http://www.antlr.org/antlr4-runtime: The ANTLR 4 Runtime (ANTLR) 
/*
 * Copyright (c) 2012-2017 The ANTLR Project. All rights reserved.
 * Use of this file is governed by the BSD 3-clause license that
 * can be found in the LICENSE.txt file in the project root.
 */

package org.antlr.v4.runtime.atn;

import org.antlr.v4.runtime.misc.AbstractEqualityComparator;
import org.antlr.v4.runtime.misc.FlexibleHashMap;
import org.antlr.v4.runtime.misc.MurmurHash;

import java.util.BitSet;
import java.util.Collection;
import java.util.HashMap;
import java.util.Iterator;
import java.util.Map;


This enumeration defines the prediction modes available in ANTLR 4 along with
utility methods for analyzing configuration sets for conflicts and/or
ambiguities.

/**
 * This enumeration defines the prediction modes available in ANTLR 4 along with
 * utility methods for analyzing configuration sets for conflicts and/or
 * ambiguities.
 */
public enum PredictionMode {
	
The SLL(*) prediction mode. This prediction mode ignores the current
parser context when making predictions. This is the fastest prediction
mode, and provides correct results for many grammars. This prediction
mode is more powerful than the prediction mode provided by ANTLR 3, but
may result in syntax errors for grammar and input combinations which are
not SLL.

 When using this prediction mode, the parser will either return a correct parse tree (i.e. the same parse tree that would be returned with the LL prediction mode), or it will report a syntax error. If a syntax error is encountered when using the SLL prediction mode, it may be due to either an actual syntax error in the input or indicate that the particular combination of grammar and input requires the more powerful LL prediction abilities to complete successfully.



This prediction mode does not provide any guarantees for prediction
behavior for syntactically-incorrect inputs.


/**
	 * The SLL(*) prediction mode. This prediction mode ignores the current
	 * parser context when making predictions. This is the fastest prediction
	 * mode, and provides correct results for many grammars. This prediction
	 * mode is more powerful than the prediction mode provided by ANTLR 3, but
	 * may result in syntax errors for grammar and input combinations which are
	 * not SLL.
	 *
	 * <p>
	 * When using this prediction mode, the parser will either return a correct
	 * parse tree (i.e. the same parse tree that would be returned with the
	 * {@link #LL} prediction mode), or it will report a syntax error. If a
	 * syntax error is encountered when using the {@link #SLL} prediction mode,
	 * it may be due to either an actual syntax error in the input or indicate
	 * that the particular combination of grammar and input requires the more
	 * powerful {@link #LL} prediction abilities to complete successfully.</p>
	 *
	 * <p>
	 * This prediction mode does not provide any guarantees for prediction
	 * behavior for syntactically-incorrect inputs.</p>
	 */
	SLL,
	
The LL(*) prediction mode. This prediction mode allows the current parser
context to be used for resolving SLL conflicts that occur during
prediction. This is the fastest prediction mode that guarantees correct
parse results for all combinations of grammars with syntactically correct
inputs.


When using this prediction mode, the parser will make correct decisions
for all syntactically-correct grammar and input combinations. However, in
cases where the grammar is truly ambiguous this prediction mode might not
report a precise answer for exactly which alternatives are
ambiguous.



This prediction mode does not provide any guarantees for prediction
behavior for syntactically-incorrect inputs.


/**
	 * The LL(*) prediction mode. This prediction mode allows the current parser
	 * context to be used for resolving SLL conflicts that occur during
	 * prediction. This is the fastest prediction mode that guarantees correct
	 * parse results for all combinations of grammars with syntactically correct
	 * inputs.
	 *
	 * <p>
	 * When using this prediction mode, the parser will make correct decisions
	 * for all syntactically-correct grammar and input combinations. However, in
	 * cases where the grammar is truly ambiguous this prediction mode might not
	 * report a precise answer for <em>exactly which</em> alternatives are
	 * ambiguous.</p>
	 *
	 * <p>
	 * This prediction mode does not provide any guarantees for prediction
	 * behavior for syntactically-incorrect inputs.</p>
	 */
	LL,
	
The LL(*) prediction mode with exact ambiguity detection. In addition to the correctness guarantees provided by the LL prediction mode, this prediction mode instructs the prediction algorithm to determine the complete and exact set of ambiguous alternatives for every ambiguous decision encountered while parsing. 

This prediction mode may be used for diagnosing ambiguities during
grammar development. Due to the performance overhead of calculating sets
of ambiguous alternatives, this prediction mode should be avoided when
the exact results are not necessary.



