hxt-8.0.0: doc/hdoc/src/Text-XML-HXT-Validator-RE.html
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<pre><a name="line-1"></a><span class='comment'>-- |</span>
<a name="line-2"></a><span class='comment'>-- A module for regular expression matching based on derivatives of regular expressions.</span>
<a name="line-3"></a><span class='comment'>--</span>
<a name="line-4"></a><span class='comment'>-- The code was taken from Joe English (<<a href="http://www.flightlab.com/~joe/sgml/validate.html">http://www.flightlab.com/~joe/sgml/validate.html</a>>).</span>
<a name="line-5"></a><span class='comment'>-- Tested and extended by Martin Schmidt.</span>
<a name="line-6"></a><span class='comment'>--</span>
<a name="line-7"></a><span class='comment'>-- Further references for the algorithm:</span>
<a name="line-8"></a><span class='comment'>--</span>
<a name="line-9"></a><span class='comment'>-- Janusz A. Brzozowski.</span>
<a name="line-10"></a><span class='comment'>--</span>
<a name="line-11"></a><span class='comment'>-- Derivatives of Regular Expressions. Journal of the ACM, Volume 11, Issue 4, 1964. </span>
<a name="line-12"></a><span class='comment'>--</span>
<a name="line-13"></a><span class='comment'>-- Mark Hopkins.</span>
<a name="line-14"></a><span class='comment'>--</span>
<a name="line-15"></a><span class='comment'>-- Regular Expression Package. Posted to comp.compilers, 1994.</span>
<a name="line-16"></a><span class='comment'>-- Available per FTP at <ftp://iecc.com/pub/file/regex.tar.gz>.</span>
<a name="line-17"></a><span class='comment'>--</span>
<a name="line-18"></a><span class='comment'>-- Version : $Id: RE.hs,v 1.1 2004/09/02 19:12:03 hxml Exp $</span>
<a name="line-19"></a>
<a name="line-20"></a><span class='keyword'>module</span> <span class='conid'>Text</span><span class='varop'>.</span><span class='conid'>XML</span><span class='varop'>.</span><span class='conid'>HXT</span><span class='varop'>.</span><span class='conid'>Validator</span><span class='varop'>.</span><span class='conid'>RE</span>
<a name="line-21"></a> <span class='layout'>(</span> <span class='conid'>RE</span><span class='layout'>(</span><span class='keyglyph'>..</span><span class='layout'>)</span>
<a name="line-22"></a>
<a name="line-23"></a> <span class='layout'>,</span> <span class='varid'>re_unit</span>
<a name="line-24"></a> <span class='layout'>,</span> <span class='varid'>re_zero</span>
<a name="line-25"></a> <span class='layout'>,</span> <span class='varid'>re_sym</span>
<a name="line-26"></a> <span class='layout'>,</span> <span class='varid'>re_rep</span>
<a name="line-27"></a> <span class='layout'>,</span> <span class='varid'>re_plus</span>
<a name="line-28"></a> <span class='layout'>,</span> <span class='varid'>re_opt</span>
<a name="line-29"></a> <span class='layout'>,</span> <span class='varid'>re_seq</span>
<a name="line-30"></a> <span class='layout'>,</span> <span class='varid'>re_alt</span>
<a name="line-31"></a> <span class='layout'>,</span> <span class='varid'>re_dot</span>
<a name="line-32"></a>
<a name="line-33"></a> <span class='layout'>,</span> <span class='varid'>checkRE</span>
<a name="line-34"></a> <span class='layout'>,</span> <span class='varid'>matches</span>
<a name="line-35"></a> <span class='layout'>,</span> <span class='varid'>nullable</span>
<a name="line-36"></a> <span class='layout'>,</span> <span class='varid'>printRE</span>
<a name="line-37"></a> <span class='layout'>)</span>
<a name="line-38"></a><span class='keyword'>where</span>
<a name="line-39"></a>
<a name="line-40"></a><span class='comment'>-- |</span>
<a name="line-41"></a><span class='comment'>-- Data type for regular expressions.</span>
<a name="line-42"></a>
<a name="line-43"></a><a name="RE"></a><span class='keyword'>data</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>=</span>
<a name="line-44"></a> <span class='conid'>RE_ZERO</span> <span class='conid'>String</span> <span class='comment'>--' L(0) = {} (empty set)</span>
<a name="line-45"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_UNIT</span> <span class='comment'>--' L(1) = { [] } (empty sequence)</span>
<a name="line-46"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_SYM</span> <span class='varid'>a</span> <span class='comment'>--' L(x) = { [x] }</span>
<a name="line-47"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_DOT</span> <span class='comment'>--' accept any single symbol</span>
<a name="line-48"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_REP</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='comment'>--' L(e*) = { [] } `union` L(e+)</span>
<a name="line-49"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_PLUS</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='comment'>--' L(e+) = { x ++ y | x <- L(e), y <- L(e*) }</span>
