This page describes an elisp implementation of the bidi algorithm described in UAX#9.
As Emacs already supports bidirectional display out of the box, this code is simply for educational use. 

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The implementation supports implicit bidirectionality. The
implicit bidirectional algorithm and the directional marks RLM and LRM
are supported.  Full bidirectionality would entail the implicit
bidirectional algorithm, the implicit directional marks, and the
explicit directional embedding codes: RLM, LRM, LRE, RLE, LRO, RLO,
PDF.

The implementation can transform logical to
visual order and back.  The visual to logical transformation may be
usefull to convert text from the clipboard, assuming that other
applications put text in visual order into the clipboard.

* [https://alexschroeder.ch/cgit/emacs-bidi/about/ emacs-bidi]

The algorithm needs tables that classify characters according to
the bidi types used in the Unicode Tech Report, UAX#9.  These tables
use the bidi type classification from unicode.org, and it uses this
info for all the 8859 charsets.  This is in ##bidi-table.el## – about
500k.

There is also a test table which only sets bidi types for ASCII
characters and which uses the bidi type R (like Hebrew and Arabic) for
capital letters.  This is great when tinkering with the code and when
writing test cases in plain ASCII.  This is in ##bidi-table-test.el##
– about 5k.

The classification of characters in Emacs relies on Category tables.
In Emacs, these categories can be modified on the Lisp level.  Since I
didn't want to reserve any categories, I'm getting some unused
categories when bidi.el is loaded.  This seems not to work in XEmacs.

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CategoryInternationalization