From 14025d22ce3d66c9d235e57221ec4653e00f972c Mon Sep 17 00:00:00 2001 From: Jedidiah Barber Date: Fri, 26 Nov 2021 20:17:43 +1300 Subject: Switched to .xhtml extension, fixed some minor bugs --- project/templates/packrat.xhtml | 167 ++++++++++++++++++++++++++++++++++++++++ 1 file changed, 167 insertions(+) create mode 100644 project/templates/packrat.xhtml (limited to 'project/templates/packrat.xhtml') diff --git a/project/templates/packrat.xhtml b/project/templates/packrat.xhtml new file mode 100644 index 0000000..ee33b41 --- /dev/null +++ b/project/templates/packrat.xhtml @@ -0,0 +1,167 @@ + +{%- extends "base.xhtml" -%} + + + +{%- block title -%}Packrat Parser Combinator Library{%- endblock -%} + + + +{%- block content %} +

Packrat Parser Combinator Library

+ +

Git repository: Link
+Paper this was based on: Link

+ +
2/2/2021
+ + +
Overview
+ +

Parser combinators are what you end up with when you start factoring out common pieces of +functionality from +recursive descent parsing. They are higher order functions that can be combined in modular ways +to create a desired parser.

+ +

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.

+ +

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:

+ +
+
+Expression ::= Expression - Term | Term
+Term ::= Term * Factor | Factor
+Factor ::= ( Expression ) | Integer
+
+
+ +

Can be turned into the following code snippet:

+ +
+ +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); + +
+ +

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.

+ + +
Features
+ +

A list of features that this library provides includes:

+ + +

More thorough documentation is provided in the /doc directory.

+ +

The name of the library comes from packrat parsing 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.

+ + +
Left Recursion
+ +

Direct left recursion, meaning a grammar non-terminal that immediately recurses to itself on the +left as in the Expression or Term 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.

+ +

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.

+ +

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.

+ +

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.

+ +

From that can be derived:

+ + +

So far the above list just covers what is in the paper. But there is a little more that can be +inferred:

+ + +

These two details should constitute a minor efficiency improvement.

+ + +
Further Work
+ +

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.

+ +

Likewise, the piecewise parsing has been unit tested to a degree but no formal proof that it is +correct has been done.

+ +

Ideas like being able to modify and resume an erroneous parsing attempt would also be interesting +to explore.

+ +

Finally, the plan is to actually use this library for something significant at some point in the +future.

+{% endblock -%} + -- cgit