This prediction mode does not provide any guarantees for prediction
behavior for syntactically-incorrect inputs.


/**
	 * The LL(*) prediction mode with exact ambiguity detection. In addition to
	 * the correctness guarantees provided by the {@link #LL} prediction mode,
	 * this prediction mode instructs the prediction algorithm to determine the
	 * complete and exact set of ambiguous alternatives for every ambiguous
	 * decision encountered while parsing.
	 *
	 * <p>
	 * This prediction mode may be used for diagnosing ambiguities during
	 * grammar development. Due to the performance overhead of calculating sets
	 * of ambiguous alternatives, this prediction mode should be avoided when
	 * the exact results are not necessary.</p>
	 *
	 * <p>
	 * This prediction mode does not provide any guarantees for prediction
	 * behavior for syntactically-incorrect inputs.</p>
	 */
	LL_EXACT_AMBIG_DETECTION;

	
A Map that uses just the state and the stack context as the key. 
/** A Map that uses just the state and the stack context as the key. */
	static class AltAndContextMap extends FlexibleHashMap<ATNConfig,BitSet> {
		public AltAndContextMap() {
			super(AltAndContextConfigEqualityComparator.INSTANCE);
		}
	}

	private static final class AltAndContextConfigEqualityComparator extends AbstractEqualityComparator<ATNConfig> {
		public static final AltAndContextConfigEqualityComparator INSTANCE = new AltAndContextConfigEqualityComparator();

		private AltAndContextConfigEqualityComparator() {
		}

		
The hash code is only a function of the ATNState.stateNumber and ATNConfig.context. 
/**
		 * The hash code is only a function of the {@link ATNState#stateNumber}
		 * and {@link ATNConfig#context}.
		 */
		@Override
		public int hashCode(ATNConfig o) {
			int hashCode = MurmurHash.initialize(7);
			hashCode = MurmurHash.update(hashCode, o.state.stateNumber);
			hashCode = MurmurHash.update(hashCode, o.context);
			hashCode = MurmurHash.finish(hashCode, 2);
	        return hashCode;
		}

		@Override
		public boolean equals(ATNConfig a, ATNConfig b) {
			if ( a==b ) return true;
			if ( a==null || b==null ) return false;
			return a.state.stateNumber==b.state.stateNumber
				&& a.context.equals(b.context);
		}
	}

	
Computes the SLL prediction termination condition.


This method computes the SLL prediction termination condition for both of
the following cases.


    

  • The usual SLL+LL fallback upon SLL conflict
    • 

  • Pure SLL without LL fallback
    • 



COMBINED SLL+LL PARSING


When LL-fallback is enabled upon SLL conflict, correct predictions are
ensured regardless of how the termination condition is computed by this
method. Due to the substantially higher cost of LL prediction, the
prediction should only fall back to LL when the additional lookahead
cannot lead to a unique SLL prediction.


Assuming combined SLL+LL parsing, an SLL configuration set with only conflicting subsets should fall back to full LL, even if the configuration sets don't resolve to the same alternative (e.g. {1,2} and {3,4}. If there is at least one non-conflicting configuration, SLL could continue with the hopes that more lookahead will resolve via one of those non-conflicting configurations.


Here's the prediction termination rule them: SLL (for SLL+LL parsing)
stops when it sees only conflicting configuration subsets. In contrast,
full LL keeps going when there is uncertainty.


HEURISTIC


As a heuristic, we stop prediction when we see any conflicting subset
unless we see a state that only has one alternative associated with it.
The single-alt-state thing lets prediction continue upon rules like
(otherwise, it would admit defeat too soon):


[12|1|[], 6|2|[], 12|2|[]]. s : (ID | ID ID?) ';' ;


When the ATN simulation reaches the state before ';', it has a DFA state that looks like: [12|1|[], 6|2|[], 12|2|[]]. Naturally 12|1|[] and 12|2|[] conflict, but we cannot stop processing this node because alternative to has another way to continue, via [6|2|[]].


It also let's us continue for this rule:


[1|1|[], 1|2|[], 8|3|[]] a : A | A | A B ;


After matching input A, we reach the stop state for rule A, state 1.
State 8 is the state right before B. Clearly alternatives 1 and 2
conflict and no amount of further lookahead will separate the two.
However, alternative 3 will be able to continue and so we do not stop
working on this state. In the previous example, we're concerned with
states associated with the conflicting alternatives. Here alt 3 is not
associated with the conflicting configs, but since we can continue
looking for input reasonably, don't declare the state done.


