-struct makes a set of rules available within its
-body. The actual parsing is initiated with @code{peg-run}:
-
-@defun peg-run peg-matcher &optional failure-function success-function
-This function accepts a single @var{peg-matcher}, which is the result of
-calling @code{peg} (see below) on a named rule, usually the entry-point
-of a larger grammar.
-
-At the end of parsing, one of @var{failure-function} or
-@var{success-function} is called, depending on whether the parsing
-succeeded or not. If @var{success-function} is called, it is passed a
-lambda form that runs all the actions collected on the stack during
-parsing -- by default this lambda form is simply executed. If parsing
-fails, the @var{failure-function} is called with a list of @acronym{PEG}
-expressions that failed during parsing; by default this list is
-discarded.
-@end defun
-
-The @var{peg-matcher} passed to @code{peg-run} is produced by a call to
-@code{peg}:
-
-@defmac peg &rest pexs
-Convert @var{pexs} into a single peg-matcher suitable for passing to
-@code{peg-run}.
+@c -*-texinfo-*-
+@c This is part of the GNU Emacs Lisp Reference Manual.
+@c Copyright (C) 1990--1995, 1998--1999, 2001--2023 Free Software
+@c Foundation, Inc.
+@c See the file elisp.texi for copying conditions.
+@node Parsing Expression Grammars
+@chapter Parsing Expression Grammars
+@cindex text parsing
+@cindex parsing expression grammar
+@cindex PEG
+
+ Emacs Lisp provides several tools for parsing and matching text,
+from regular expressions (@pxref{Regular Expressions}) to full
+left-to-right (a.k.a.@: @acronym{LL}) grammar parsers (@pxref{Top,,
+Bovine parser development,bovine}). @dfn{Parsing Expression Grammars}
+(@acronym{PEG}) are another approach to text parsing that offer more
+structure and composibility than regular expressions, but less
+complexity than context-free grammars.
+
+A Parsing Expression Grammar (@acronym{PEG}) describes a formal language
+in terms of a set of rules for recognizing strings in the language. In
+Emacs, a @acronym{PEG} parser is defined as a list of named rules, each
+of which matches text patterns and/or contains references to other
+rules. Parsing is initiated with the function @code{peg-run} or the
+macro @code{peg-parse} (see below), and parses text after point in the
+current buffer, using a given set of rules.
+
+@cindex parsing expression
+@cindex root, of parsing expression grammar
+@cindex entry-point, of parsing expression grammar
+Each rule in a @acronym{PEG} is referred to as a @dfn{parsing
+expression} (@acronym{PEX}), and can be specified a a literal string, a
+regexp-like character range or set, a peg-specific construct resembling
+an Emacs Lisp function call, a reference to another rule, or a
+combination of any of these. A grammar is expressed as a tree of rules
+in which one rule is typically treated as a ``root'' or ``entry-point''
+rule. For instance:
+
+@example
+@group
+((number sign digit (* digit))
+ (sign (or "+" "-" ""))
+ (digit [0-9]))
+@end group
+@end example
+
+Once defined, grammars can be used to parse text after point in the
+current buffer, in the following ways:
+
+@defmac peg-parse &rest pexs
+Match @var{pexs} at point. If @var{pexs} is a list of PEG rules, the
+first rule is considered the ``entry-point'':
@end defmac
-The @code{peg-parse} example above expands to just this set of calls,
-and could be written as:
+@example
+@group
+(peg-parse
+ ((number sign digit (* digit))
+ (sign (or "+" "-" ""))
+ (digit [0-9])))
+@end group
+@end example
+
+@c FIXME: These two should be formally defined using @defmac and @defun.
+@findex with-peg-rules
+@findex peg-run
+The @code{peg-parse} macro represents the simplest use of the
+@acronym{PEG} library, but also the least flexible, as the rules must be
+written directly into the source code. A more flexible approach
+involves use of three macros in conjunction: @code{with-peg-rules}, a
+@code{let}-like construct that makes a set of rules available within the
+macro body; @code{peg-run}, which initiates parsing given a single rule;
+and @code{peg}, which is used to wrap the entry-point rule name. In
+fact, a call to @code{peg-parse} expands to just this set of calls. The
+above example could be written as:
@example
@group
@end group
@end example
-This approach allows more explicit control over the ``entry-point'' of
-parsing, and allows the combination of rules from different sources.
+This allows more explicit control over the ``entry-point'' of parsing,
+and allows the combination of rules from different sources.
+@c FIXME: Use @defmac.
+@findex define-peg-rule
Individual rules can also be defined using a more @code{defun}-like
syntax, using the macro @code{define-peg-rule}:
-@defmac define-peg-rule name args &rest pexs
-Define @var{name} as a PEG rule that accepts @var{args} and matches
-@var{pexs} at point.
-@end defmac
-
-For instance:
-
@example
@group
(define-peg-rule digit ()
@end group
@end example
-Arguments can be supplied to rules by the @code{funcall} PEG rule
-(@pxref{PEX Definitions}).
+This also allows for rules that accept an argument (supplied by the
+@code{funcall} PEG rule, @pxref{PEX Definitions}).
+@c FIXME: Use @defmac.
+@findex define-peg-ruleset
Another possibility is to define a named set of rules with
@code{define-peg-ruleset}:
-@defmac define-peg-ruleset name &rest rules
-Define @var{name} as an identifier for @var{rules}.
-@end defmac
-
@example
@group
(define-peg-ruleset number-grammar
Treats the value of the Lisp expression @var{exp} as a boolean.
@end table
+@c FIXME: peg-char-classes should be mentioned in the text below.
@vindex peg-char-classes
-Character-class matching can refer to the classes named in
-@code{peg-char-classes}, equivalent to character classes in regular
-expressions (@pxref{Top,, Character Classes,elisp})
+Character class matching can use the same named character classes as
+in regular expressions (@pxref{Top,, Character Classes,elisp})
@node Parsing Actions
@section Parsing Actions
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