While higher-order resolution and
+  rewriting operate modulo @{text "\<alpha>\<beta>\<eta>"}-conversion, some other tools
+  might look at terms more discretely.
+
+  \item @{attribute goals_limit} controls the maximum number of
+  subgoals to be shown in goal output.
+
+  \item @{attribute show_main_goal} controls whether the main result
+  to be proven should be displayed.  This information might be
+  relevant for schematic goals, to inspect the current claim that has
+  been synthesized so far.
+
+  \item @{attribute show_hyps} controls printing of implicit
+  hypotheses of local facts.  Normally, only those hypotheses are
+  displayed that are \emph{not} covered by the assumptions of the
+  current context: this situation indicates a fault in some tool being
+  used.
+
+  By enabling @{attribute show_hyps}, output of \emph{all} hypotheses
+  can be enforced, which is occasionally useful for diagnostic
+  purposes.
+
+  \item @{attribute show_tags} controls printing of extra annotations
+  within theorems, such as internal position information, or the case
+  names being attached by the attribute @{attribute case_names}.
+
+  Note that the @{attribute tagged} and @{attribute untagged}
+  attributes provide low-level access to the collection of tags
+  associated with a theorem.
+
+  \item @{attribute show_question_marks} controls printing of question
+  marks for schematic variables, such as @{text ?x}.  Only the leading
+  question mark is affected, the remaining text is unchanged
+  (including proper markup for schematic variables that might be
+  relevant for user interfaces).
+
+  \end{description}
+*}
+
+
+subsection {* Alternative print modes \label{sec:print-modes} *}
+
+text {*
+  \begin{mldecls}
+    @{index_ML print_mode_value: "unit -> string list"} \\
+    @{index_ML Print_Mode.with_modes: "string list -> ('a -> 'b) -> 'a -> 'b"} \\
+  \end{mldecls}
+
+  The \emph{print mode} facility allows to modify various operations
+  for printing.  Commands like @{command typ}, @{command term},
+  @{command thm} (see \secref{sec:print-diag}) take additional print
+  modes as optional argument.  The underlying ML operations are as
+  follows.
+
+  \begin{description}
+
+  \item @{ML "print_mode_value ()"} yields the list of currently
+  active print mode names.  This should be understood as symbolic
+  representation of certain individual features for printing (with
+  precedence from left to right).
+
+  \item @{ML Print_Mode.with_modes}~@{text "modes f x"} evaluates
+  @{text "f x"} in an execution context where the print mode is
+  prepended by the given @{text "modes"}.  This provides a thread-safe
+  way to augment print modes.  It is also monotonic in the set of mode
+  names: it retains the default print mode that certain
+  user-interfaces might have installed for their proper functioning!
+
+  \end{description}
+
+  \begin{warn}
+  The old global reference @{ML print_mode} should never be used
+  directly in applications.  Its main reason for being publicly
+  accessible is to support historic versions of Proof~General.
+  \end{warn}
+
+  \medskip The pretty printer for inner syntax maintains alternative
+  mixfix productions for any print mode name invented by the user, say
+  in commands like @{command notation} or @{command abbreviation}.
+  Mode names can be arbitrary, but the following ones have a specific
+  meaning by convention:
+
+  \begin{itemize}
+
+  \item @{verbatim "\"\""} (the empty string): default mode;
+  implicitly active as last element in the list of modes.
+
+  \item @{verbatim input}: dummy print mode that is never active; may
+  be used to specify notation that is only available for input.
+
+  \item @{verbatim internal} dummy print mode that is never active;
+  used internally in Isabelle/Pure.
+
+  \item @{verbatim xsymbols}: enable proper mathematical symbols
+  instead of ASCII art.\footnote{This traditional mode name stems from
+  the ``X-Symbol'' package for old versions Proof~General with XEmacs,
+  although that package has been superseded by Unicode in recent
+  years.}
+
+  \item @{verbatim HTML}: additional mode that is active in HTML
+  presentation of Isabelle theory sources; allows to provide
+  alternative output notation.
+
+  \item @{verbatim latex}: additional mode that is active in {\LaTeX}
+  document preparation of Isabelle theory sources; allows to provide
+  alternative output notation.
+
+  \end{itemize}
+*}
+
+
+subsection {* Printing limits *}
+
+text {*
+  \begin{mldecls}
+    @{index_ML Pretty.margin_default: "int Unsynchronized.ref"} \\
+    @{index_ML print_depth: "int -> unit"} \\
+  \end{mldecls}
+
+  These ML functions set limits for pretty printed text.
+
+  \begin{description}
+
+  \item @{ML Pretty.margin_default} indicates the global default for
+  the right margin of the built-in pretty printer, with initial value
+  76.  Note that user-interfaces typically control margins
+  automatically when resizing windows, or even bypass the formatting
+  engine of Isabelle/ML altogether and do it within the front end via
+  Isabelle/Scala.
+
+  \item @{ML print_depth}~@{text n} limits the printing depth of the
+  ML toplevel pretty printer; the precise effect depends on the ML
+  compiler and run-time system.  Typically @{text n} should be less
+  than 10.  Bigger values such as 100--1000 are useful for debugging.
+
+  \end{description}
+*}
+
+
+section {* Mixfix annotations \label{sec:mixfix} *}
+
+text {* Mixfix annotations specify concrete \emph{inner syntax} of
+  Isabelle types and terms.  Locally fixed parameters in toplevel
+  theorem statements, locale and class specifications also admit
+  mixfix annotations in a fairly uniform manner.  A mixfix annotation
+  describes describes the concrete syntax, the translation to abstract
+  syntax, and the pretty printing.  Special case annotations provide a
+  simple means of specifying infix operators and binders.
+
+  Isabelle mixfix syntax is inspired by {\OBJ} \cite{OBJ}.  It allows
+  to specify any context-free priority grammar, which is more general
+  than the fixity declarations of ML and Prolog.
+
+  @{rail "
+    @{syntax_def mixfix}: '(' mfix ')'
+    ;
+    @{syntax_def struct_mixfix}: '(' ( mfix | @'structure' ) ')'
+    ;
+
+    mfix: @{syntax template} prios? @{syntax nat}? |
+      (@'infix' | @'infixl' | @'infixr') @{syntax template} @{syntax nat} |
+      @'binder' @{syntax template} prios? @{syntax nat}
+    ;
+    template: string
+    ;
+    prios: '[' (@{syntax nat} + ',') ']'
+  "}
+
+  The string given as @{text template} may include literal text,
+  spacing, blocks, and arguments (denoted by ``@{text _}''); the
+  special symbol ``@{verbatim "\<index>"}'' (printed as ``@{text "\<index>"}'')
+  represents an index argument that specifies an implicit structure
+  reference (see also \secref{sec:locale}).  Infix and binder
+  declarations provide common abbreviations for particular mixfix
+  declarations.  So in practice, mixfix templates mostly degenerate to
+  literal text for concrete syntax, such as ``@{verbatim "++"}'' for
+  an infix symbol.
+*}
+
+
+subsection {* The general mixfix form *}
+
+text {* In full generality, mixfix declarations work as follows.
+  Suppose a constant @{text "c :: \<tau>\<^sub>1 \<Rightarrow> \<dots> \<tau>\<^sub>n \<Rightarrow> \<tau>"} is annotated by
+  @{text "(mixfix [p\<^sub>1, \<dots>, p\<^sub>n] p)"}, where @{text "mixfix"} is a string
+  @{text "d\<^sub>0 _ d\<^sub>1 _ \<dots> _ d\<^sub>n"} consisting of delimiters that surround
+  argument positions as indicated by underscores.
+
+  Altogether this determines a production for a context-free priority
+  grammar, where for each argument @{text "i"} the syntactic category
+  is determined by @{text "\<tau>\<^sub>i"} (with priority @{text "p\<^sub>i"}), and the
+  result category is determined from @{text "\<tau>"} (with priority @{text
+  "p"}).  Priority specifications are optional, with default 0 for
+  arguments and 1000 for the result.\footnote{Omitting priorities is
+  prone to syntactic ambiguities unless the delimiter tokens determine
+  fully bracketed notation, as in @{text "if _ then _ else _ fi"}.}
+
+  Since @{text "\<tau>"} may be again a function type, the constant
+  type scheme may have more argument positions than the mixfix
+  pattern.  Printing a nested application @{text "c t\<^sub>1 \<dots> t\<^sub>m"} for
+  @{text "m > n"} works by attaching concrete notation only to the
+  innermost part, essentially by printing @{text "(c t\<^sub>1 \<dots> t\<^sub>n) \<dots> t\<^sub>m"}
+  instead.  If a term has fewer arguments than specified in the mixfix
+  template, the concrete syntax is ignored.