PURE SLL PARSING


To handle pure SLL parsing, all we have to do is make sure that we
combine stack contexts for configurations that differ only by semantic
predicate. From there, we can do the usual SLL termination heuristic.


PREDICATES IN SLL+LL PARSING


SLL decisions don't evaluate predicates until after they reach DFA stop
states because they need to create the DFA cache that works in all
semantic situations. In contrast, full LL evaluates predicates collected
during start state computation so it can ignore predicates thereafter.
This means that SLL termination detection can totally ignore semantic
predicates.


Implementation-wise, ATNConfigSet combines stack contexts but not semantic predicate contexts so we might see two configurations like the following.


(s, 1, x, {}), (s, 1, x', {p})


Before testing these configurations against others, we have to merge x and x' (without modifying the existing configurations). For example, we test (x+x')==x'' when looking for conflicts in the following configurations.


(s, 1, x, {}), (s, 1, x', {p}), (s, 2, x'', {})


If the configuration set has predicates (as indicated by ATNConfigSet.hasSemanticContext), this algorithm makes a copy of the configurations to strip out all of the predicates so that a standard ATNConfigSet will merge everything ignoring predicates.


/**
	 * Computes the SLL prediction termination condition.
	 *
	 * <p>
	 * This method computes the SLL prediction termination condition for both of
	 * the following cases.</p>
	 *
	 * <ul>
	 * <li>The usual SLL+LL fallback upon SLL conflict</li>
	 * <li>Pure SLL without LL fallback</li>
	 * </ul>
	 *
	 * <p><strong>COMBINED SLL+LL PARSING</strong></p>
	 *
	 * <p>When LL-fallback is enabled upon SLL conflict, correct predictions are
	 * ensured regardless of how the termination condition is computed by this
	 * method. Due to the substantially higher cost of LL prediction, the
	 * prediction should only fall back to LL when the additional lookahead
	 * cannot lead to a unique SLL prediction.</p>
	 *
	 * <p>Assuming combined SLL+LL parsing, an SLL configuration set with only
	 * conflicting subsets should fall back to full LL, even if the
	 * configuration sets don't resolve to the same alternative (e.g.
	 * {@code {1,2}} and {@code {3,4}}. If there is at least one non-conflicting
	 * configuration, SLL could continue with the hopes that more lookahead will
	 * resolve via one of those non-conflicting configurations.</p>
	 *
	 * <p>Here's the prediction termination rule them: SLL (for SLL+LL parsing)
	 * stops when it sees only conflicting configuration subsets. In contrast,
	 * full LL keeps going when there is uncertainty.</p>
	 *
	 * <p><strong>HEURISTIC</strong></p>
	 *
	 * <p>As a heuristic, we stop prediction when we see any conflicting subset
	 * unless we see a state that only has one alternative associated with it.
	 * The single-alt-state thing lets prediction continue upon rules like
	 * (otherwise, it would admit defeat too soon):</p>
	 *
	 * <p>{@code [12|1|[], 6|2|[], 12|2|[]]. s : (ID | ID ID?) ';' ;}</p>
	 *
	 * <p>When the ATN simulation reaches the state before {@code ';'}, it has a
	 * DFA state that looks like: {@code [12|1|[], 6|2|[], 12|2|[]]}. Naturally
	 * {@code 12|1|[]} and {@code 12|2|[]} conflict, but we cannot stop
	 * processing this node because alternative to has another way to continue,
	 * via {@code [6|2|[]]}.</p>
	 *
	 * <p>It also let's us continue for this rule:</p>
	 *
	 * <p>{@code [1|1|[], 1|2|[], 8|3|[]] a : A | A | A B ;}</p>
	 *
	 * <p>After matching input A, we reach the stop state for rule A, state 1.
	 * State 8 is the state right before B. Clearly alternatives 1 and 2
	 * conflict and no amount of further lookahead will separate the two.
	 * However, alternative 3 will be able to continue and so we do not stop
	 * working on this state. In the previous example, we're concerned with
	 * states associated with the conflicting alternatives. Here alt 3 is not
	 * associated with the conflicting configs, but since we can continue
	 * looking for input reasonably, don't declare the state done.</p>
	 *
	 * <p><strong>PURE SLL PARSING</strong></p>
	 *
	 * <p>To handle pure SLL parsing, all we have to do is make sure that we
	 * combine stack contexts for configurations that differ only by semantic
	 * predicate. From there, we can do the usual SLL termination heuristic.</p>
	 *
	 * <p><strong>PREDICATES IN SLL+LL PARSING</strong></p>
	 *
	 * <p>SLL decisions don't evaluate predicates until after they reach DFA stop
	 * states because they need to create the DFA cache that works in all
	 * semantic situations. In contrast, full LL evaluates predicates collected
	 * during start state computation so it can ignore predicates thereafter.
	 * This means that SLL termination detection can totally ignore semantic
	 * predicates.</p>
	 *
	 * <p>Implementation-wise, {@link ATNConfigSet} combines stack contexts but not
	 * semantic predicate contexts so we might see two configurations like the
	 * following.</p>
	 *
	 * <p>{@code (s, 1, x, {}), (s, 1, x', {p})}</p>
	 *
	 * <p>Before testing these configurations against others, we have to merge
	 * {@code x} and {@code x'} (without modifying the existing configurations).
	 * For example, we test {@code (x+x')==x''} when looking for conflicts in
	 * the following configurations.</p>
	 *
	 * <p>{@code (s, 1, x, {}), (s, 1, x', {p}), (s, 2, x'', {})}</p>
	 *
	 * <p>If the configuration set has predicates (as indicated by
	 * {@link ATNConfigSet#hasSemanticContext}), this algorithm makes a copy of
	 * the configurations to strip out all of the predicates so that a standard
	 * {@link ATNConfigSet} will merge everything ignoring predicates.</p>
	 */
	public static boolean hasSLLConflictTerminatingPrediction(PredictionMode mode, ATNConfigSet configs) {
		/* Configs in rule stop states indicate reaching the end of the decision
		 * rule (local context) or end of start rule (full context). If all
		 * configs meet this condition, then none of the configurations is able
		 * to match additional input so we terminate prediction.
		 */
		if (allConfigsInRuleStopStates(configs)) {
			return true;
		}