<a name="line-50"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_OPT</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='comment'>--' L(e?) = L(e) `union` { [] }</span>
<a name="line-51"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_SEQ</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='comment'>--' L(e,f) = { x ++ y | x <- L(e), y <- L(f) }</span>
<a name="line-52"></a> <span class='keyglyph'>|</span> <span class='conid'>RE_ALT</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='layout'>(</span><span class='conid'>RE</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='comment'>--' L(e|f) = L(e) `union` L(f)</span>
<a name="line-53"></a> <span class='keyword'>deriving</span> <span class='layout'>(</span><span class='conid'>Show</span><span class='layout'>,</span> <span class='conid'>Eq</span><span class='layout'>)</span>
<a name="line-54"></a>
<a name="line-55"></a>
<a name="line-56"></a>
<a name="line-57"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-58"></a><span class='comment'>-- Constructor functions to simplify regular expressions when constructing them.</span>
<a name="line-59"></a>
<a name="line-60"></a><span class='comment'>-- |</span>
<a name="line-61"></a><span class='comment'>-- Constructs a regular expression for an empty set.</span>
<a name="line-62"></a><span class='comment'>--</span>
<a name="line-63"></a><span class='comment'>-- * 1.parameter errMsg : error message</span>
<a name="line-64"></a><span class='comment'>--</span>
<a name="line-65"></a><span class='comment'>-- - returns : regular expression for an empty set</span>
<a name="line-66"></a>
<a name="line-67"></a><a name="re_zero"></a><span class='definition'>re_zero</span> <span class='keyglyph'>::</span> <span class='conid'>String</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-68"></a><span class='definition'>re_zero</span> <span class='varid'>m</span> <span class='keyglyph'>=</span> <span class='conid'>RE_ZERO</span> <span class='varid'>m</span>
<a name="line-69"></a>
<a name="line-70"></a>
<a name="line-71"></a><span class='comment'>-- |</span>
<a name="line-72"></a><span class='comment'>-- Constructs a regular expression for an empty sequence.</span>
<a name="line-73"></a><span class='comment'>--</span>
<a name="line-74"></a><span class='comment'>-- - returns : regular expression for an empty sequence</span>
<a name="line-75"></a>
<a name="line-76"></a><a name="re_unit"></a><span class='definition'>re_unit</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-77"></a><span class='definition'>re_unit</span> <span class='keyglyph'>=</span> <span class='conid'>RE_UNIT</span>
<a name="line-78"></a>
<a name="line-79"></a>
<a name="line-80"></a><span class='comment'>-- |</span>
<a name="line-81"></a><span class='comment'>-- Constructs a regular expression for accepting a symbol</span>
<a name="line-82"></a><span class='comment'>--</span>
<a name="line-83"></a><span class='comment'>-- * 1.parameter sym : the symbol to be accepted</span>
<a name="line-84"></a><span class='comment'>--</span>
<a name="line-85"></a><span class='comment'>-- - returns : regular expression for accepting a symbol</span>
<a name="line-86"></a>
<a name="line-87"></a><a name="re_sym"></a><span class='definition'>re_sym</span> <span class='keyglyph'>::</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-88"></a><span class='definition'>re_sym</span> <span class='varid'>x</span> <span class='keyglyph'>=</span> <span class='conid'>RE_SYM</span> <span class='varid'>x</span>
<a name="line-89"></a>
<a name="line-90"></a>
<a name="line-91"></a><span class='comment'>-- |</span>
<a name="line-92"></a><span class='comment'>-- Constructs a regular expression for accepting any singel symbol</span>
<a name="line-93"></a><span class='comment'>--</span>
<a name="line-94"></a><span class='comment'>-- - returns : regular expression for accepting any singel symbol</span>
<a name="line-95"></a>
<a name="line-96"></a><a name="re_dot"></a><span class='definition'>re_dot</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-97"></a><span class='definition'>re_dot</span> <span class='keyglyph'>=</span> <span class='conid'>RE_DOT</span>
<a name="line-98"></a>
<a name="line-99"></a>
<a name="line-100"></a><span class='comment'>-- |</span>
<a name="line-101"></a><span class='comment'>-- Constructs an optional repetition (*) of a regular expression</span>
<a name="line-102"></a><span class='comment'>--</span>
<a name="line-103"></a><span class='comment'>-- * 1.parameter re_a : regular expression to be repeted</span>
<a name="line-104"></a><span class='comment'>--</span>
<a name="line-105"></a><span class='comment'>-- - returns : new regular expression</span>
<a name="line-106"></a>