+
+  \medskip A mixfix template may also contain additional directives
+  for pretty printing, notably spaces, blocks, and breaks.  The
+  general template format is a sequence over any of the following
+  entities.
+
+  \begin{description}
+
+  \item @{text "d"} is a delimiter, namely a non-empty sequence of
+  characters other than the following special characters:
+
+  \smallskip
+  \begin{tabular}{ll}
+    @{verbatim "'"} & single quote \\
+    @{verbatim "_"} & underscore \\
+    @{text "\<index>"} & index symbol \\
+    @{verbatim "("} & open parenthesis \\
+    @{verbatim ")"} & close parenthesis \\
+    @{verbatim "/"} & slash \\
+  \end{tabular}
+  \medskip
+
+  \item @{verbatim "'"} escapes the special meaning of these
+  meta-characters, producing a literal version of the following
+  character, unless that is a blank.
+
+  A single quote followed by a blank separates delimiters, without
+  affecting printing, but input tokens may have additional white space
+  here.
+
+  \item @{verbatim "_"} is an argument position, which stands for a
+  certain syntactic category in the underlying grammar.
+
+  \item @{text "\<index>"} is an indexed argument position; this is the place
+  where implicit structure arguments can be attached.
+
+  \item @{text "s"} is a non-empty sequence of spaces for printing.
+  This and the following specifications do not affect parsing at all.
+
+  \item @{verbatim "("}@{text n} opens a pretty printing block.  The
+  optional number specifies how much indentation to add when a line
+  break occurs within the block.  If the parenthesis is not followed
+  by digits, the indentation defaults to 0.  A block specified via
+  @{verbatim "(00"} is unbreakable.
+
+  \item @{verbatim ")"} closes a pretty printing block.
+
+  \item @{verbatim "//"} forces a line break.
+
+  \item @{verbatim "/"}@{text s} allows a line break.  Here @{text s}
+  stands for the string of spaces (zero or more) right after the
+  slash.  These spaces are printed if the break is \emph{not} taken.
+
+  \end{description}
+
+  The general idea of pretty printing with blocks and breaks is also
+  described in \cite{paulson-ml2}; it goes back to \cite{Oppen:1980}.
+*}
+
+
+subsection {* Infixes *}
+
+text {* Infix operators are specified by convenient short forms that
+  abbreviate general mixfix annotations as follows:
+
+  \begin{center}
+  \begin{tabular}{lll}
+
+  @{verbatim "("}@{keyword_def "infix"}~@{verbatim "\""}@{text sy}@{verbatim "\""} @{text "p"}@{verbatim ")"}
+  & @{text "\<mapsto>"} &
+  @{verbatim "(\"(_ "}@{text sy}@{verbatim "/ _)\" ["}@{text "p + 1"}@{verbatim ", "}@{text "p + 1"}@{verbatim "]"}@{text " p"}@{verbatim ")"} \\
+  @{verbatim "("}@{keyword_def "infixl"}~@{verbatim "\""}@{text sy}@{verbatim "\""} @{text "p"}@{verbatim ")"}
+  & @{text "\<mapsto>"} &
+  @{verbatim "(\"(_ "}@{text sy}@{verbatim "/ _)\" ["}@{text "p"}@{verbatim ", "}@{text "p + 1"}@{verbatim "]"}@{text " p"}@{verbatim ")"} \\
+  @{verbatim "("}@{keyword_def "infixr"}~@{verbatim "\""}@{text sy}@{verbatim "\""} @{text "p"}@{verbatim ")"}
+  & @{text "\<mapsto>"} &
+  @{verbatim "(\"(_ "}@{text sy}@{verbatim "/ _)\" ["}@{text "p + 1"}@{verbatim ", "}@{text "p"}@{verbatim "]"}@{text " p"}@{verbatim ")"} \\
+
+  \end{tabular}
+  \end{center}
+
+  The mixfix template @{verbatim "\"(_ "}@{text sy}@{verbatim "/ _)\""}
+  specifies two argument positions; the delimiter is preceded by a
+  space and followed by a space or line break; the entire phrase is a
+  pretty printing block.
+
+  The alternative notation @{verbatim "op"}~@{text sy} is introduced
+  in addition.  Thus any infix operator may be written in prefix form
+  (as in ML), independently of the number of arguments in the term.
+*}
+
+
+subsection {* Binders *}
+
+text {* A \emph{binder} is a variable-binding construct such as a
+  quantifier.  The idea to formalize @{text "\<forall>x. b"} as @{text "All
+  (\<lambda>x. b)"} for @{text "All :: ('a \<Rightarrow> bool) \<Rightarrow> bool"} already goes back
+  to \cite{church40}.  Isabelle declarations of certain higher-order
+  operators may be annotated with @{keyword_def "binder"} annotations
+  as follows:
+
+  \begin{center}
+  @{text "c :: "}@{verbatim "\""}@{text "(\<tau>\<^sub>1 \<Rightarrow> \<tau>\<^sub>2) \<Rightarrow> \<tau>\<^sub>3"}@{verbatim "\"  ("}@{keyword "binder"}@{verbatim " \""}@{text "sy"}@{verbatim "\" ["}@{text "p"}@{verbatim "] "}@{text "q"}@{verbatim ")"}
+  \end{center}
+
+  This introduces concrete binder syntax @{text "sy x. b"}, where
+  @{text x} is a bound variable of type @{text "\<tau>\<^sub>1"}, the body @{text
+  b} has type @{text "\<tau>\<^sub>2"} and the whole term has type @{text "\<tau>\<^sub>3"}.
+  The optional integer @{text p} specifies the syntactic priority of
+  the body; the default is @{text "q"}, which is also the priority of
+  the whole construct.
+
+  Internally, the binder syntax is expanded to something like this:
+  \begin{center}
+  @{text "c_binder :: "}@{verbatim "\""}@{text "idts \<Rightarrow> \<tau>\<^sub>2 \<Rightarrow> \<tau>\<^sub>3"}@{verbatim "\"  (\"(3"}@{text sy}@{verbatim "_./ _)\" [0, "}@{text "p"}@{verbatim "] "}@{text "q"}@{verbatim ")"}
+  \end{center}
+
+  Here @{syntax (inner) idts} is the nonterminal symbol for a list of
+  identifiers with optional type constraints (see also
+  \secref{sec:pure-grammar}).  The mixfix template @{verbatim
+  "\"(3"}@{text sy}@{verbatim "_./ _)\""} defines argument positions
+  for the bound identifiers and the body, separated by a dot with
+  optional line break; the entire phrase is a pretty printing block of
+  indentation level 3.  Note that there is no extra space after @{text
+  "sy"}, so it needs to be included user specification if the binder
+  syntax ends with a token that may be continued by an identifier
+  token at the start of @{syntax (inner) idts}.
+
+  Furthermore, a syntax translation to transforms @{text "c_binder x\<^sub>1
+  \<dots> x\<^sub>n b"} into iterated application @{text "c (\<lambda>x\<^sub>1. \<dots> c (\<lambda>x\<^sub>n. b)\<dots>)"}.
+  This works in both directions, for parsing and printing.  *}
+
+
+section {* Explicit notation \label{sec:notation} *}
+
+text {*
+  \begin{matharray}{rcll}
+    @{command_def "type_notation"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
+    @{command_def "no_type_notation"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
+    @{command_def "notation"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
+    @{command_def "no_notation"} & : & @{text "local_theory \<rightarrow> local_theory"} \\
+    @{command_def "write"} & : & @{text "proof(state) \<rightarrow> proof(state)"} \\
+  \end{matharray}
+
+  Commands that introduce new logical entities (terms or types)
+  usually allow to provide mixfix annotations on the spot, which is
+  convenient for default notation.  Nonetheless, the syntax may be
+  modified later on by declarations for explicit notation.  This
+  allows to add or delete mixfix annotations for of existing logical
+  entities within the current context.
+
+  @{rail "
+    (@@{command type_notation} | @@{command no_type_notation}) @{syntax target}?
+      @{syntax mode}? \\ (@{syntax nameref} @{syntax mixfix} + @'and')
+    ;
+    (@@{command notation} | @@{command no_notation}) @{syntax target}? @{syntax mode}? \\
+      (@{syntax nameref} @{syntax struct_mixfix} + @'and')
+    ;
+    @@{command write} @{syntax mode}? (@{syntax nameref} @{syntax struct_mixfix} + @'and')
+  "}
+
+  \begin{description}
+
+  \item @{command "type_notation"}~@{text "c (mx)"} associates mixfix
+  syntax with an existing type constructor.  The arity of the
+  constructor is retrieved from the context.
+
+  \item @{command "no_type_notation"} is similar to @{command
+  "type_notation"}, but removes the specified syntax annotation from
+  the present context.