		// pure SLL mode parsing
		if ( mode == PredictionMode.SLL ) {
			// Don't bother with combining configs from different semantic
			// contexts if we can fail over to full LL; costs more time
			// since we'll often fail over anyway.
			if ( configs.hasSemanticContext ) {
				// dup configs, tossing out semantic predicates
				ATNConfigSet dup = new ATNConfigSet();
				for (ATNConfig c : configs) {
					c = new ATNConfig(c,SemanticContext.NONE);
					dup.add(c);
				}
				configs = dup;
			}
			// now we have combined contexts for configs with dissimilar preds
		}

		// pure SLL or combined SLL+LL mode parsing

		Collection<BitSet> altsets = getConflictingAltSubsets(configs);
		boolean heuristic =
			hasConflictingAltSet(altsets) && !hasStateAssociatedWithOneAlt(configs);
		return heuristic;
	}

	
Checks if any configuration in configs is in a RuleStopState. Configurations meeting this condition have reached the end of the decision rule (local context) or end of start rule (full context). 
Params:
  • configs – the configuration set to test
Returns:true if any configuration in configs is in a RuleStopState, otherwise false
/**
	 * Checks if any configuration in {@code configs} is in a
	 * {@link RuleStopState}. Configurations meeting this condition have reached
	 * the end of the decision rule (local context) or end of start rule (full
	 * context).
	 *
	 * @param configs the configuration set to test
	 * @return {@code true} if any configuration in {@code configs} is in a
	 * {@link RuleStopState}, otherwise {@code false}
	 */
	public static boolean hasConfigInRuleStopState(ATNConfigSet configs) {
		for (ATNConfig c : configs) {
			if (c.state instanceof RuleStopState) {
				return true;
			}
		}

		return false;
	}

	
Checks if all configurations in configs are in a RuleStopState. Configurations meeting this condition have reached the end of the decision rule (local context) or end of start rule (full context). 
Params:
  • configs – the configuration set to test
Returns:true if all configurations in configs are in a RuleStopState, otherwise false
/**
	 * Checks if all configurations in {@code configs} are in a
	 * {@link RuleStopState}. Configurations meeting this condition have reached
	 * the end of the decision rule (local context) or end of start rule (full
	 * context).
	 *
	 * @param configs the configuration set to test
	 * @return {@code true} if all configurations in {@code configs} are in a
	 * {@link RuleStopState}, otherwise {@code false}
	 */
	public static boolean allConfigsInRuleStopStates(ATNConfigSet configs) {
		for (ATNConfig config : configs) {
			if (!(config.state instanceof RuleStopState)) {
				return false;
			}
		}

		return true;
	}

	
Full LL prediction termination.

