src/Doc/IsarImplementation/Syntax.thy

+theory Syntax
+imports Base
+begin
+
+chapter {* Concrete syntax and type-checking *}
+
+text {* Pure @{text "\<lambda>"}-calculus as introduced in \chref{ch:logic} is
+  an adequate foundation for logical languages --- in the tradition of
+  \emph{higher-order abstract syntax} --- but end-users require
+  additional means for reading and printing of terms and types.  This
+  important add-on outside the logical core is called \emph{inner
+  syntax} in Isabelle jargon, as opposed to the \emph{outer syntax} of
+  the theory and proof language (cf.\ \cite{isabelle-isar-ref}).
+
+  For example, according to \cite{church40} quantifiers are
+  represented as higher-order constants @{text "All :: ('a \<Rightarrow> bool) \<Rightarrow>
+  bool"} such that @{text "All (\<lambda>x::'a. B x)"} faithfully represents
+  the idea that is displayed as @{text "\<forall>x::'a. B x"} via @{keyword
+  "binder"} notation.  Moreover, type-inference in the style of
+  Hindley-Milner \cite{hindleymilner} (and extensions) enables users
+  to write @{text "\<forall>x. B x"} concisely, when the type @{text "'a"} is
+  already clear from the context.\footnote{Type-inference taken to the
+  extreme can easily confuse users, though.  Beginners often stumble
+  over unexpectedly general types inferred by the system.}
+
+  \medskip The main inner syntax operations are \emph{read} for
+  parsing together with type-checking, and \emph{pretty} for formatted
+  output.  See also \secref{sec:read-print}.
+
+  Furthermore, the input and output syntax layers are sub-divided into
+  separate phases for \emph{concrete syntax} versus \emph{abstract
+  syntax}, see also \secref{sec:parse-unparse} and
+  \secref{sec:term-check}, respectively.  This results in the
+  following decomposition of the main operations:
+
+  \begin{itemize}
+
+  \item @{text "read = parse; check"}
+
+  \item @{text "pretty = uncheck; unparse"}
+
+  \end{itemize}
+
+  Some specification package might thus intercept syntax processing at
+  a well-defined stage after @{text "parse"}, to a augment the
+  resulting pre-term before full type-reconstruction is performed by
+  @{text "check"}, for example.  Note that the formal status of bound
+  variables, versus free variables, versus constants must not be
+  changed here! *}
+
+
+section {* Reading and pretty printing \label{sec:read-print} *}
+
+text {* Read and print operations are roughly dual to each other, such
+  that for the user @{text "s' = pretty (read s)"} looks similar to
+  the original source text @{text "s"}, but the details depend on many
+  side-conditions.  There are also explicit options to control
+  suppressing of type information in the output.  The default
+  configuration routinely looses information, so @{text "t' = read
+  (pretty t)"} might fail, produce a differently typed term, or a
+  completely different term in the face of syntactic overloading!  *}
+
+text %mlref {*
+  \begin{mldecls}
+  @{index_ML Syntax.read_typ: "Proof.context -> string -> typ"} \\
+  @{index_ML Syntax.read_term: "Proof.context -> string -> term"} \\
+  @{index_ML Syntax.read_prop: "Proof.context -> string -> term"} \\
+  @{index_ML Syntax.pretty_typ: "Proof.context -> typ -> Pretty.T"} \\
+  @{index_ML Syntax.pretty_term: "Proof.context -> term -> Pretty.T"} \\
+  \end{mldecls}
+
+  \begin{description}
+
+  \item FIXME
+
+  \end{description}
+*}
+
+
+section {* Parsing and unparsing \label{sec:parse-unparse} *}
+
+text {* Parsing and unparsing converts between actual source text and
+  a certain \emph{pre-term} format, where all bindings and scopes are
+  resolved faithfully.  Thus the names of free variables or constants
+  are already determined in the sense of the logical context, but type
+  information might is still missing.  Pre-terms support an explicit
+  language of \emph{type constraints} that may be augmented by user
+  code to guide the later \emph{check} phase, for example.
+
+  Actual parsing is based on traditional lexical analysis and Earley
+  parsing for arbitrary context-free grammars.  The user can specify
+  this via mixfix annotations.  Moreover, there are \emph{syntax
+  translations} that can be augmented by the user, either
+  declaratively via @{command translations} or programmatically via
+  @{command parse_translation}, @{command print_translation} etc.  The
+  final scope resolution is performed by the system, according to name
+  spaces for types, constants etc.\ determined by the context.
+*}
+
+text %mlref {*
+  \begin{mldecls}
+  @{index_ML Syntax.parse_typ: "Proof.context -> string -> typ"} \\
+  @{index_ML Syntax.parse_term: "Proof.context -> string -> term"} \\
+  @{index_ML Syntax.parse_prop: "Proof.context -> string -> term"} \\
+  @{index_ML Syntax.unparse_typ: "Proof.context -> typ -> Pretty.T"} \\
+  @{index_ML Syntax.unparse_term: "Proof.context -> term -> Pretty.T"} \\
+  \end{mldecls}
+
+  \begin{description}
+
+  \item FIXME
+
+  \end{description}
+*}
+
+
+section {* Checking and unchecking \label{sec:term-check} *}
+
+text {* These operations define the transition from pre-terms and
+  fully-annotated terms in the sense of the logical core
+  (\chref{ch:logic}).
+
+  The \emph{check} phase is meant to subsume a variety of mechanisms
+  in the manner of ``type-inference'' or ``type-reconstruction'' or
+  ``type-improvement'', not just type-checking in the narrow sense.
+  The \emph{uncheck} phase is roughly dual, it prunes type-information
+  before pretty printing.
+
+  A typical add-on for the check/uncheck syntax layer is the @{command
+  abbreviation} mechanism.  Here the user specifies syntactic
+  definitions that are managed by the system as polymorphic @{text
+  "let"} bindings.  These are expanded during the @{text "check"}
+  phase, and contracted during the @{text "uncheck"} phase, without
+  affecting the type-assignment of the given terms.
+
+  \medskip The precise meaning of type checking depends on the context
+  --- additional check/uncheck plugins might be defined in user space!
+
+  For example, the @{command class} command defines a context where
+  @{text "check"} treats certain type instances of overloaded
+  constants according to the ``dictionary construction'' of its
+  logical foundation.  This involves ``type improvement''
+  (specialization of slightly too general types) and replacement by
+  certain locale parameters.  See also \cite{Haftmann-Wenzel:2009}.
+*}
+
+text %mlref {*
+  \begin{mldecls}
+  @{index_ML Syntax.check_typs: "Proof.context -> typ list -> typ list"} \\
+  @{index_ML Syntax.check_terms: "Proof.context -> term list -> term list"} \\
+  @{index_ML Syntax.check_props: "Proof.context -> term list -> term list"} \\
+  @{index_ML Syntax.uncheck_typs: "Proof.context -> typ list -> typ list"} \\
+  @{index_ML Syntax.uncheck_terms: "Proof.context -> term list -> term list"} \\
+  \end{mldecls}
+
+  \begin{description}
+
+  \item FIXME
+
+  \end{description}
+*}
+
+end