+
+  \item @{command "notation"}~@{text "c (mx)"} associates mixfix
+  syntax with an existing constant or fixed variable.  The type
+  declaration of the given entity is retrieved from the context.
+
+  \item @{command "no_notation"} is similar to @{command "notation"},
+  but removes the specified syntax annotation from the present
+  context.
+
+  \item @{command "write"} is similar to @{command "notation"}, but
+  works within an Isar proof body.
+
+  \end{description}
+*}
+
+
+section {* The Pure syntax \label{sec:pure-syntax} *}
+
+subsection {* Lexical matters \label{sec:inner-lex} *}
+
+text {* The inner lexical syntax vaguely resembles the outer one
+  (\secref{sec:outer-lex}), but some details are different.  There are
+  two main categories of inner syntax tokens:
+
+  \begin{enumerate}
+
+  \item \emph{delimiters} --- the literal tokens occurring in
+  productions of the given priority grammar (cf.\
+  \secref{sec:priority-grammar});
+
+  \item \emph{named tokens} --- various categories of identifiers etc.
+
+  \end{enumerate}
+
+  Delimiters override named tokens and may thus render certain
+  identifiers inaccessible.  Sometimes the logical context admits
+  alternative ways to refer to the same entity, potentially via
+  qualified names.
+
+  \medskip The categories for named tokens are defined once and for
+  all as follows, reusing some categories of the outer token syntax
+  (\secref{sec:outer-lex}).
+
+  \begin{center}
+  \begin{supertabular}{rcl}
+    @{syntax_def (inner) id} & = & @{syntax_ref ident} \\
+    @{syntax_def (inner) longid} & = & @{syntax_ref longident} \\
+    @{syntax_def (inner) var} & = & @{syntax_ref var} \\
+    @{syntax_def (inner) tid} & = & @{syntax_ref typefree} \\
+    @{syntax_def (inner) tvar} & = & @{syntax_ref typevar} \\
+    @{syntax_def (inner) num_token} & = & @{syntax_ref nat}@{text "  |  "}@{verbatim "-"}@{syntax_ref nat} \\
+    @{syntax_def (inner) float_token} & = & @{syntax_ref nat}@{verbatim "."}@{syntax_ref nat}@{text "  |  "}@{verbatim "-"}@{syntax_ref nat}@{verbatim "."}@{syntax_ref nat} \\
+    @{syntax_def (inner) xnum_token} & = & @{verbatim "#"}@{syntax_ref nat}@{text "  |  "}@{verbatim "#-"}@{syntax_ref nat} \\
+
+    @{syntax_def (inner) str_token} & = & @{verbatim "''"} @{text "\<dots>"} @{verbatim "''"} \\
+  \end{supertabular}
+  \end{center}
+
+  The token categories @{syntax (inner) num_token}, @{syntax (inner)
+  float_token}, @{syntax (inner) xnum_token}, and @{syntax (inner)
+  str_token} are not used in Pure.  Object-logics may implement numerals
+  and string constants by adding appropriate syntax declarations,
+  together with some translation functions (e.g.\ see Isabelle/HOL).
+
+  The derived categories @{syntax_def (inner) num_const}, @{syntax_def
+  (inner) float_const}, and @{syntax_def (inner) num_const} provide
+  robust access to the respective tokens: the syntax tree holds a
+  syntactic constant instead of a free variable.
+*}
+
+
+subsection {* Priority grammars \label{sec:priority-grammar} *}
+
+text {* A context-free grammar consists of a set of \emph{terminal
+  symbols}, a set of \emph{nonterminal symbols} and a set of
+  \emph{productions}.  Productions have the form @{text "A = \<gamma>"},
+  where @{text A} is a nonterminal and @{text \<gamma>} is a string of
+  terminals and nonterminals.  One designated nonterminal is called
+  the \emph{root symbol}.  The language defined by the grammar
+  consists of all strings of terminals that can be derived from the
+  root symbol by applying productions as rewrite rules.
+
+  The standard Isabelle parser for inner syntax uses a \emph{priority
+  grammar}.  Each nonterminal is decorated by an integer priority:
+  @{text "A\<^sup>(\<^sup>p\<^sup>)"}.  In a derivation, @{text "A\<^sup>(\<^sup>p\<^sup>)"} may be rewritten
+  using a production @{text "A\<^sup>(\<^sup>q\<^sup>) = \<gamma>"} only if @{text "p \<le> q"}.  Any
+  priority grammar can be translated into a normal context-free
+  grammar by introducing new nonterminals and productions.
+
+  \medskip Formally, a set of context free productions @{text G}
+  induces a derivation relation @{text "\<longrightarrow>\<^sub>G"} as follows.  Let @{text
+  \<alpha>} and @{text \<beta>} denote strings of terminal or nonterminal symbols.
+  Then @{text "\<alpha> A\<^sup>(\<^sup>p\<^sup>) \<beta> \<longrightarrow>\<^sub>G \<alpha> \<gamma> \<beta>"} holds if and only if @{text G}
+  contains some production @{text "A\<^sup>(\<^sup>q\<^sup>) = \<gamma>"} for @{text "p \<le> q"}.
+
+  \medskip The following grammar for arithmetic expressions
+  demonstrates how binding power and associativity of operators can be
+  enforced by priorities.
+
+  \begin{center}
+  \begin{tabular}{rclr}
+  @{text "A\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)"} & @{text "="} & @{verbatim "("} @{text "A\<^sup>(\<^sup>0\<^sup>)"} @{verbatim ")"} \\
+  @{text "A\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)"} & @{text "="} & @{verbatim 0} \\
+  @{text "A\<^sup>(\<^sup>0\<^sup>)"} & @{text "="} & @{text "A\<^sup>(\<^sup>0\<^sup>)"} @{verbatim "+"} @{text "A\<^sup>(\<^sup>1\<^sup>)"} \\
+  @{text "A\<^sup>(\<^sup>2\<^sup>)"} & @{text "="} & @{text "A\<^sup>(\<^sup>3\<^sup>)"} @{verbatim "*"} @{text "A\<^sup>(\<^sup>2\<^sup>)"} \\
+  @{text "A\<^sup>(\<^sup>3\<^sup>)"} & @{text "="} & @{verbatim "-"} @{text "A\<^sup>(\<^sup>3\<^sup>)"} \\
+  \end{tabular}
+  \end{center}
+  The choice of priorities determines that @{verbatim "-"} binds
+  tighter than @{verbatim "*"}, which binds tighter than @{verbatim
+  "+"}.  Furthermore @{verbatim "+"} associates to the left and
+  @{verbatim "*"} to the right.
+
+  \medskip For clarity, grammars obey these conventions:
+  \begin{itemize}
+
+  \item All priorities must lie between 0 and 1000.
+
+  \item Priority 0 on the right-hand side and priority 1000 on the
+  left-hand side may be omitted.
+
+  \item The production @{text "A\<^sup>(\<^sup>p\<^sup>) = \<alpha>"} is written as @{text "A = \<alpha>
+  (p)"}, i.e.\ the priority of the left-hand side actually appears in
+  a column on the far right.
+
+  \item Alternatives are separated by @{text "|"}.
+
+  \item Repetition is indicated by dots @{text "(\<dots>)"} in an informal
+  but obvious way.
