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}
%FIXME 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}
%FIXME 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}
%FIXME description
*}
end