Can we stop looking ahead during ATN simulation or is there some
uncertainty as to which alternative we will ultimately pick, after
consuming more input? Even if there are partial conflicts, we might know
that everything is going to resolve to the same minimum alternative. That
means we can stop since no more lookahead will change that fact. On the
other hand, there might be multiple conflicts that resolve to different
minimums. That means we need more look ahead to decide which of those
alternatives we should predict.


The basic idea is to split the set of configurations C, into conflicting subsets (s, _, ctx, _) and singleton subsets with non-conflicting configurations. Two configurations conflict if they have identical ATNConfig.state and ATNConfig.context values but different ATNConfig.alt value, e.g. (s, i, ctx, _) and (s, j, ctx, _) for i!=j.


Reduce these configuration subsets to the set of possible alternatives.
You can compute the alternative subsets in one pass as follows:


A_s,ctx = {i | (s, i, ctx, _)} for each configuration in C holding s and ctx fixed.


Or in pseudo-code, for each configuration c in C:


map[c] U= c.alt # map hash/equals uses s and x, not alt and not pred 


The values in map are the set of A_s,ctx sets.


If |A_s,ctx|=1 then there is no conflict associated with s and ctx.


Reduce the subsets to singletons by choosing a minimum of each subset. If
the union of these alternative subsets is a singleton, then no amount of
more lookahead will help us. We will always pick that alternative. If,
however, there is more than one alternative, then we are uncertain which
alternative to predict and must continue looking for resolution. We may
or may not discover an ambiguity in the future, even if there are no
conflicting subsets this round.


The biggest sin is to terminate early because it means we've made a
decision but were uncertain as to the eventual outcome. We haven't used
enough lookahead. On the other hand, announcing a conflict too late is no
big deal; you will still have the conflict. It's just inefficient. It
might even look until the end of file.


No special consideration for semantic predicates is required because
predicates are evaluated on-the-fly for full LL prediction, ensuring that
no configuration contains a semantic context during the termination
check.


CONFLICTING CONFIGS


Two configurations (s, i, x) and (s, j, x'), conflict when i!=j but x=x'. Because we merge all (s, i, _) configurations together, that means that there are at most n configurations associated with state s for n possible alternatives in the decision. The merged stacks complicate the comparison of configuration contexts x and x'. Sam checks to see if one is a subset of the other by calling merge and checking to see if the merged result is either x or x'. If the x associated with lowest alternative i is the superset, then i is the only possible prediction since the others resolve to min(i) as well. However, if x is associated with j>i then at least one stack configuration for j is not in conflict with alternative i. The algorithm should keep going, looking for more lookahead due to the uncertainty.


For simplicity, I'm doing a equality check between x and x' that lets the algorithm continue to consume lookahead longer than necessary. The reason I like the equality is of course the simplicity but also because that is the test you need to detect the alternatives that are actually in conflict.


CONTINUE/STOP RULE


Continue if union of resolved alternative sets from non-conflicting and
conflicting alternative subsets has more than one alternative. We are
uncertain about which alternative to predict.


The complete set of alternatives, [i for (_,i,_)], tells us which alternatives are still in the running for the amount of input we've consumed at this point. The conflicting sets let us to strip away configurations that won't lead to more states because we resolve conflicts to the configuration with a minimum alternate for the conflicting set.


CASES


    

  • no conflicts and more than 1 alternative in set => continue
    • 

  •  (s, 1, x), (s, 2, x), (s, 3, z), (s', 1, y), (s', 2, y) yields non-conflicting set {3} U conflicting sets min({1,2}) U min({1,2}) = {1,3} => continue 
    • 

  • (s, 1, x), (s, 2, x), (s', 1, y), (s', 2, y), (s'', 1, z) yields non-conflicting set {1} U conflicting sets min({1,2}) U min({1,2}) = {1} => stop and predict 1
    • 

  • (s, 1, x), (s, 2, x), (s', 1, y), (s', 2, y) yields conflicting, reduced sets {1} U {1} = {1} => stop and predict 1, can announce ambiguity {1,2}
    • 

  • (s, 1, x), (s, 2, x), (s', 2, y), (s', 3, y) yields conflicting, reduced sets {1} U {2} = {1,2} => continue
    • 

  • (s, 1, x), (s, 2, x), (s', 3, y), (s', 4, y) yields conflicting, reduced sets {1} U {3} = {1,3} => continue
    • 



EXACT AMBIGUITY DETECTION


If all states report the same conflicting set of alternatives, then we
know we have the exact ambiguity set.


|A_i|>1 and
A_i = A_j for all i, j.


