Marpa::R2::Semantics::Order(3) 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.

Duplicate parses are eliminated

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.

Default parse order

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.

Ranking methods

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 ranking method

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.

The high_rule_only ranking method

The "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.

The "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.

Rule ranking

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.

Note that, in the above, the logic is the same regardless of the DSL rule to which the rule alternatives belong. Different rule alternatives can, in the case of a prioritized rule, belong to the same DSL rule. But two rule alternatives may also be different because they are from two different DSL rules.

Null variant ranking

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.

The "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.

A general approach to sorting parses

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.

Formal definitions

This section is a restatement of earlier material in more formal language. It is recorded here for those who find it helpful. Most readers will want to ignore this section.

Call the set of parse trees, "T". Semantic equivalence is an equivalence relation on "T". Call this relation "~". Call "E", the quotient set of "T" by "~". In this document, the term arbitrary parse order is used to mean an arbitrary choice among the relations which are strict total orders of "E".

Copyright and License

  Copyright 2014 Jeffrey Kegler
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