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diff --git a/project/templates/packrat.html b/project/templates/packrat.html deleted file mode 100644 index 4ae1c3e..0000000 --- a/project/templates/packrat.html +++ /dev/null @@ -1,167 +0,0 @@ - -{%- extends "base.html" -%} - - - -{%- block title -%}Packrat Parser Combinator Library{%- endblock -%} - - - -{%- block content %} -<h4>Packrat Parser Combinator Library</h4> - -<p>Git repository: <a href="/cgi-bin/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" -class="external">Link</a></p> - -<h5>2/2/2021</h5> - - -<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" class="external"> -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>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> -Expression ::= Expression - Term | Term -Term ::= Term * Factor | Factor -Factor ::= ( Expression ) | Integer -</pre> -</div> - -<p>Can be turned into the following code snippet:</p> - -<div class="precontain"> -<code> -package Expr_Redir is new Redirect; -package Term_Redir is new Redirect; - -function Left_Parens is new Match ('('); -function Right_Parens is new Match (')'); -function Fac_Expr is new Between (Left_Parens, Expr_Redir.Call, Right_Parens); -function Fac_Choice is new Choice_2 (Fac_Expr, Integer_Num); -function Factor is new Stamp (Factor_Label, Fac_Choice); - -function Multiply is new Match ('*'); -function Term_Mult is new Sequence (Term_Redir.Call'Access, Multiply'Access, Factor'Access); -function Term_Choice is new Choice_2 (Term_Mult, Factor); -function Term is new Stamp (Term_Label, Term_Choice); - -function Minus is new Match ('-'); -function Expr_Minus is new Sequence (Expr_Redir.Call'Access, Minus'Access, Term'Access); -function Expr_Choice is new Choice_2 (Expr_Minus, Term); -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> - - -<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>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>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" -class="external">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>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> -</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> -<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> -</ul> - -<p>These two details should constitute a minor efficiency improvement.</p> - - -<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>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>Finally, the plan is to actually use this library for something significant at some point in the -future.</p> -{% endblock -%} - |