In other words, we continue examining lookahead until all A_i have more than one alternative and all A_i are the same. If A={{1,2}, {1,3}}, then regular LL prediction would terminate because the resolved set is {1}. To determine what the real ambiguity is, we have to know whether the ambiguity is between one and two or one and three so we keep going. We can only stop prediction when we need exact ambiguity detection when the sets look like A={{1,2}} or {{1,2},{1,2}}, etc...


/**
	 * Full LL prediction termination.
	 *
	 * <p>Can we stop looking ahead during ATN simulation or is there some
	 * uncertainty as to which alternative we will ultimately pick, after
	 * consuming more input? Even if there are partial conflicts, we might know
	 * that everything is going to resolve to the same minimum alternative. That
	 * means we can stop since no more lookahead will change that fact. On the
	 * other hand, there might be multiple conflicts that resolve to different
	 * minimums. That means we need more look ahead to decide which of those
	 * alternatives we should predict.</p>
	 *
	 * <p>The basic idea is to split the set of configurations {@code C}, into
	 * conflicting subsets {@code (s, _, ctx, _)} and singleton subsets with
	 * non-conflicting configurations. Two configurations conflict if they have
	 * identical {@link ATNConfig#state} and {@link ATNConfig#context} values
	 * but different {@link ATNConfig#alt} value, e.g. {@code (s, i, ctx, _)}
	 * and {@code (s, j, ctx, _)} for {@code i!=j}.</p>
	 *
	 * <p>Reduce these configuration subsets to the set of possible alternatives.
	 * You can compute the alternative subsets in one pass as follows:</p>
	 *
	 * <p>{@code A_s,ctx = {i | (s, i, ctx, _)}} for each configuration in
	 * {@code C} holding {@code s} and {@code ctx} fixed.</p>
	 *
	 * <p>Or in pseudo-code, for each configuration {@code c} in {@code C}:</p>
	 *
	 * <pre>
	 * map[c] U= c.{@link ATNConfig#alt alt} # map hash/equals uses s and x, not
	 * alt and not pred
	 * </pre>
	 *
	 * <p>The values in {@code map} are the set of {@code A_s,ctx} sets.</p>
	 *
	 * <p>If {@code |A_s,ctx|=1} then there is no conflict associated with
	 * {@code s} and {@code ctx}.</p>
	 *
	 * <p>Reduce the subsets to singletons by choosing a minimum of each subset. If
	 * the union of these alternative subsets is a singleton, then no amount of
	 * more lookahead will help us. We will always pick that alternative. If,
	 * however, there is more than one alternative, then we are uncertain which
	 * alternative to predict and must continue looking for resolution. We may
	 * or may not discover an ambiguity in the future, even if there are no
	 * conflicting subsets this round.</p>
	 *
	 * <p>The biggest sin is to terminate early because it means we've made a
	 * decision but were uncertain as to the eventual outcome. We haven't used
	 * enough lookahead. On the other hand, announcing a conflict too late is no
	 * big deal; you will still have the conflict. It's just inefficient. It
	 * might even look until the end of file.</p>
	 *
	 * <p>No special consideration for semantic predicates is required because
	 * predicates are evaluated on-the-fly for full LL prediction, ensuring that
	 * no configuration contains a semantic context during the termination
	 * check.</p>
	 *
	 * <p><strong>CONFLICTING CONFIGS</strong></p>
	 *
	 * <p>Two configurations {@code (s, i, x)} and {@code (s, j, x')}, conflict
	 * when {@code i!=j} but {@code x=x'}. Because we merge all
	 * {@code (s, i, _)} configurations together, that means that there are at
	 * most {@code n} configurations associated with state {@code s} for
	 * {@code n} possible alternatives in the decision. The merged stacks
	 * complicate the comparison of configuration contexts {@code x} and
	 * {@code x'}. Sam checks to see if one is a subset of the other by calling