+
+  \end{itemize}
+
+  Using these conventions, the example grammar specification above
+  takes the form:
+  \begin{center}
+  \begin{tabular}{rclc}
+    @{text A} & @{text "="} & @{verbatim "("} @{text A} @{verbatim ")"} \\
+              & @{text "|"} & @{verbatim 0} & \qquad\qquad \\
+              & @{text "|"} & @{text A} @{verbatim "+"} @{text "A\<^sup>(\<^sup>1\<^sup>)"} & @{text "(0)"} \\
+              & @{text "|"} & @{text "A\<^sup>(\<^sup>3\<^sup>)"} @{verbatim "*"} @{text "A\<^sup>(\<^sup>2\<^sup>)"} & @{text "(2)"} \\
+              & @{text "|"} & @{verbatim "-"} @{text "A\<^sup>(\<^sup>3\<^sup>)"} & @{text "(3)"} \\
+  \end{tabular}
+  \end{center}
+*}
+
+
+subsection {* The Pure grammar \label{sec:pure-grammar} *}
+
+text {* The priority grammar of the @{text "Pure"} theory is defined
+  approximately like this:
+
+  \begin{center}
+  \begin{supertabular}{rclr}
+
+  @{syntax_def (inner) any} & = & @{text "prop  |  logic"} \\\\
+
+  @{syntax_def (inner) prop} & = & @{verbatim "("} @{text prop} @{verbatim ")"} \\
+    & @{text "|"} & @{text "prop\<^sup>(\<^sup>4\<^sup>)"} @{verbatim "::"} @{text type} & @{text "(3)"} \\
+    & @{text "|"} & @{text "any\<^sup>(\<^sup>3\<^sup>)"} @{verbatim "=="} @{text "any\<^sup>(\<^sup>2\<^sup>)"} & @{text "(2)"} \\
+    & @{text "|"} & @{text "any\<^sup>(\<^sup>3\<^sup>)"} @{text "\<equiv>"} @{text "any\<^sup>(\<^sup>2\<^sup>)"} & @{text "(2)"} \\
+    & @{text "|"} & @{text "prop\<^sup>(\<^sup>3\<^sup>)"} @{verbatim "&&&"} @{text "prop\<^sup>(\<^sup>2\<^sup>)"} & @{text "(2)"} \\
+    & @{text "|"} & @{text "prop\<^sup>(\<^sup>2\<^sup>)"} @{verbatim "==>"} @{text "prop\<^sup>(\<^sup>1\<^sup>)"} & @{text "(1)"} \\
+    & @{text "|"} & @{text "prop\<^sup>(\<^sup>2\<^sup>)"} @{text "\<Longrightarrow>"} @{text "prop\<^sup>(\<^sup>1\<^sup>)"} & @{text "(1)"} \\
+    & @{text "|"} & @{verbatim "[|"} @{text prop} @{verbatim ";"} @{text "\<dots>"} @{verbatim ";"} @{text prop} @{verbatim "|]"} @{verbatim "==>"} @{text "prop\<^sup>(\<^sup>1\<^sup>)"} & @{text "(1)"} \\
+    & @{text "|"} & @{text "\<lbrakk>"} @{text prop} @{verbatim ";"} @{text "\<dots>"} @{verbatim ";"} @{text prop} @{text "\<rbrakk>"} @{text "\<Longrightarrow>"} @{text "prop\<^sup>(\<^sup>1\<^sup>)"} & @{text "(1)"} \\
+    & @{text "|"} & @{verbatim "!!"} @{text idts} @{verbatim "."} @{text prop} & @{text "(0)"} \\
+    & @{text "|"} & @{text "\<And>"} @{text idts} @{verbatim "."} @{text prop} & @{text "(0)"} \\
+    & @{text "|"} & @{verbatim OFCLASS} @{verbatim "("} @{text type} @{verbatim ","} @{text logic} @{verbatim ")"} \\
+    & @{text "|"} & @{verbatim SORT_CONSTRAINT} @{verbatim "("} @{text type} @{verbatim ")"} \\
+    & @{text "|"} & @{verbatim TERM} @{text logic} \\
+    & @{text "|"} & @{verbatim PROP} @{text aprop} \\\\
+
+  @{syntax_def (inner) aprop} & = & @{verbatim "("} @{text aprop} @{verbatim ")"} \\
+    & @{text "|"} & @{text "id  |  longid  |  var  |  "}@{verbatim "_"}@{text "  |  "}@{verbatim "..."} \\
+    & @{text "|"} & @{verbatim CONST} @{text "id  |  "}@{verbatim CONST} @{text "longid"} \\
+    & @{text "|"} & @{verbatim XCONST} @{text "id  |  "}@{verbatim XCONST} @{text "longid"} \\
+    & @{text "|"} & @{text "logic\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)  any\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>) \<dots> any\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)"} & @{text "(999)"} \\\\
+
+  @{syntax_def (inner) logic} & = & @{verbatim "("} @{text logic} @{verbatim ")"} \\
+    & @{text "|"} & @{text "logic\<^sup>(\<^sup>4\<^sup>)"} @{verbatim "::"} @{text type} & @{text "(3)"} \\
+    & @{text "|"} & @{text "id  |  longid  |  var  |  "}@{verbatim "_"}@{text "  |  "}@{verbatim "..."} \\
+    & @{text "|"} & @{verbatim CONST} @{text "id  |  "}@{verbatim CONST} @{text "longid"} \\
+    & @{text "|"} & @{verbatim XCONST} @{text "id  |  "}@{verbatim XCONST} @{text "longid"} \\
+    & @{text "|"} & @{text "logic\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)  any\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>) \<dots> any\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)"} & @{text "(999)"} \\
+    & @{text "|"} & @{text "\<struct> index\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>)"} \\
+    & @{text "|"} & @{verbatim "%"} @{text pttrns} @{verbatim "."} @{text "any\<^sup>(\<^sup>3\<^sup>)"} & @{text "(3)"} \\
+    & @{text "|"} & @{text \<lambda>} @{text pttrns} @{verbatim "."} @{text "any\<^sup>(\<^sup>3\<^sup>)"} & @{text "(3)"} \\
+    & @{text "|"} & @{verbatim op} @{verbatim "=="}@{text "  |  "}@{verbatim op} @{text "\<equiv>"}@{text "  |  "}@{verbatim op} @{verbatim "&&&"} \\
+    & @{text "|"} & @{verbatim op} @{verbatim "==>"}@{text "  |  "}@{verbatim op} @{text "\<Longrightarrow>"} \\
+    & @{text "|"} & @{verbatim TYPE} @{verbatim "("} @{text type} @{verbatim ")"} \\\\
+
+  @{syntax_def (inner) idt} & = & @{verbatim "("} @{text idt} @{verbatim ")"}@{text "  |  id  |  "}@{verbatim "_"} \\
+    & @{text "|"} & @{text id} @{verbatim "::"} @{text type} & @{text "(0)"} \\
+    & @{text "|"} & @{verbatim "_"} @{verbatim "::"} @{text type} & @{text "(0)"} \\\\
+
+  @{syntax_def (inner) index} & = & @{verbatim "\<^bsub>"} @{text "logic\<^sup>(\<^sup>0\<^sup>)"} @{verbatim "\<^esub>"}@{text "  |  |  \<index>"} \\\\
+
+  @{syntax_def (inner) idts} & = & @{text "idt  |  idt\<^sup>(\<^sup>1\<^sup>) idts"} & @{text "(0)"} \\\\
+
+  @{syntax_def (inner) pttrn} & = & @{text idt} \\\\
+
+  @{syntax_def (inner) pttrns} & = & @{text "pttrn  |  pttrn\<^sup>(\<^sup>1\<^sup>) pttrns"} & @{text "(0)"} \\\\
+
+  @{syntax_def (inner) type} & = & @{verbatim "("} @{text type} @{verbatim ")"} \\
+    & @{text "|"} & @{text "tid  |  tvar  |  "}@{verbatim "_"} \\
+    & @{text "|"} & @{text "tid"} @{verbatim "::"} @{text "sort  |  tvar  "}@{verbatim "::"} @{text "sort  |  "}@{verbatim "_"} @{verbatim "::"} @{text "sort"} \\
+    & @{text "|"} & @{text "type_name  |  type\<^sup>(\<^sup>1\<^sup>0\<^sup>0\<^sup>0\<^sup>) type_name"} \\
+    & @{text "|"} & @{verbatim "("} @{text type} @{verbatim ","} @{text "\<dots>"} @{verbatim ","} @{text type} @{verbatim ")"} @{text type_name} \\
+    & @{text "|"} & @{text "type\<^sup>(\<^sup>1\<^sup>)"} @{verbatim "=>"} @{text type} & @{text "(0)"} \\
+    & @{text "|"} & @{text "type\<^sup>(\<^sup>1\<^sup>)"} @{text "\<Rightarrow>"} @{text type} & @{text "(0)"} \\
+    & @{text "|"} & @{verbatim "["} @{text type} @{verbatim ","} @{text "\<dots>"} @{verbatim ","} @{text type} @{verbatim "]"} @{verbatim "=>"} @{text type} & @{text "(0)"} \\
+    & @{text "|"} & @{verbatim "["} @{text type} @{verbatim ","} @{text "\<dots>"} @{verbatim ","} @{text type} @{verbatim "]"} @{text "\<Rightarrow>"} @{text type} & @{text "(0)"} \\
+  @{syntax_def (inner) type_name} & = & @{text "id  |  longid"} \\\\
+
+  @{syntax_def (inner) sort} & = & @{syntax class_name}~@{text "  |  "}@{verbatim "{}"} \\
+    & @{text "|"} & @{verbatim "{"} @{syntax class_name} @{verbatim ","} @{text "\<dots>"} @{verbatim ","} @{syntax class_name} @{verbatim "}"} \\
+  @{syntax_def (inner) class_name} & = & @{text "id  |  longid"} \\
+  \end{supertabular}
+  \end{center}
+
+  \medskip Here literal terminals are printed @{verbatim "verbatim"};
+  see also \secref{sec:inner-lex} for further token categories of the
+  inner syntax.  The meaning of the nonterminals defined by the above
+  grammar is as follows:
+
+  \begin{description}
+
+  \item @{syntax_ref (inner) any} denotes any term.