<a name="line-107"></a><a name="re_rep"></a><span class='definition'>re_rep</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-108"></a><span class='definition'>re_rep</span> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>=</span> <span class='conid'>RE_UNIT</span>
<a name="line-109"></a><span class='definition'>re_rep</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_UNIT</span>
<a name="line-110"></a><span class='definition'>re_rep</span> <span class='varid'>e</span><span class='keyglyph'>@</span><span class='layout'>(</span><span class='conid'>RE_REP</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_REP</span> <span class='layout'>(</span><span class='varid'>rem_rep</span> <span class='varid'>e</span><span class='layout'>)</span> <span class='comment'>-- remove nested reps</span>
<a name="line-111"></a><span class='definition'>re_rep</span> <span class='varid'>e</span><span class='keyglyph'>@</span><span class='layout'>(</span><span class='conid'>RE_ALT</span> <span class='keyword'>_</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_REP</span> <span class='layout'>(</span><span class='varid'>rem_rep</span> <span class='varid'>e</span><span class='layout'>)</span> <span class='comment'>-- remove nested reps in alternatives</span>
<a name="line-112"></a><span class='definition'>re_rep</span> <span class='varid'>e</span> <span class='keyglyph'>=</span> <span class='conid'>RE_REP</span> <span class='varid'>e</span>
<a name="line-113"></a>
<a name="line-114"></a><span class='comment'>-- |</span>
<a name="line-115"></a><span class='comment'>-- remove redundant nested *'s in RE</span>
<a name="line-116"></a><span class='comment'>-- theoretically this is unneccessary,</span>
<a name="line-117"></a><span class='comment'>-- but without this simplification the runtime can increase exponentally</span>
<a name="line-118"></a><span class='comment'>-- when computing deltas, e.g. for a** or (a|b*)* which is the same as (a|b)*</span>
<a name="line-119"></a>
<a name="line-120"></a><a name="rem_rep"></a><span class='definition'>rem_rep</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-121"></a><span class='definition'>rem_rep</span> <span class='layout'>(</span><span class='conid'>RE_ALT</span> <span class='varid'>e1</span> <span class='varid'>e2</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_ALT</span> <span class='layout'>(</span><span class='varid'>rem_rep</span> <span class='varid'>e1</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>rem_rep</span> <span class='varid'>e2</span><span class='layout'>)</span>
<a name="line-122"></a><span class='definition'>rem_rep</span> <span class='layout'>(</span><span class='conid'>RE_REP</span> <span class='varid'>e1</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>rem_rep</span> <span class='varid'>e1</span>
<a name="line-123"></a><span class='definition'>rem_rep</span> <span class='varid'>e1</span> <span class='keyglyph'>=</span> <span class='varid'>e1</span>
<a name="line-124"></a>
<a name="line-125"></a>
<a name="line-126"></a><span class='comment'>-- |</span>
<a name="line-127"></a><span class='comment'>-- Constructs a repetition (+) of a regular expression</span>
<a name="line-128"></a><span class='comment'>--</span>
<a name="line-129"></a><span class='comment'>-- * 1.parameter re_a : regular expression to be repeted</span>
<a name="line-130"></a><span class='comment'>--</span>
<a name="line-131"></a><span class='comment'>-- - returns : new regular expression</span>
<a name="line-132"></a>
<a name="line-133"></a><a name="re_plus"></a><span class='definition'>re_plus</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-134"></a><span class='definition'>re_plus</span> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>=</span> <span class='conid'>RE_UNIT</span>
<a name="line-135"></a><span class='definition'>re_plus</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='varid'>m</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_ZERO</span> <span class='varid'>m</span>
<a name="line-136"></a><span class='definition'>re_plus</span> <span class='varid'>e</span> <span class='keyglyph'>=</span> <span class='conid'>RE_PLUS</span> <span class='varid'>e</span>
<a name="line-137"></a>
<a name="line-138"></a>
<a name="line-139"></a><span class='comment'>-- |</span>
<a name="line-140"></a><span class='comment'>-- Constructs an option (?) of a regular expression</span>
<a name="line-141"></a><span class='comment'>--</span>
<a name="line-142"></a><span class='comment'>-- * 1.parameter re_a : regular expression to be optional</span>
<a name="line-143"></a><span class='comment'>--</span>
<a name="line-144"></a><span class='comment'>-- - returns : new regular expression</span>
<a name="line-145"></a>