	 * merge and checking to see if the merged result is either {@code x} or
	 * {@code x'}. If the {@code x} associated with lowest alternative {@code i}
	 * is the superset, then {@code i} is the only possible prediction since the
	 * others resolve to {@code min(i)} as well. However, if {@code x} is
	 * associated with {@code j>i} then at least one stack configuration for
	 * {@code j} is not in conflict with alternative {@code i}. The algorithm
	 * should keep going, looking for more lookahead due to the uncertainty.</p>
	 *
	 * <p>For simplicity, I'm doing a equality check between {@code x} and
	 * {@code x'} that lets the algorithm continue to consume lookahead longer
	 * than necessary. The reason I like the equality is of course the
	 * simplicity but also because that is the test you need to detect the
	 * alternatives that are actually in conflict.</p>
	 *
	 * <p><strong>CONTINUE/STOP RULE</strong></p>
	 *
	 * <p>Continue if union of resolved alternative sets from non-conflicting and
	 * conflicting alternative subsets has more than one alternative. We are
	 * uncertain about which alternative to predict.</p>
	 *
	 * <p>The complete set of alternatives, {@code [i for (_,i,_)]}, tells us which
	 * alternatives are still in the running for the amount of input we've
	 * consumed at this point. The conflicting sets let us to strip away
	 * configurations that won't lead to more states because we resolve
	 * conflicts to the configuration with a minimum alternate for the
	 * conflicting set.</p>
	 *
	 * <p><strong>CASES</strong></p>
	 *
	 * <ul>
	 *
	 * <li>no conflicts and more than 1 alternative in set =&gt; continue</li>
	 *
	 * <li> {@code (s, 1, x)}, {@code (s, 2, x)}, {@code (s, 3, z)},
	 * {@code (s', 1, y)}, {@code (s', 2, y)} yields non-conflicting set
	 * {@code {3}} U conflicting sets {@code min({1,2})} U {@code min({1,2})} =
	 * {@code {1,3}} =&gt; continue
	 * </li>
	 *
	 * <li>{@code (s, 1, x)}, {@code (s, 2, x)}, {@code (s', 1, y)},
	 * {@code (s', 2, y)}, {@code (s'', 1, z)} yields non-conflicting set
	 * {@code {1}} U conflicting sets {@code min({1,2})} U {@code min({1,2})} =
	 * {@code {1}} =&gt; stop and predict 1</li>
	 *
	 * <li>{@code (s, 1, x)}, {@code (s, 2, x)}, {@code (s', 1, y)},
	 * {@code (s', 2, y)} yields conflicting, reduced sets {@code {1}} U
	 * {@code {1}} = {@code {1}} =&gt; stop and predict 1, can announce
	 * ambiguity {@code {1,2}}</li>
	 *
	 * <li>{@code (s, 1, x)}, {@code (s, 2, x)}, {@code (s', 2, y)},
	 * {@code (s', 3, y)} yields conflicting, reduced sets {@code {1}} U
	 * {@code {2}} = {@code {1,2}} =&gt; continue</li>
	 *
	 * <li>{@code (s, 1, x)}, {@code (s, 2, x)}, {@code (s', 3, y)},
	 * {@code (s', 4, y)} yields conflicting, reduced sets {@code {1}} U
	 * {@code {3}} = {@code {1,3}} =&gt; continue</li>
	 *
	 * </ul>
	 *
	 * <p><strong>EXACT AMBIGUITY DETECTION</strong></p>
	 *
	 * <p>If all states report the same conflicting set of alternatives, then we
	 * know we have the exact ambiguity set.</p>
	 *
	 * <p><code>|A_<em>i</em>|&gt;1</code> and
	 * <code>A_<em>i</em> = A_<em>j</em></code> for all <em>i</em>, <em>j</em>.</p>
	 *
	 * <p>In other words, we continue examining lookahead until all {@code A_i}
	 * have more than one alternative and all {@code A_i} are the same. If
	 * {@code A={{1,2}, {1,3}}}, then regular LL prediction would terminate
	 * because the resolved set is {@code {1}}. To determine what the real
	 * ambiguity is, we have to know whether the ambiguity is between one and
	 * two or one and three so we keep going. We can only stop prediction when
	 * we need exact ambiguity detection when the sets look like
	 * {@code A={{1,2}}} or {@code {{1,2},{1,2}}}, etc...</p>
	 */
	public static int resolvesToJustOneViableAlt(Collection<BitSet> altsets) {
		return getSingleViableAlt(altsets);
	}

