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@@ -12,7 +12,7 @@
 
 <h4>Packrat Parser Combinator Library</h4>
 
-<p>Git repository: <a href="/cgit/cgit.cgi/packrat">Link</a><br>
+<p>Git repository: <a href="/cgit/cgit.cgi/packrat">Link</a><br />
 Paper this was based on: <a href="http://richard.myweb.cs.uwindsor.ca/PUBLICATIONS/PREPRINT_PADL_NOV_07.pdf">Link</a></p>
 
 <h5>2/2/2021</h5>
@@ -20,17 +20,16 @@ Paper this was based on: <a href="http://richard.myweb.cs.uwindsor.ca/PUBLICATIO
 
 <h5>Overview</h5>
 
-<p>Parser combinators are what you end up with when you start factoring out common pieces of functionality from
-<a href="http://www.engr.mun.ca/~theo/Misc/exp_parsing.htm">recursive descent parsing</a>. They are higher order
-functions that can be combined in modular ways to create a desired parser.</p>
+<p>Parser combinators are what you end up with when you start factoring out common pieces of
+functionality from <a href="http://www.engr.mun.ca/~theo/Misc/exp_parsing.htm">recursive descent parsing</a>. They are higher order functions that can be combined in modular ways to create a desired parser.</p>
 
-<p>However they also inherit the drawbacks of recursive descent parsing, and in particular recursive descent
-parsing with backtracking. If the grammar that the parser is designed to accept contains left recursion then
-the parser will loop infinitely. If the grammar is ambiguous then only one result will be obtained. And any result
-may require exponential time and space to calculate.</p>
+<p>However they also inherit the drawbacks of recursive descent parsing, and in particular recursive
+descent parsing with backtracking. If the grammar that the parser is designed to accept contains
+left recursion then the parser will loop infinitely. If the grammar is ambiguous then only one
+result will be obtained. And any result may require exponential time and space to calculate.</p>
 
-<p>This library, based on the paper linked at the top, solves all those problems and a few bits more. As an
-example, the following grammar portion:</p>
+<p>This library, based on the paper linked at the top, solves all those problems and a few bits
+more. As an example, the following grammar portion:</p>
 
 <div class="precontain">
 <pre>
@@ -65,74 +64,81 @@ function Expression is new Stamp (Expression_Label, Expr_Choice);
 </code>
 </div>
 
-<p>Most of the verbosity is caused by the need to individually instantiate each combinator, as generics are
-used to serve the same purpose as higher order functions. Some bits are also omitted, such as the label
-enumeration and the actual setting of the redirectors. But the above should provide a good general
-impression.</p>
+<p>Most of the verbosity is caused by the need to individually instantiate each combinator, as
+generics are used to serve the same purpose as higher order functions. Some bits are also omitted,
+such as the label enumeration and the actual setting of the redirectors. But the above should
+provide a good general impression.</p>
 
 
 <h5>Features</h5>
 
 <p>A list of features that this library provides includes:</p>
 <ul>
-  <li>Higher order combinator functions in Ada, a language that does not support functional programming</li>
+  <li>Higher order combinator functions in Ada, a language that does not support functional
+  programming</li>
   <li>Both parser combinators and simpler lexer combinators are available</li>
   <li>Input can be any array, whether that is text strings or otherwise</li>
   <li>Left recursive grammars are parsed correctly with no infinite loops</li>
-  <li>Ambiguity is handled by incorporating all possible valid options into the resulting parse tree</li>
-  <li>Parsing and lexing can both be done piecewise, providing input in successive parts instead of all at once</li>
-  <li>Error messages are generated when applicable that note what would have been needed and where for a successful parse</li>
+  <li>Ambiguity is handled by incorporating all possible valid options into the resulting parse tree
+  </li>
+  <li>Parsing and lexing can both be done piecewise, providing input in successive parts instead of
+  all at once</li>
+  <li>Error messages are generated when applicable that note what would have been needed and where
+  for a successful parse</li>
   <li>All of the above is accomplished in polynomial worst case time and space complexity</li>
 </ul>
 
 <p>More thorough documentation is provided in the <em>/doc</em> directory.</p>
 
-<p>The name of the library comes from <a href="https://bford.info/pub/lang/packrat-icfp02.pdf">packrat parsing</a>
-which is a parsing algorithm that avoids exponential time complexity by memoizing all intermediate results. As that
-is what this library does, both so as to reduce the time complexity and to enable piecewise parsing, the name
-seemed appropriate.</p>
+<p>The name of the library comes from <a href="https://bford.info/pub/lang/packrat-icfp02.pdf">packrat parsing</a> which is a parsing algorithm that avoids exponential time complexity by memoizing all intermediate results. As that is what this library does, both so as to reduce the time complexity
+and to enable piecewise parsing, the name seemed appropriate.</p>
 