<a name="line-146"></a><a name="re_opt"></a><span class='definition'>re_opt</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-147"></a><span class='definition'>re_opt</span> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>=</span> <span class='conid'>RE_UNIT</span>
<a name="line-148"></a><span class='definition'>re_opt</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_UNIT</span>
<a name="line-149"></a><span class='definition'>re_opt</span> <span class='varid'>e</span> <span class='keyglyph'>=</span> <span class='conid'>RE_OPT</span> <span class='varid'>e</span>
<a name="line-150"></a>
<a name="line-151"></a>
<a name="line-152"></a><span class='comment'>-- |</span>
<a name="line-153"></a><span class='comment'>-- Constructs a sequence (,) of two regular expressions</span>
<a name="line-154"></a><span class='comment'>--</span>
<a name="line-155"></a><span class='comment'>-- * 1.parameter re_a : first regular expression in sequence</span>
<a name="line-156"></a><span class='comment'>--</span>
<a name="line-157"></a><span class='comment'>-- - 2.parameter re_b : second regular expression in sequence</span>
<a name="line-158"></a><span class='comment'>--</span>
<a name="line-159"></a><span class='comment'>-- - returns : new regular expression</span>
<a name="line-160"></a>
<a name="line-161"></a><a name="re_seq"></a><span class='definition'>re_seq</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-162"></a><span class='definition'>re_seq</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='varid'>m</span><span class='layout'>)</span> <span class='keyword'>_</span> <span class='keyglyph'>=</span> <span class='conid'>RE_ZERO</span> <span class='varid'>m</span>
<a name="line-163"></a><span class='definition'>re_seq</span> <span class='conid'>RE_UNIT</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>f</span>
<a name="line-164"></a><span class='definition'>re_seq</span> <span class='keyword'>_</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='varid'>m</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>RE_ZERO</span> <span class='varid'>m</span>
<a name="line-165"></a><span class='definition'>re_seq</span> <span class='varid'>e</span> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>=</span> <span class='varid'>e</span>
<a name="line-166"></a><span class='definition'>re_seq</span> <span class='varid'>e</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='conid'>RE_SEQ</span> <span class='varid'>e</span> <span class='varid'>f</span>
<a name="line-167"></a>
<a name="line-168"></a>
<a name="line-169"></a><span class='comment'>-- |</span>
<a name="line-170"></a><span class='comment'>-- Constructs an alternative (|) of two regular expressions</span>
<a name="line-171"></a><span class='comment'>--</span>
<a name="line-172"></a><span class='comment'>-- * 1.parameter re_a : first regular expression of alternative</span>
<a name="line-173"></a><span class='comment'>--</span>
<a name="line-174"></a><span class='comment'>-- - 2.parameter re_b : second regular expression of alternative</span>
<a name="line-175"></a><span class='comment'>--</span>
<a name="line-176"></a><span class='comment'>-- - returns : new regular expression</span>
<a name="line-177"></a>
<a name="line-178"></a><a name="re_alt"></a><span class='definition'>re_alt</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-179"></a><span class='definition'>re_alt</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='varid'>f</span>
<a name="line-180"></a><span class='definition'>re_alt</span> <span class='varid'>e</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>e</span>
<a name="line-181"></a><span class='definition'>re_alt</span> <span class='varid'>e</span> <span class='varid'>f</span> <span class='keyglyph'>=</span> <span class='conid'>RE_ALT</span> <span class='varid'>e</span> <span class='varid'>f</span>
<a name="line-182"></a>
<a name="line-183"></a>
<a name="line-184"></a>
<a name="line-185"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-186"></a>
<a name="line-187"></a>
<a name="line-188"></a><span class='comment'>-- |</span>
<a name="line-189"></a><span class='comment'>-- Checks if a regular expression matches the empty sequence.</span>
<a name="line-190"></a><span class='comment'>--</span>
<a name="line-191"></a><span class='comment'>-- nullable e == [] `in` L(e)</span>
<a name="line-192"></a><span class='comment'>--</span>
<a name="line-193"></a><span class='comment'>-- This check indicates if a regular expression fits to a sentence or not.</span>
<a name="line-194"></a><span class='comment'>--</span>
<a name="line-195"></a><span class='comment'>-- * 1.parameter re : regular expression to be checked</span>
<a name="line-196"></a><span class='comment'>--</span>
<a name="line-197"></a><span class='comment'>-- - returns : true if regular expression matches the empty sequence,</span>