+
+  \item @{syntax_ref (inner) prop} denotes meta-level propositions,
+  which are terms of type @{typ prop}.  The syntax of such formulae of
+  the meta-logic is carefully distinguished from usual conventions for
+  object-logics.  In particular, plain @{text "\<lambda>"}-term notation is
+  \emph{not} recognized as @{syntax (inner) prop}.
+
+  \item @{syntax_ref (inner) aprop} denotes atomic propositions, which
+  are embedded into regular @{syntax (inner) prop} by means of an
+  explicit @{verbatim PROP} token.
+
+  Terms of type @{typ prop} with non-constant head, e.g.\ a plain
+  variable, are printed in this form.  Constants that yield type @{typ
+  prop} are expected to provide their own concrete syntax; otherwise
+  the printed version will appear like @{syntax (inner) logic} and
+  cannot be parsed again as @{syntax (inner) prop}.
+
+  \item @{syntax_ref (inner) logic} denotes arbitrary terms of a
+  logical type, excluding type @{typ prop}.  This is the main
+  syntactic category of object-logic entities, covering plain @{text
+  \<lambda>}-term notation (variables, abstraction, application), plus
+  anything defined by the user.
+
+  When specifying notation for logical entities, all logical types
+  (excluding @{typ prop}) are \emph{collapsed} to this single category
+  of @{syntax (inner) logic}.
+
+  \item @{syntax_ref (inner) index} denotes an optional index term for
+  indexed syntax.  If omitted, it refers to the first @{keyword
+  "structure"} variable in the context.  The special dummy ``@{text
+  "\<index>"}'' serves as pattern variable in mixfix annotations that
+  introduce indexed notation.
+
+  \item @{syntax_ref (inner) idt} denotes identifiers, possibly
+  constrained by types.
+
+  \item @{syntax_ref (inner) idts} denotes a sequence of @{syntax_ref
+  (inner) idt}.  This is the most basic category for variables in
+  iterated binders, such as @{text "\<lambda>"} or @{text "\<And>"}.
+
+  \item @{syntax_ref (inner) pttrn} and @{syntax_ref (inner) pttrns}
+  denote patterns for abstraction, cases bindings etc.  In Pure, these
+  categories start as a merely copy of @{syntax (inner) idt} and
+  @{syntax (inner) idts}, respectively.  Object-logics may add
+  additional productions for binding forms.
+
+  \item @{syntax_ref (inner) type} denotes types of the meta-logic.
+
+  \item @{syntax_ref (inner) sort} denotes meta-level sorts.
+
+  \end{description}
+
+  Here are some further explanations of certain syntax features.
+
+  \begin{itemize}
+
+  \item In @{syntax (inner) idts}, note that @{text "x :: nat y"} is
+  parsed as @{text "x :: (nat y)"}, treating @{text y} like a type
+  constructor applied to @{text nat}.  To avoid this interpretation,
+  write @{text "(x :: nat) y"} with explicit parentheses.
+
+  \item Similarly, @{text "x :: nat y :: nat"} is parsed as @{text "x ::
+  (nat y :: nat)"}.  The correct form is @{text "(x :: nat) (y ::
+  nat)"}, or @{text "(x :: nat) y :: nat"} if @{text y} is last in the
+  sequence of identifiers.
+
+  \item Type constraints for terms bind very weakly.  For example,
+  @{text "x < y :: nat"} is normally parsed as @{text "(x < y) ::
+  nat"}, unless @{text "<"} has a very low priority, in which case the
+  input is likely to be ambiguous.  The correct form is @{text "x < (y
+  :: nat)"}.
+
+  \item Constraints may be either written with two literal colons
+  ``@{verbatim "::"}'' or the double-colon symbol @{verbatim "\<Colon>"},
+  which actually looks exactly the same in some {\LaTeX} styles.
+
+  \item Dummy variables (written as underscore) may occur in different
+  roles.
+
+  \begin{description}
+
+  \item A type ``@{text "_"}'' or ``@{text "_ :: sort"}'' acts like an
+  anonymous inference parameter, which is filled-in according to the
+  most general type produced by the type-checking phase.
+
+  \item A bound ``@{text "_"}'' refers to a vacuous abstraction, where
+  the body does not refer to the binding introduced here.  As in the
+  term @{term "\<lambda>x _. x"}, which is @{text "\<alpha>"}-equivalent to @{text
+  "\<lambda>x y. x"}.
+
+  \item A free ``@{text "_"}'' refers to an implicit outer binding.
+  Higher definitional packages usually allow forms like @{text "f x _
+  = x"}.
+
+  \item A schematic ``@{text "_"}'' (within a term pattern, see
+  \secref{sec:term-decls}) refers to an anonymous variable that is
+  implicitly abstracted over its context of locally bound variables.
+  For example, this allows pattern matching of @{text "{x. f x = g
+  x}"} against @{text "{x. _ = _}"}, or even @{text "{_. _ = _}"} by
+  using both bound and schematic dummies.
+
+  \end{description}
+
+  \item The three literal dots ``@{verbatim "..."}'' may be also
+  written as ellipsis symbol @{verbatim "\<dots>"}.  In both cases this
+  refers to a special schematic variable, which is bound in the
+  context.  This special term abbreviation works nicely with
+  calculational reasoning (\secref{sec:calculation}).
+
+  \item @{verbatim CONST} ensures that the given identifier is treated
+  as constant term, and passed through the parse tree in fully
+  internalized form.  This is particularly relevant for translation
+  rules (\secref{sec:syn-trans}), notably on the RHS.
+
+  \item @{verbatim XCONST} is similar to @{verbatim CONST}, but
+  retains the constant name as given.  This is only relevant to
+  translation rules (\secref{sec:syn-trans}), notably on the LHS.
+
+  \end{itemize}
+*}
+
+
+subsection {* Inspecting the syntax *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def "print_syntax"}@{text "\<^sup>*"} & : & @{text "context \<rightarrow>"} \\
+  \end{matharray}
+
+  \begin{description}
+
+  \item @{command "print_syntax"} prints the inner syntax of the
+  current context.  The output can be quite large; the most important
+  sections are explained below.
+
+  \begin{description}
+
+  \item @{text "lexicon"} lists the delimiters of the inner token
+  language; see \secref{sec:inner-lex}.
+
+  \item @{text "prods"} lists the productions of the underlying
+  priority grammar; see \secref{sec:priority-grammar}.
+
+  The nonterminal @{text "A\<^sup>(\<^sup>p\<^sup>)"} is rendered in plain text as @{text
+  "A[p]"}; delimiters are quoted.  Many productions have an extra
+  @{text "\<dots> => name"}.  These names later become the heads of parse
+  trees; they also guide the pretty printer.
+
+  Productions without such parse tree names are called \emph{copy
+  productions}.  Their right-hand side must have exactly one
+  nonterminal symbol (or named token).  The parser does not create a
+  new parse tree node for copy productions, but simply returns the
+  parse tree of the right-hand symbol.
+
+  If the right-hand side of a copy production consists of a single
+  nonterminal without any delimiters, then it is called a \emph{chain
+  production}.  Chain productions act as abbreviations: conceptually,
+  they are removed from the grammar by adding new productions.
+  Priority information attached to chain productions is ignored; only
+  the dummy value @{text "-1"} is displayed.
+
+  \item @{text "print modes"} lists the alternative print modes
+  provided by this grammar; see \secref{sec:print-modes}.
+
+  \item @{text "parse_rules"} and @{text "print_rules"} relate to
+  syntax translations (macros); see \secref{sec:syn-trans}.
+
+  \item @{text "parse_ast_translation"} and @{text
+  "print_ast_translation"} list sets of constants that invoke
+  translation functions for abstract syntax trees, which are only
+  required in very special situations; see \secref{sec:tr-funs}.
+
+  \item @{text "parse_translation"} and @{text "print_translation"}
+  list the sets of constants that invoke regular translation
+  functions; see \secref{sec:tr-funs}.
+
+  \end{description}
+
+  \end{description}
+*}
+
+
+subsection {* Ambiguity of parsed expressions *}
+
+text {*
+  \begin{tabular}{rcll}
+    @{attribute_def syntax_ambiguity_warning} & : & @{text attribute} & default @{text true} \\
+    @{attribute_def syntax_ambiguity_limit} & : & @{text attribute} & default @{text 10} \\
+  \end{tabular}
+
+  Depending on the grammar and the given input, parsing may be
+  ambiguous.  Isabelle lets the Earley parser enumerate all possible
+  parse trees, and then tries to make the best out of the situation.
+  Terms that cannot be type-checked are filtered out, which often
+  leads to a unique result in the end.  Unlike regular type
+  reconstruction, which is applied to the whole collection of input
+  terms simultaneously, the filtering stage only treats each given
+  term in isolation.  Filtering is also not attempted for individual
+  types or raw ASTs (as required for @{command translations}).