 
 <h5>Left Recursion</h5>
 
-<p>Direct left recursion, meaning a grammar non-terminal that immediately recurses to itself on the left as in
-the <em>Expression</em> or <em>Term</em> used above, is fairly easy to handle. A counter is used to keep track
-of how many times a particular combinator has been applied to the input at a particular position, and when that
-counter exceeds the number of unconsumed input tokens plus one the result is curtailed. This is explained on
-pages 7 and 8 of the paper.</p>
-
-<p>The really thorny issue that caused the most problems with this library is indirect left recursion. This is
-when a non-terminal recurses to itself on the left only after first evaluating to one or more other non-terminals.
-Curtailment in these circumstances can easily cause those other non-terminals to also be curtailed, and reusing
-the results for those other non-terminals may be incorrect. This issue along with a proposed solution is
-explained on page 9 of the paper. However that solution was not as clear as would be preferred. So some minor
-rephrasing and reworking was needed.</p>
-
-<p>Bringing this problem back to the start: What are we really doing when we curtail a result due to left
-recursion? It is not a matter of cutting off branches in a parse tree. We are identifying conditions where the
-parse result of a particular non-terminal can be calculated without further recursion. The word "curtailment" is
-somewhat misleading in this regard. Once this reframing is done then a clearer view immediately follows.</p>
-
-<p>What is the condition? Exactly as described above for direct left recursion. Through comparing recursion counts
-with the amount of unconsumed input we determine that a result of no successful parse can be calculated, and that
-the result is valid for reuse for any deeper recursion of the same combinator at that input position.</p>
+<p>Direct left recursion, meaning a grammar non-terminal that immediately recurses to itself on the
+left as in the <em>Expression</em> or <em>Term</em> used above, is fairly easy to handle. A counter
+is used to keep track of how many times a particular combinator has been applied to the input at a
+particular position, and when that counter exceeds the number of unconsumed input tokens plus one
+the result is curtailed. This is explained on pages 7 and 8 of the paper.</p>
+
+<p>The really thorny issue that caused the most problems with this library is indirect left
+recursion. This is when a non-terminal recurses to itself on the left only after first evaluating to
+one or more other non-terminals. Curtailment in these circumstances can easily cause those other
+non-terminals to also be curtailed, and reusing the results for those other non-terminals may be
+incorrect. This issue along with a proposed solution is explained on page 9 of the paper. However
+that solution was not as clear as would be preferred. So some minor rephrasing and reworking was
+needed.</p>
+
+<p>Bringing this problem back to the start: What are we really doing when we curtail a result due to
+left recursion? It is not a matter of cutting off branches in a parse tree. We are identifying
+conditions where the parse result of a particular non-terminal can be calculated without further
+recursion. The word "curtailment" is somewhat misleading in this regard. Once this reframing is done
+then a clearer view immediately follows.</p>
+
+<p>What is the condition? Exactly as described above for direct left recursion. Through comparing
+recursion counts with the amount of unconsumed input we determine that a result of no successful
+parse can be calculated, and that the result is valid for reuse for any deeper recursion of the same combinator at that input position.</p>
 
 <p>From that can be derived:</p>
 <ul>
-  <li>When merging two results that have different left recursion count conditions for the same non-terminal,
-  the larger count should be used</li>
-  <li>Conditions of subresults should also be made part of any result that includes those subresults</li>
-  <li>Any memoized result is only reusable if all the recursion count conditions of the stored result are less
-  than or equal to the recursion counts for the current input position</li>
+  <li>When merging two results that have different left recursion count conditions for the same
+  non-terminal, the larger count should be used</li>
+  <li>Conditions of subresults should also be made part of any result that includes those subresults
+  </li>
+  <li>Any memoized result is only reusable if all the recursion count conditions of the stored
+  result are less than or equal to the recursion counts for the current input position</li>
 </ul>
 
-<p>So far the above list just covers what is in the paper. But there is a little more that can be inferred:</p>
+<p>So far the above list just covers what is in the paper. But there is a little more that can be
+inferred:</p>
 <ul>
-  <li>If a result is not reusable and a new result is calculated, then the recursion count conditions of the
-  old result should be updated to the recursion counts at the current position and applied to the new result</li>
-  <li>When the recursion count of a condition applied to a result plus the number of unconsumed input tokens after
-  the result is less than the number of input tokens available at the beginning of the result, then that
-  condition can be omitted from the result</li>
+  <li>If a result is not reusable and a new result is calculated, then the recursion count
+  conditions of the old result should be updated to the recursion counts at the current position and
+  applied to the new result</li>
+  <li>When the recursion count of a condition applied to a result plus the number of unconsumed
+  input tokens after the result is less than the number of input tokens available at the beginning
+  of the result, then that condition can be omitted from the result</li>
 </ul>
 
 <p>These two details should constitute a minor efficiency improvement.</p>
@@ -140,17 +146,19 @@ the result is valid for reuse for any deeper recursion of the same combinator at
 
 <h5>Further Work</h5>
 
-<p>While the polynomial complexity of this library has been experimentally confirmed, no effort has yet been
-made to prove that it is actually polynomial in the same way that the parser combinators in the paper are. It
-is possible that due to the changes involved with using a non-functional language and enabling piecewise
-parsing that some subtle complexity difference may have arisen.</p>
+<p>While the polynomial complexity of this library has been experimentally confirmed, no effort has
+yet been made to prove that it is actually polynomial in the same way that the parser combinators in
+the paper are. It is possible that due to the changes involved with using a non-functional language
+and enabling piecewise parsing that some subtle complexity difference may have arisen.</p>
 
-<p>Likewise, the piecewise parsing has been unit tested to a degree but no formal proof that it is correct has
-been done.</p>
+<p>Likewise, the piecewise parsing has been unit tested to a degree but no formal proof that it is
+correct has been done.</p>
 
-<p>Ideas like being able to modify and resume an erroneous parsing attempt would also be interesting to explore.</p>
+<p>Ideas like being able to modify and resume an erroneous parsing attempt would also be interesting
+to explore.</p>
 
-<p>Finally, the plan is to actually use this library for something significant at some point in the future.</p>
+<p>Finally, the plan is to actually use this library for something significant at some point in the
+future.</p>
 
 
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