<a name="line-198"></a><span class='comment'>-- otherwise false</span>
<a name="line-199"></a>
<a name="line-200"></a><a name="nullable"></a><span class='definition'>nullable</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='conid'>Show</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span>
<a name="line-201"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
<a name="line-202"></a><span class='definition'>nullable</span> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-203"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_SYM</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
<a name="line-204"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_REP</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-205"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_PLUS</span> <span class='varid'>e</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>nullable</span> <span class='varid'>e</span>
<a name="line-206"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_OPT</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-207"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_SEQ</span> <span class='varid'>e</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>nullable</span> <span class='varid'>e</span> <span class='varop'>&&</span> <span class='varid'>nullable</span> <span class='varid'>f</span>
<a name="line-208"></a><span class='definition'>nullable</span> <span class='layout'>(</span><span class='conid'>RE_ALT</span> <span class='varid'>e</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>nullable</span> <span class='varid'>e</span> <span class='varop'>||</span> <span class='varid'>nullable</span> <span class='varid'>f</span>
<a name="line-209"></a><span class='definition'>nullable</span> <span class='conid'>RE_DOT</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
<a name="line-210"></a>
<a name="line-211"></a>
<a name="line-212"></a><span class='comment'>-- |</span>
<a name="line-213"></a><span class='comment'>-- Derives a regular expression with respect to one symbol.</span>
<a name="line-214"></a><span class='comment'>--</span>
<a name="line-215"></a><span class='comment'>-- L(delta e x) = x \ L(e)</span>
<a name="line-216"></a><span class='comment'>--</span>
<a name="line-217"></a><span class='comment'>-- * 1.parameter re : regular expression to be derived</span>
<a name="line-218"></a><span class='comment'>--</span>
<a name="line-219"></a><span class='comment'>-- - 2.parameter sym : the symbol on which the regular expression is applied</span>
<a name="line-220"></a><span class='comment'>--</span>
<a name="line-221"></a><span class='comment'>-- - returns : the derived regular expression</span>
<a name="line-222"></a>
<a name="line-223"></a><a name="delta"></a><span class='definition'>delta</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='conid'>Eq</span> <span class='varid'>a</span><span class='layout'>,</span> <span class='conid'>Show</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-224"></a><span class='definition'>delta</span> <span class='varid'>re</span> <span class='varid'>x</span> <span class='keyglyph'>=</span> <span class='keyword'>case</span> <span class='varid'>re</span> <span class='keyword'>of</span>
<a name="line-225"></a> <span class='conid'>RE_ZERO</span> <span class='keyword'>_</span> <span class='keyglyph'>-></span> <span class='varid'>re</span> <span class='comment'>-- re_zero m</span>
<a name="line-226"></a> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>-></span> <span class='varid'>re_zero</span> <span class='layout'>(</span><span class='str'>"Symbol "</span> <span class='varop'>++</span> <span class='varid'>show</span> <span class='varid'>x</span> <span class='varop'>++</span> <span class='str'>" unexpected."</span><span class='layout'>)</span>
<a name="line-227"></a> <span class='conid'>RE_SYM</span> <span class='varid'>sym</span>
<a name="line-228"></a> <span class='keyglyph'>|</span> <span class='varid'>x</span> <span class='varop'>==</span> <span class='varid'>sym</span> <span class='keyglyph'>-></span> <span class='varid'>re_unit</span>
<a name="line-229"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='varid'>re_zero</span> <span class='layout'>(</span><span class='str'>"Symbol "</span> <span class='varop'>++</span> <span class='varid'>show</span> <span class='varid'>sym</span> <span class='varop'>++</span> <span class='str'>" expected, but symbol "</span> <span class='varop'>++</span> <span class='varid'>show</span> <span class='varid'>x</span> <span class='varop'>++</span> <span class='str'>" found."</span><span class='layout'>)</span>