+
+  Certain warning or error messages are printed, depending on the
+  situation and the given configuration options.  Parsing ultimately
+  fails, if multiple results remain after the filtering phase.
+
+  \begin{description}
+
+  \item @{attribute syntax_ambiguity_warning} controls output of
+  explicit warning messages about syntax ambiguity.
+
+  \item @{attribute syntax_ambiguity_limit} determines the number of
+  resulting parse trees that are shown as part of the printed message
+  in case of an ambiguity.
+
+  \end{description}
+*}
+
+
+section {* Syntax transformations \label{sec:syntax-transformations} *}
+
+text {* The inner syntax engine of Isabelle provides separate
+  mechanisms to transform parse trees either as rewrite systems on
+  first-order ASTs (\secref{sec:syn-trans}), or ML functions on ASTs
+  or syntactic @{text "\<lambda>"}-terms (\secref{sec:tr-funs}).  This works
+  both for parsing and printing, as outlined in
+  \figref{fig:parse-print}.
+
+  \begin{figure}[htbp]
+  \begin{center}
+  \begin{tabular}{cl}
+  string          & \\
+  @{text "\<down>"}     & lexer + parser \\
+  parse tree      & \\
+  @{text "\<down>"}     & parse AST translation \\
+  AST             & \\
+  @{text "\<down>"}     & AST rewriting (macros) \\
+  AST             & \\
+  @{text "\<down>"}     & parse translation \\
+  --- pre-term ---    & \\
+  @{text "\<down>"}     & print translation \\
+  AST             & \\
+  @{text "\<down>"}     & AST rewriting (macros) \\
+  AST             & \\
+  @{text "\<down>"}     & print AST translation \\
+  string          &
+  \end{tabular}
+  \end{center}
+  \caption{Parsing and printing with translations}\label{fig:parse-print}
+  \end{figure}
+
+  These intermediate syntax tree formats eventually lead to a pre-term
+  with all names and binding scopes resolved, but most type
+  information still missing.  Explicit type constraints might be given by
+  the user, or implicit position information by the system --- both
+  need to be passed-through carefully by syntax transformations.
+
+  Pre-terms are further processed by the so-called \emph{check} and
+  \emph{unckeck} phases that are intertwined with type-inference (see
+  also \cite{isabelle-implementation}).  The latter allows to operate
+  on higher-order abstract syntax with proper binding and type
+  information already available.
+
+  As a rule of thumb, anything that manipulates bindings of variables
+  or constants needs to be implemented as syntax transformation (see
+  below).  Anything else is better done via check/uncheck: a prominent
+  example application is the @{command abbreviation} concept of
+  Isabelle/Pure. *}
+
+
+subsection {* Abstract syntax trees \label{sec:ast} *}
+
+text {* The ML datatype @{ML_type Ast.ast} explicitly represents the
+  intermediate AST format that is used for syntax rewriting
+  (\secref{sec:syn-trans}).  It is defined in ML as follows:
+  \begin{ttbox}
+  datatype ast =
+    Constant of string |
+    Variable of string |
+    Appl of ast list
+  \end{ttbox}
+
+  An AST is either an atom (constant or variable) or a list of (at
+  least two) subtrees.  Occasional diagnostic output of ASTs uses
+  notation that resembles S-expression of LISP.  Constant atoms are
+  shown as quoted strings, variable atoms as non-quoted strings and
+  applications as a parenthesized list of subtrees.  For example, the
+  AST
+  @{ML [display] "Ast.Appl
+  [Ast.Constant \"_abs\", Ast.Variable \"x\", Ast.Variable \"t\"]"}
+  is pretty-printed as @{verbatim "(\"_abs\" x t)"}.  Note that
+  @{verbatim "()"} and @{verbatim "(x)"} are excluded as ASTs, because
+  they have too few subtrees.
+
+  \medskip AST application is merely a pro-forma mechanism to indicate
+  certain syntactic structures.  Thus @{verbatim "(c a b)"} could mean
+  either term application or type application, depending on the
+  syntactic context.
+
+  Nested application like @{verbatim "((\"_abs\" x t) u)"} is also
+  possible, but ASTs are definitely first-order: the syntax constant
+  @{verbatim "\"_abs\""} does not bind the @{verbatim x} in any way.
+  Proper bindings are introduced in later stages of the term syntax,
+  where @{verbatim "(\"_abs\" x t)"} becomes an @{ML Abs} node and
+  occurrences of @{verbatim x} in @{verbatim t} are replaced by bound
+  variables (represented as de-Bruijn indices).
+*}
+
+
+subsubsection {* AST constants versus variables *}
+
+text {* Depending on the situation --- input syntax, output syntax,
+  translation patterns --- the distinction of atomic asts as @{ML
+  Ast.Constant} versus @{ML Ast.Variable} serves slightly different
+  purposes.
+
+  Input syntax of a term such as @{text "f a b = c"} does not yet
+  indicate the scopes of atomic entities @{text "f, a, b, c"}: they
+  could be global constants or local variables, even bound ones
+  depending on the context of the term.  @{ML Ast.Variable} leaves
+  this choice still open: later syntax layers (or translation
+  functions) may capture such a variable to determine its role
+  specifically, to make it a constant, bound variable, free variable
+  etc.  In contrast, syntax translations that introduce already known
+  constants would rather do it via @{ML Ast.Constant} to prevent
+  accidental re-interpretation later on.
+
+  Output syntax turns term constants into @{ML Ast.Constant} and
+  variables (free or schematic) into @{ML Ast.Variable}.  This
+  information is precise when printing fully formal @{text "\<lambda>"}-terms.
+
+  In AST translation patterns (\secref{sec:syn-trans}) the system
+  guesses from the current theory context which atoms should be
+  treated as constant versus variable for the matching process.
+  Sometimes this needs to be indicated more explicitly using @{text
+  "CONST c"} inside the term language.  It is also possible to use
+  @{command syntax} declarations (without mixfix annotation) to
+  enforce that certain unqualified names are always treated as
+  constant within the syntax machinery.
+
+  \medskip For ASTs that represent the language of types or sorts, the
+  situation is much simpler, since the concrete syntax already
+  distinguishes type variables from type constants (constructors).  So
+  @{text "('a, 'b) foo"} corresponds to an AST application of some
+  constant for @{text foo} and variable arguments for @{text "'a"} and
+  @{text "'b"}.  Note that the postfix application is merely a feature
+  of the concrete syntax, while in the AST the constructor occurs in
+  head position.  *}
+
+
+subsubsection {* Authentic syntax names *}
+
+text {* Naming constant entities within ASTs is another delicate
+  issue.  Unqualified names are looked up in the name space tables in
+  the last stage of parsing, after all translations have been applied.
+  Since syntax transformations do not know about this later name
+  resolution yet, there can be surprises in boundary cases.
+
+  \emph{Authentic syntax names} for @{ML Ast.Constant} avoid this
+  problem: the fully-qualified constant name with a special prefix for
+  its formal category (@{text "class"}, @{text "type"}, @{text
+  "const"}, @{text "fixed"}) represents the information faithfully
+  within the untyped AST format.  Accidental overlap with free or
+  bound variables is excluded as well.  Authentic syntax names work
+  implicitly in the following situations:
+
+  \begin{itemize}
+
+  \item Input of term constants (or fixed variables) that are
+  introduced by concrete syntax via @{command notation}: the
+  correspondence of a particular grammar production to some known term
+  entity is preserved.
+
+  \item Input of type constants (constructors) and type classes ---
+  thanks to explicit syntactic distinction independently on the
+  context.
+
+  \item Output of term constants, type constants, type classes ---
+  this information is already available from the internal term to be
+  printed.
+
+  \end{itemize}
+
+  In other words, syntax transformations that operate on input terms
+  written as prefix applications are difficult to make robust.
+  Luckily, this case rarely occurs in practice, because syntax forms
+  to be translated usually correspond to some bits of concrete
+  notation. *}
+
+
+subsection {* Raw syntax and translations \label{sec:syn-trans} *}
+
+text {*
+  \begin{tabular}{rcll}
+    @{command_def "nonterminal"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "syntax"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "no_syntax"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "translations"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "no_translations"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{attribute_def syntax_ast_trace} & : & @{text attribute} & default @{text false} \\
+    @{attribute_def syntax_ast_stats} & : & @{text attribute} & default @{text false} \\
+  \end{tabular}
+
+  Unlike mixfix notation for existing formal entities
+  (\secref{sec:notation}), raw syntax declarations provide full access
+  to the priority grammar of the inner syntax, without any sanity
+  checks.  This includes additional syntactic categories (via
+  @{command nonterminal}) and free-form grammar productions (via
+  @{command syntax}).  Additional syntax translations (or macros, via
+  @{command translations}) are required to turn resulting parse trees
+  into proper representations of formal entities again.
