- A formal definition
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Marpa::R2::Semantics::Order - How the SLIF ranks ambiguous parses
Marpa allows ambiguous parses. While an unambiguous parse can produce at most one parse tree and one parse result, an ambiguous parse will produce a parse series. A parse series is a sequence of parse trees, each of which will have its own parse result.
This document describes ways of controlling the order in which the SLIF recognizer's
value() method evaluates the parse trees of an ambiguous parse. It also describes ways to exclude selected parse trees from the parse series.
When evaluating the parse trees in a parse series, Marpa never evaluates the same parse tree twice. What this means probably matches the programmer's intuition of what it should mean. Marpa considers two parse trees to be the same if they are semantic equivalents.
Two parse trees are semantic equivalents if and only if a recursive, top-down evaluation of each applies the same rules in the same order at the same G1 locations. If the semantics are deterministic, and if two parse trees are semantic equivalents according to this definition, the two parse trees will always produce the same parse result.
The two parse trees are called semantic equivalents, because from the point of view of a deterministic semantics they are indistinguishable. When the Marpa documentation refers to duplicate parses, unless otherwise stated, it means that the two are semantic equivalents.
By calling the recognizer's
value() method repeatedly, Marpa can produce all the parse results in the current parse series. The default is for the parse results to be returned in an arbitrary parse order. This corresponds to the "
none" value of the recognizer's
ranking_method named argument.
Traversal of the parse trees in arbitrary parse order will be always be well-behaved in the sense that no two parse trees will be semantic duplicates, and no unique (semantic non-duplicate) parse tree will be omitted in it. No other property of arbitrary parse order is guaranteed. For example, the order may change each time the parse series is traversed.
SLIF recognizer objects have a
ranking_method named argument, whose value can be the name of a ranking method, or "
none", indicating that the default ranking method is to be used.
The rule method ranks alternative parses according to their rule alternatives. Every rule alternative has a numeric rank. A rule's rank can be specified using the the
rank adverb argument for that RHS alternative. Rule ranks must be integers. They may be negative. If no numeric rank is specified, the numeric rank is 0.
high_rule_only ranking method is similar to the
rule ranking method, except that, at every choice point, it discards all of the choices which have a rank lower than that of the highest ranked choice.
high_rule_only ranking method can reduce the ambiguity of a parse, but it does not necessarily do so. This is because, at each choice point among the parse trees, it is possible that several of the choices, or all of them, will have the same rank as the highest ranked choice.
A parse series is kept in a structure called a parse bocage. The parse bocage is a tree-like structure, whose root node is the common root of all the parse trees of the parse series. In an unambiguous parse, there will be only one parse tree, and the parse bocage will be equivalent to that parse tree. In an ambiguous parse, there will be choice points in the parse bocage. At the choice points, there will be two or more alternatives -- choices which result in different parse trees.
When ranking, the logic traverses the parse bocage, looking for choice points. From the point of view of the individual parse trees, this traversal will be top-down and left-to-right. At the choice points, the choices are ranked as follows:
Different numeric ranks:
If the two choices have different numeric ranks, they must also have different rule alternatives. The choice whose rule alternative has the higher numeric rank will rank high.
Same rule alternative:
If the two choices have the same rule alternative, they rank as described under "Null variant ranking".
Same numeric rank, different rule alternatives:
Two different rule alternatives can have the same numeric rank. If the two choices are for rule alternatives that are different, but that have the same numeric rank, the relative order of the two choices is arbitrary.
Rule alternatives may be part of a single rule in the DSL -- for example, a prioritized rule. Placement with a DSL rule makes no difference when ranking rule alternatives. For example, it makes no difference if two rule alternatives come from the same prioritized rule; or from two different prioritized rules.
Some rules have a RHS which contains proper nullables: symbols which may be nulled, but which are not nulling symbols. (Nulling symbols are symbols which are always nulled.)
When a rule alternative contains proper nullables, each instance of that rule creates a nulling variant. A nulling variant is a specific pattern of null and non-null symbols in a rule instance's RHS. In many cases, this creates an ambiguity -- different nulling variants can match the same substring in the input. In ambiguous parsings of this kind, some applications may want to rank nulling variants that start with non-null symbols higher. Other applications may want to do the opposite -- to rank nulling variants that start with null symbols higher.
null-ranking adverb for RHS alternatives specifies which nulling variants are ranked high or low. If the
null-ranking is "
low", then the closer a nulling variant places its visible (non-null) symbols to the start of the rule instance, the higher it ranks. A null ranking of
low is the default. If the
null-ranking is "
high", then the closer a nulling variant places its null symbols to the start of the rule instance, the higher it ranks. In ranking nulling variants with more than one proper nullable, major-to-minor is left-to-right.
The most general way to sort Marpa parses is for the application to take control. The application can set up the Marpa semantic actions so that the parse result of every parse tree is a
<rank, true_value> duple. The duples can then be sorted by
rank. Once the results are sorted, the
rank element of the duple can be discarded. (Those familiar with the Schwartzian transform may note a resemblance. In Perl, duples can be implemented as references to arrays of 2 elements.)
The user needs to be careful. In theory, ambiguity can cause an exponential explosion in the number of results. In practice, ambiguity tends to get out of hand very easily. Producing and sorting all the parses can take a very long time.
This section is a restatement of earlier definition in more formal language. It is recorded here for those who find it helpful. Most readers will want to ignore this. Call the set of parse trees,
T. Semantic equivalence is an equivalence relation on
T. Call this relation
E, the quotient set of
~. In this document, the term arbitrary parse order is used to mean an arbitrary choice among the relations which are strict total orders of
Copyright 2015 Jeffrey Kegler This file is part of Marpa::R2. Marpa::R2 is free software: you can redistribute it and/or modify it under the terms of the GNU Lesser General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. Marpa::R2 is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public License for more details. You should have received a copy of the GNU Lesser General Public License along with Marpa::R2. If not, see http://www.gnu.org/licenses/.