<a name="line-230"></a> <span class='conid'>RE_REP</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>re_seq</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>e</span> <span class='varid'>x</span><span class='layout'>)</span> <span class='varid'>re</span> <span class='comment'>-- (re_rep e)</span>
<a name="line-231"></a> <span class='conid'>RE_PLUS</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>re_seq</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>e</span> <span class='varid'>x</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>re_rep</span> <span class='varid'>e</span><span class='layout'>)</span>
<a name="line-232"></a> <span class='conid'>RE_OPT</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>delta</span> <span class='varid'>e</span> <span class='varid'>x</span>
<a name="line-233"></a> <span class='conid'>RE_SEQ</span> <span class='varid'>e</span> <span class='varid'>f</span>
<a name="line-234"></a> <span class='keyglyph'>|</span> <span class='varid'>nullable</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>re_alt</span> <span class='layout'>(</span><span class='varid'>re_seq</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>e</span> <span class='varid'>x</span><span class='layout'>)</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>f</span> <span class='varid'>x</span><span class='layout'>)</span>
<a name="line-235"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='varid'>re_seq</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>e</span> <span class='varid'>x</span><span class='layout'>)</span> <span class='varid'>f</span>
<a name="line-236"></a> <span class='conid'>RE_ALT</span> <span class='varid'>e</span> <span class='varid'>f</span> <span class='keyglyph'>-></span> <span class='varid'>re_alt</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>e</span> <span class='varid'>x</span><span class='layout'>)</span> <span class='layout'>(</span><span class='varid'>delta</span> <span class='varid'>f</span> <span class='varid'>x</span><span class='layout'>)</span>
<a name="line-237"></a> <span class='conid'>RE_DOT</span> <span class='keyglyph'>-></span> <span class='varid'>re_unit</span>
<a name="line-238"></a>
<a name="line-239"></a>
<a name="line-240"></a><span class='comment'>-- |</span>
<a name="line-241"></a><span class='comment'>-- Derives a regular expression with respect to a sentence.</span>
<a name="line-242"></a><span class='comment'>--</span>
<a name="line-243"></a><span class='comment'>-- * 1.parameter re : regular expression</span>
<a name="line-244"></a><span class='comment'>--</span>
<a name="line-245"></a><span class='comment'>-- - 2.parameter s : sentence to which the regular expression is applied</span>
<a name="line-246"></a><span class='comment'>--</span>
<a name="line-247"></a><span class='comment'>-- - returns : the derived regular expression</span>
<a name="line-248"></a>
<a name="line-249"></a><a name="matches"></a><span class='definition'>matches</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='conid'>Eq</span> <span class='varid'>a</span><span class='layout'>,</span> <span class='conid'>Show</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='keyglyph'>[</span><span class='varid'>a</span><span class='keyglyph'>]</span> <span class='keyglyph'>-></span> <span class='conid'>RE</span> <span class='varid'>a</span>
<a name="line-250"></a><span class='definition'>matches</span> <span class='varid'>e</span> <span class='keyglyph'>=</span> <span class='varid'>foldl</span> <span class='varid'>delta</span> <span class='varid'>e</span>
<a name="line-251"></a>
<a name="line-252"></a>
<a name="line-253"></a><span class='comment'>-- |</span>
<a name="line-254"></a><span class='comment'>-- Checks if an input matched a regular expression. The function should be</span>
<a name="line-255"></a><span class='comment'>-- called after matches.</span>
<a name="line-256"></a><span class='comment'>--</span>
<a name="line-257"></a><span class='comment'>-- Was the sentence used in @matches@ in the language of the regular expression?</span>
<a name="line-258"></a><span class='comment'>-- -> matches e s == s `in` L(e)?</span>
<a name="line-259"></a><span class='comment'>--</span>
<a name="line-260"></a><span class='comment'>-- * 1.parameter re : the derived regular expression</span>
<a name="line-261"></a><span class='comment'>--</span>
<a name="line-262"></a><span class='comment'>-- - returns : empty String if input matched the regular expression, otherwise</span>
<a name="line-263"></a><span class='comment'>-- an error message is returned</span>
<a name="line-264"></a>
<a name="line-265"></a><a name="checkRE"></a><span class='definition'>checkRE</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='conid'>Show</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>String</span>