+
+  @{rail "
+    @@{command nonterminal} (@{syntax name} + @'and')
+    ;
+    (@@{command syntax} | @@{command no_syntax}) @{syntax mode}? (constdecl +)
+    ;
+    (@@{command translations} | @@{command no_translations})
+      (transpat ('==' | '=>' | '<=' | '\<rightleftharpoons>' | '\<rightharpoonup>' | '\<leftharpoondown>') transpat +)
+    ;
+
+    constdecl: @{syntax name} '::' @{syntax type} @{syntax mixfix}?
+    ;
+    mode: ('(' ( @{syntax name} | @'output' | @{syntax name} @'output' ) ')')
+    ;
+    transpat: ('(' @{syntax nameref} ')')? @{syntax string}
+  "}
+
+  \begin{description}
+
+  \item @{command "nonterminal"}~@{text c} declares a type
+  constructor @{text c} (without arguments) to act as purely syntactic
+  type: a nonterminal symbol of the inner syntax.
+
+  \item @{command "syntax"}~@{text "(mode) c :: \<sigma> (mx)"} augments the
+  priority grammar and the pretty printer table for the given print
+  mode (default @{verbatim "\"\""}). An optional keyword @{keyword_ref
+  "output"} means that only the pretty printer table is affected.
+
+  Following \secref{sec:mixfix}, the mixfix annotation @{text "mx =
+  template ps q"} together with type @{text "\<sigma> = \<tau>\<^sub>1 \<Rightarrow> \<dots> \<tau>\<^sub>n \<Rightarrow> \<tau>"} and
+  specify a grammar production.  The @{text template} contains
+  delimiter tokens that surround @{text "n"} argument positions
+  (@{verbatim "_"}).  The latter correspond to nonterminal symbols
+  @{text "A\<^sub>i"} derived from the argument types @{text "\<tau>\<^sub>i"} as
+  follows:
+  \begin{itemize}
+
+  \item @{text "prop"} if @{text "\<tau>\<^sub>i = prop"}
+
+  \item @{text "logic"} if @{text "\<tau>\<^sub>i = (\<dots>)\<kappa>"} for logical type
+  constructor @{text "\<kappa> \<noteq> prop"}
+
+  \item @{text any} if @{text "\<tau>\<^sub>i = \<alpha>"} for type variables
+
+  \item @{text "\<kappa>"} if @{text "\<tau>\<^sub>i = \<kappa>"} for nonterminal @{text "\<kappa>"}
+  (syntactic type constructor)
+
+  \end{itemize}
+
+  Each @{text "A\<^sub>i"} is decorated by priority @{text "p\<^sub>i"} from the
+  given list @{text "ps"}; misssing priorities default to 0.
+
+  The resulting nonterminal of the production is determined similarly
+  from type @{text "\<tau>"}, with priority @{text "q"} and default 1000.
+
+  \medskip Parsing via this production produces parse trees @{text
+  "t\<^sub>1, \<dots>, t\<^sub>n"} for the argument slots.  The resulting parse tree is
+  composed as @{text "c t\<^sub>1 \<dots> t\<^sub>n"}, by using the syntax constant @{text
+  "c"} of the syntax declaration.
+
+  Such syntactic constants are invented on the spot, without formal
+  check wrt.\ existing declarations.  It is conventional to use plain
+  identifiers prefixed by a single underscore (e.g.\ @{text
+  "_foobar"}).  Names should be chosen with care, to avoid clashes
+  with other syntax declarations.
+
+  \medskip The special case of copy production is specified by @{text
+  "c = "}@{verbatim "\"\""} (empty string).  It means that the
+  resulting parse tree @{text "t"} is copied directly, without any
+  further decoration.
+
+  \item @{command "no_syntax"}~@{text "(mode) decls"} removes grammar
+  declarations (and translations) resulting from @{text decls}, which
+  are interpreted in the same manner as for @{command "syntax"} above.
+
+  \item @{command "translations"}~@{text rules} specifies syntactic
+  translation rules (i.e.\ macros) as first-order rewrite rules on
+  ASTs (\secref{sec:ast}).  The theory context maintains two
+  independent lists translation rules: parse rules (@{verbatim "=>"}
+  or @{text "\<rightharpoonup>"}) and print rules (@{verbatim "<="} or @{text "\<leftharpoondown>"}).
+  For convenience, both can be specified simultaneously as parse~/
+  print rules (@{verbatim "=="} or @{text "\<rightleftharpoons>"}).
+
+  Translation patterns may be prefixed by the syntactic category to be
+  used for parsing; the default is @{text logic} which means that
+  regular term syntax is used.  Both sides of the syntax translation
+  rule undergo parsing and parse AST translations
+  \secref{sec:tr-funs}, in order to perform some fundamental
+  normalization like @{text "\<lambda>x y. b \<leadsto> \<lambda>x. \<lambda>y. b"}, but other AST
+  translation rules are \emph{not} applied recursively here.
+
+  When processing AST patterns, the inner syntax lexer runs in a
+  different mode that allows identifiers to start with underscore.
+  This accommodates the usual naming convention for auxiliary syntax
+  constants --- those that do not have a logical counter part --- by
+  allowing to specify arbitrary AST applications within the term
+  syntax, independently of the corresponding concrete syntax.
+
+  Atomic ASTs are distinguished as @{ML Ast.Constant} versus @{ML
+  Ast.Variable} as follows: a qualified name or syntax constant
+  declared via @{command syntax}, or parse tree head of concrete
+  notation becomes @{ML Ast.Constant}, anything else @{ML
+  Ast.Variable}.  Note that @{text CONST} and @{text XCONST} within
+  the term language (\secref{sec:pure-grammar}) allow to enforce
+  treatment as constants.
+
+  AST rewrite rules @{text "(lhs, rhs)"} need to obey the following
+  side-conditions:
+
+  \begin{itemize}
+
+  \item Rules must be left linear: @{text "lhs"} must not contain
+  repeated variables.\footnote{The deeper reason for this is that AST
+  equality is not well-defined: different occurrences of the ``same''
+  AST could be decorated differently by accidental type-constraints or
+  source position information, for example.}
+
+  \item Every variable in @{text "rhs"} must also occur in @{text
+  "lhs"}.
+
+  \end{itemize}
+
+  \item @{command "no_translations"}~@{text rules} removes syntactic
+  translation rules, which are interpreted in the same manner as for
+  @{command "translations"} above.
+
+  \item @{attribute syntax_ast_trace} and @{attribute
+  syntax_ast_stats} control diagnostic output in the AST normalization
+  process, when translation rules are applied to concrete input or
+  output.
+
+  \end{description}
+
+  Raw syntax and translations provides a slightly more low-level
+  access to the grammar and the form of resulting parse trees.  It is
+  often possible to avoid this untyped macro mechanism, and use
+  type-safe @{command abbreviation} or @{command notation} instead.
+  Some important situations where @{command syntax} and @{command
+  translations} are really need are as follows:
+
+  \begin{itemize}
+
+  \item Iterated replacement via recursive @{command translations}.
+  For example, consider list enumeration @{term "[a, b, c, d]"} as
+  defined in theory @{theory List} in Isabelle/HOL.
+
+  \item Change of binding status of variables: anything beyond the
+  built-in @{keyword "binder"} mixfix annotation requires explicit
+  syntax translations.  For example, consider list filter
+  comprehension @{term "[x \<leftarrow> xs . P]"} as defined in theory @{theory
+  List} in Isabelle/HOL.
+
+  \end{itemize}
+*}
+
+subsubsection {* Applying translation rules *}
+
+text {* As a term is being parsed or printed, an AST is generated as
+  an intermediate form according to \figref{fig:parse-print}.  The AST
+  is normalized by applying translation rules in the manner of a
+  first-order term rewriting system.  We first examine how a single
+  rule is applied.
+
+  Let @{text "t"} be the abstract syntax tree to be normalized and
+  @{text "(lhs, rhs)"} some translation rule.  A subtree @{text "u"}
+  of @{text "t"} is called \emph{redex} if it is an instance of @{text
+  "lhs"}; in this case the pattern @{text "lhs"} is said to match the
+  object @{text "u"}.  A redex matched by @{text "lhs"} may be
+  replaced by the corresponding instance of @{text "rhs"}, thus
+  \emph{rewriting} the AST @{text "t"}.  Matching requires some notion
+  of \emph{place-holders} in rule patterns: @{ML Ast.Variable} serves
+  this purpose.
+
+  More precisely, the matching of the object @{text "u"} against the
+  pattern @{text "lhs"} is performed as follows:
+
+  \begin{itemize}
+
+  \item Objects of the form @{ML Ast.Variable}~@{text "x"} or @{ML
+  Ast.Constant}~@{text "x"} are matched by pattern @{ML
+  Ast.Constant}~@{text "x"}.  Thus all atomic ASTs in the object are
+  treated as (potential) constants, and a successful match makes them
+  actual constants even before name space resolution (see also
+  \secref{sec:ast}).