<a name="line-266"></a><span class='definition'>checkRE</span> <span class='layout'>(</span><span class='conid'>RE_UNIT</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='str'>""</span>
<a name="line-267"></a><span class='definition'>checkRE</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='varid'>m</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='varid'>m</span>
<a name="line-268"></a><span class='definition'>checkRE</span> <span class='varid'>re</span>
<a name="line-269"></a> <span class='keyglyph'>|</span> <span class='varid'>nullable</span> <span class='varid'>re</span> <span class='keyglyph'>=</span> <span class='str'>""</span>
<a name="line-270"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>=</span> <span class='str'>"Input must match "</span> <span class='varop'>++</span> <span class='varid'>printRE</span> <span class='varid'>re</span>
<a name="line-271"></a>
<a name="line-272"></a>
<a name="line-273"></a>
<a name="line-274"></a><span class='comment'>-- ------------------------------------------------------------</span>
<a name="line-275"></a>
<a name="line-276"></a>
<a name="line-277"></a>
<a name="line-278"></a><span class='comment'>-- |</span>
<a name="line-279"></a><span class='comment'>-- Constructs a string representation of a regular expression.</span>
<a name="line-280"></a><span class='comment'>--</span>
<a name="line-281"></a><span class='comment'>-- * 1.parameter re : a regular expression</span>
<a name="line-282"></a><span class='comment'>--</span>
<a name="line-283"></a><span class='comment'>-- - returns : the string representation of the regular expression</span>
<a name="line-284"></a>
<a name="line-285"></a><a name="printRE"></a><span class='definition'>printRE</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='conid'>Show</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>String</span>
<a name="line-286"></a><span class='definition'>printRE</span> <span class='varid'>re'</span>
<a name="line-287"></a> <span class='keyglyph'>=</span> <span class='str'>"( "</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>re'</span> <span class='varop'>++</span> <span class='str'>" )"</span>
<a name="line-288"></a> <span class='keyword'>where</span>
<a name="line-289"></a> <span class='varid'>printRE1</span> <span class='keyglyph'>::</span> <span class='layout'>(</span><span class='conid'>Show</span> <span class='varid'>a</span><span class='layout'>)</span> <span class='keyglyph'>=></span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>String</span>
<a name="line-290"></a> <span class='varid'>printRE1</span> <span class='varid'>re</span> <span class='keyglyph'>=</span> <span class='keyword'>case</span> <span class='varid'>re</span> <span class='keyword'>of</span>
<a name="line-291"></a> <span class='conid'>RE_ZERO</span> <span class='varid'>m</span> <span class='keyglyph'>-></span> <span class='str'>"ERROR: "</span> <span class='varop'>++</span> <span class='varid'>m</span>
<a name="line-292"></a> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>-></span> <span class='str'>""</span>
<a name="line-293"></a> <span class='conid'>RE_SYM</span> <span class='varid'>sym</span> <span class='keyglyph'>-></span> <span class='varid'>show</span> <span class='varid'>sym</span>
<a name="line-294"></a> <span class='conid'>RE_DOT</span> <span class='keyglyph'>-></span> <span class='str'>"."</span>
<a name="line-295"></a> <span class='conid'>RE_REP</span> <span class='varid'>e</span>
<a name="line-296"></a> <span class='keyglyph'>|</span> <span class='varid'>isSingle</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>"*"</span>
<a name="line-297"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>")*"</span>
<a name="line-298"></a> <span class='conid'>RE_PLUS</span> <span class='varid'>e</span>
<a name="line-299"></a> <span class='keyglyph'>|</span> <span class='varid'>isSingle</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>"+"</span>
<a name="line-300"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>")+"</span>
<a name="line-301"></a> <span class='conid'>RE_OPT</span> <span class='varid'>e</span>
<a name="line-302"></a> <span class='keyglyph'>|</span> <span class='varid'>isSingle</span> <span class='varid'>e</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>"?"</span>
<a name="line-303"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>")?"</span>
<a name="line-304"></a> <span class='conid'>RE_SEQ</span> <span class='varid'>e</span> <span class='varid'>f</span>
<a name="line-305"></a> <span class='keyglyph'>|</span> <span class='varid'>isAlt</span> <span class='varid'>e</span> <span class='varop'>&&</span> <span class='varid'>not</span> <span class='layout'>(</span><span class='varid'>isAlt</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>") , "</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span>
<a name="line-306"></a> <span class='keyglyph'>|</span> <span class='varid'>not</span> <span class='layout'>(</span><span class='varid'>isAlt</span> <span class='varid'>e</span><span class='layout'>)</span> <span class='varop'>&&</span> <span class='varid'>isAlt</span> <span class='varid'>f</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>" , ("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span> <span class='varop'>++</span> <span class='str'>")"</span>
<a name="line-307"></a> <span class='keyglyph'>|</span> <span class='varid'>isAlt</span> <span class='varid'>e</span> <span class='varop'>&&</span> <span class='varid'>isAlt</span> <span class='varid'>f</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>") , ("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span> <span class='varop'>++</span> <span class='str'>")"</span>
<a name="line-308"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>" , "</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span>
<a name="line-309"></a> <span class='conid'>RE_ALT</span> <span class='varid'>e</span> <span class='varid'>f</span>
<a name="line-310"></a> <span class='keyglyph'>|</span> <span class='varid'>isSeq</span> <span class='varid'>e</span> <span class='varop'>&&</span> <span class='varid'>not</span> <span class='layout'>(</span><span class='varid'>isSeq</span> <span class='varid'>f</span><span class='layout'>)</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>") | "</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span>
<a name="line-311"></a> <span class='keyglyph'>|</span> <span class='varid'>not</span> <span class='layout'>(</span><span class='varid'>isSeq</span> <span class='varid'>e</span><span class='layout'>)</span> <span class='varop'>&&</span> <span class='varid'>isSeq</span> <span class='varid'>f</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>" | ("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span> <span class='varop'>++</span> <span class='str'>")"</span>
<a name="line-312"></a> <span class='keyglyph'>|</span> <span class='varid'>isSeq</span> <span class='varid'>e</span> <span class='varop'>&&</span> <span class='varid'>isSeq</span> <span class='varid'>f</span> <span class='keyglyph'>-></span> <span class='str'>"("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>") | ("</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span> <span class='varop'>++</span> <span class='str'>")"</span>
<a name="line-313"></a> <span class='keyglyph'>|</span> <span class='varid'>otherwise</span> <span class='keyglyph'>-></span> <span class='varid'>printRE1</span> <span class='varid'>e</span> <span class='varop'>++</span> <span class='str'>" | "</span> <span class='varop'>++</span> <span class='varid'>printRE1</span> <span class='varid'>f</span>
<a name="line-314"></a>
<a name="line-315"></a>
<a name="line-316"></a> <span class='varid'>isSingle</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span>
<a name="line-317"></a> <span class='varid'>isSingle</span> <span class='layout'>(</span><span class='conid'>RE_ZERO</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-318"></a> <span class='varid'>isSingle</span> <span class='conid'>RE_UNIT</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-319"></a> <span class='varid'>isSingle</span> <span class='layout'>(</span><span class='conid'>RE_SYM</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-320"></a> <span class='varid'>isSingle</span> <span class='keyword'>_</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
<a name="line-321"></a>
<a name="line-322"></a>
<a name="line-323"></a> <span class='varid'>isSeq</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span>
<a name="line-324"></a> <span class='varid'>isSeq</span> <span class='layout'>(</span><span class='conid'>RE_SEQ</span> <span class='keyword'>_</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-325"></a> <span class='varid'>isSeq</span> <span class='keyword'>_</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
<a name="line-326"></a>
<a name="line-327"></a>
<a name="line-328"></a> <span class='varid'>isAlt</span> <span class='keyglyph'>::</span> <span class='conid'>RE</span> <span class='varid'>a</span> <span class='keyglyph'>-></span> <span class='conid'>Bool</span>
<a name="line-329"></a> <span class='varid'>isAlt</span> <span class='layout'>(</span><span class='conid'>RE_ALT</span> <span class='keyword'>_</span> <span class='keyword'>_</span><span class='layout'>)</span> <span class='keyglyph'>=</span> <span class='conid'>True</span>
<a name="line-330"></a> <span class='varid'>isAlt</span> <span class='keyword'>_</span> <span class='keyglyph'>=</span> <span class='conid'>False</span>
</pre></body>
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