+
+  \item Object @{text "u"} is matched by pattern @{ML
+  Ast.Variable}~@{text "x"}, binding @{text "x"} to @{text "u"}.
+
+  \item Object @{ML Ast.Appl}~@{text "us"} is matched by @{ML
+  Ast.Appl}~@{text "ts"} if @{text "us"} and @{text "ts"} have the
+  same length and each corresponding subtree matches.
+
+  \item In every other case, matching fails.
+
+  \end{itemize}
+
+  A successful match yields a substitution that is applied to @{text
+  "rhs"}, generating the instance that replaces @{text "u"}.
+
+  Normalizing an AST involves repeatedly applying translation rules
+  until none are applicable.  This works yoyo-like: top-down,
+  bottom-up, top-down, etc.  At each subtree position, rules are
+  chosen in order of appearance in the theory definitions.
+
+  The configuration options @{attribute syntax_ast_trace} and
+  @{attribute syntax_ast_stats} might help to understand this process
+  and diagnose problems.
+
+  \begin{warn}
+  If syntax translation rules work incorrectly, the output of
+  @{command_ref print_syntax} with its \emph{rules} sections reveals the
+  actual internal forms of AST pattern, without potentially confusing
+  concrete syntax.  Recall that AST constants appear as quoted strings
+  and variables without quotes.
+  \end{warn}
+
+  \begin{warn}
+  If @{attribute_ref eta_contract} is set to @{text "true"}, terms
+  will be @{text "\<eta>"}-contracted \emph{before} the AST rewriter sees
+  them.  Thus some abstraction nodes needed for print rules to match
+  may vanish.  For example, @{text "Ball A (\<lambda>x. P x)"} would contract
+  to @{text "Ball A P"} and the standard print rule would fail to
+  apply.  This problem can be avoided by hand-written ML translation
+  functions (see also \secref{sec:tr-funs}), which is in fact the same
+  mechanism used in built-in @{keyword "binder"} declarations.
+  \end{warn}
+*}
+
+
+subsection {* Syntax translation functions \label{sec:tr-funs} *}
+
+text {*
+  \begin{matharray}{rcl}
+    @{command_def "parse_ast_translation"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "parse_translation"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "print_translation"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "typed_print_translation"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{command_def "print_ast_translation"} & : & @{text "theory \<rightarrow> theory"} \\
+    @{ML_antiquotation_def "class_syntax"} & : & @{text ML_antiquotation} \\
+    @{ML_antiquotation_def "type_syntax"} & : & @{text ML_antiquotation} \\
+    @{ML_antiquotation_def "const_syntax"} & : & @{text ML_antiquotation} \\
+    @{ML_antiquotation_def "syntax_const"} & : & @{text ML_antiquotation} \\
+  \end{matharray}
+
+  Syntax translation functions written in ML admit almost arbitrary
+  manipulations of inner syntax, at the expense of some complexity and
+  obscurity in the implementation.
+
+  @{rail "
+  ( @@{command parse_ast_translation} | @@{command parse_translation} |
+    @@{command print_translation} | @@{command typed_print_translation} |
+    @@{command print_ast_translation}) ('(' @'advanced' ')')? @{syntax text}
+  ;
+  (@@{ML_antiquotation class_syntax} |
+   @@{ML_antiquotation type_syntax} |
+   @@{ML_antiquotation const_syntax} |
+   @@{ML_antiquotation syntax_const}) name
+  "}
+
+  \begin{description}
+
+  \item @{command parse_translation} etc. declare syntax translation
+  functions to the theory.  Any of these commands have a single
+  @{syntax text} argument that refers to an ML expression of
+  appropriate type, which are as follows by default:
+
+  \medskip
+  {\footnotesize
+  \begin{tabular}{ll}
+  @{command parse_ast_translation} & : @{ML_type "(string * (Ast.ast list -> Ast.ast)) list"} \\
+  @{command parse_translation} & : @{ML_type "(string * (term list -> term)) list"} \\
+  @{command print_translation} & : @{ML_type "(string * (term list -> term)) list"} \\
+  @{command typed_print_translation} & : @{ML_type "(string * (typ -> term list -> term)) list"} \\
+  @{command print_ast_translation} & : @{ML_type "(string * (Ast.ast list -> Ast.ast)) list"} \\
+  \end{tabular}}
+  \medskip
+
+  The argument list consists of @{text "(c, tr)"} pairs, where @{text
+  "c"} is the syntax name of the formal entity involved, and @{text
+  "tr"} a function that translates a syntax form @{text "c args"} into
+  @{text "tr args"}.  The ML naming convention for parse translations
+  is @{text "c_tr"} and for print translations @{text "c_tr'"}.
+
+  The @{command_ref print_syntax} command displays the sets of names
+  associated with the translation functions of a theory under @{text
+  "parse_ast_translation"} etc.
+
+  If the @{verbatim "("}@{keyword "advanced"}@{verbatim ")"} option is
+  given, the corresponding translation functions depend on the current
+  theory or proof context as additional argument.  This allows to
+  implement advanced syntax mechanisms, as translations functions may
+  refer to specific theory declarations or auxiliary proof data.
+
+  \item @{text "@{class_syntax c}"}, @{text "@{type_syntax c}"},
+  @{text "@{const_syntax c}"} inline the authentic syntax name of the
+  given formal entities into the ML source.  This is the
+  fully-qualified logical name prefixed by a special marker to
+  indicate its kind: thus different logical name spaces are properly
+  distinguished within parse trees.
+
+  \item @{text "@{const_syntax c}"} inlines the name @{text "c"} of
+  the given syntax constant, having checked that it has been declared
+  via some @{command syntax} commands within the theory context.  Note
+  that the usual naming convention makes syntax constants start with
+  underscore, to reduce the chance of accidental clashes with other
+  names occurring in parse trees (unqualified constants etc.).
+
+  \end{description}
+*}
+
+
+subsubsection {* The translation strategy *}
+
+text {* The different kinds of translation functions are invoked during
+  the transformations between parse trees, ASTs and syntactic terms
+  (cf.\ \figref{fig:parse-print}).  Whenever a combination of the form
+  @{text "c x\<^sub>1 \<dots> x\<^sub>n"} is encountered, and a translation function
+  @{text "f"} of appropriate kind is declared for @{text "c"}, the
+  result is produced by evaluation of @{text "f [x\<^sub>1, \<dots>, x\<^sub>n]"} in ML.
+
+  For AST translations, the arguments @{text "x\<^sub>1, \<dots>, x\<^sub>n"} are ASTs.  A
+  combination has the form @{ML "Ast.Constant"}~@{text "c"} or @{ML
+  "Ast.Appl"}~@{text "["}@{ML Ast.Constant}~@{text "c, x\<^sub>1, \<dots>, x\<^sub>n]"}.
+  For term translations, the arguments are terms and a combination has
+  the form @{ML Const}~@{text "(c, \<tau>)"} or @{ML Const}~@{text "(c, \<tau>)
+  $ x\<^sub>1 $ \<dots> $ x\<^sub>n"}.  Terms allow more sophisticated transformations
+  than ASTs do, typically involving abstractions and bound
+  variables. \emph{Typed} print translations may even peek at the type
+  @{text "\<tau>"} of the constant they are invoked on, although that information
+  may be inaccurate.
+
+  Regardless of whether they act on ASTs or terms, translation
+  functions called during the parsing process differ from those for
+  printing in their overall behaviour:
+
+  \begin{description}
+
+  \item [Parse translations] are applied bottom-up.  The arguments are
+  already in translated form.  The translations must not fail;
+  exceptions trigger an error message.  There may be at most one
+  function associated with any syntactic name.
+
+  \item [Print translations] are applied top-down.  They are supplied
+  with arguments that are partly still in internal form.  The result
+  again undergoes translation; therefore a print translation should
+  not introduce as head the very constant that invoked it.  The
+  function may raise exception @{ML Match} to indicate failure; in
+  this event it has no effect.  Multiple functions associated with
+  some syntactic name are tried in the order of declaration in the
+  theory.
+
+  \end{description}
+
+  Only constant atoms --- constructor @{ML Ast.Constant} for ASTs and
+  @{ML Const} for terms --- can invoke translation functions.  This
+  means that parse translations can only be associated with parse tree
+  heads of concrete syntax, or syntactic constants introduced via
+  other translations.  For plain identifiers within the term language,
+  the status of constant versus variable is not yet know during
+  parsing.  This is in contrast to print translations, where constants
+  are explicitly known from the given term in its fully internal form.
+*}
+
+end