	
Determines if every alternative subset in altsets contains more than one alternative. 
Params:
  • altsets – a collection of alternative subsets
Returns:true if every BitSet in altsets has cardinality > 1, otherwise false
/**
	 * Determines if every alternative subset in {@code altsets} contains more
	 * than one alternative.
	 *
	 * @param altsets a collection of alternative subsets
	 * @return {@code true} if every {@link BitSet} in {@code altsets} has
	 * {@link BitSet#cardinality cardinality} &gt; 1, otherwise {@code false}
	 */
	public static boolean allSubsetsConflict(Collection<BitSet> altsets) {
		return !hasNonConflictingAltSet(altsets);
	}

	
Determines if any single alternative subset in altsets contains exactly one alternative. 
Params:
  • altsets – a collection of alternative subsets
Returns:true if altsets contains a BitSet with cardinality 1, otherwise false
/**
	 * Determines if any single alternative subset in {@code altsets} contains
	 * exactly one alternative.
	 *
	 * @param altsets a collection of alternative subsets
	 * @return {@code true} if {@code altsets} contains a {@link BitSet} with
	 * {@link BitSet#cardinality cardinality} 1, otherwise {@code false}
	 */
	public static boolean hasNonConflictingAltSet(Collection<BitSet> altsets) {
		for (BitSet alts : altsets) {
			if ( alts.cardinality()==1 ) {
				return true;
			}
		}
		return false;
	}

	
Determines if any single alternative subset in altsets contains more than one alternative. 
Params:
  • altsets – a collection of alternative subsets
Returns:true if altsets contains a BitSet with cardinality > 1, otherwise false
/**
	 * Determines if any single alternative subset in {@code altsets} contains
	 * more than one alternative.
	 *
	 * @param altsets a collection of alternative subsets
	 * @return {@code true} if {@code altsets} contains a {@link BitSet} with
	 * {@link BitSet#cardinality cardinality} &gt; 1, otherwise {@code false}
	 */
	public static boolean hasConflictingAltSet(Collection<BitSet> altsets) {
		for (BitSet alts : altsets) {
			if ( alts.cardinality()>1 ) {
				return true;
			}
		}
		return false;
	}

	
Determines if every alternative subset in altsets is equivalent. 
Params:
  • altsets – a collection of alternative subsets
Returns:true if every member of altsets is equal to the others, otherwise false
/**
	 * Determines if every alternative subset in {@code altsets} is equivalent.
	 *
	 * @param altsets a collection of alternative subsets
	 * @return {@code true} if every member of {@code altsets} is equal to the
	 * others, otherwise {@code false}
	 */
	public static boolean allSubsetsEqual(Collection<BitSet> altsets) {
		Iterator<BitSet> it = altsets.iterator();
		BitSet first = it.next();
		while ( it.hasNext() ) {
			BitSet next = it.next();
			if ( !next.equals(first) ) return false;
		}
		return true;
	}

	
Returns the unique alternative predicted by all alternative subsets in altsets. If no such alternative exists, this method returns ATN.INVALID_ALT_NUMBER. 
Params:
  • altsets – a collection of alternative subsets
/**
	 * Returns the unique alternative predicted by all alternative subsets in
	 * {@code altsets}. If no such alternative exists, this method returns
	 * {@link ATN#INVALID_ALT_NUMBER}.
	 *
	 * @param altsets a collection of alternative subsets
	 */
	public static int getUniqueAlt(Collection<BitSet> altsets) {
		BitSet all = getAlts(altsets);
		if ( all.cardinality()==1 ) return all.nextSetBit(0);
		return ATN.INVALID_ALT_NUMBER;
	}

	
Gets the complete set of represented alternatives for a collection of alternative subsets. This method returns the union of each BitSet in altsets. 
Params:
  • altsets – a collection of alternative subsets
Returns:the set of represented alternatives in altsets
/**
	 * Gets the complete set of represented alternatives for a collection of
	 * alternative subsets. This method returns the union of each {@link BitSet}
	 * in {@code altsets}.
	 *
	 * @param altsets a collection of alternative subsets
	 * @return the set of represented alternatives in {@code altsets}
	 */
	public static BitSet getAlts(Collection<BitSet> altsets) {
		BitSet all = new BitSet();
		for (BitSet alts : altsets) {
			all.or(alts);
		}
		return all;
	}

	
Get union of all alts from configs.

Since:4.5.1
/**
	 * Get union of all alts from configs.
	 *
	 * @since 4.5.1
	 */
	public static BitSet getAlts(ATNConfigSet configs) {
		BitSet alts = new BitSet();
		for (ATNConfig config : configs) {
			alts.set(config.alt);
		}
		return alts;
	}

	
This function gets the conflicting alt subsets from a configuration set. For each configuration c in configs: 
map[c] U= c.alt # map hash/equals uses s and x, not alt and not pred 


/**
	 * This function gets the conflicting alt subsets from a configuration set.
	 * For each configuration {@code c} in {@code configs}:
	 *
	 * <pre>
	 * map[c] U= c.{@link ATNConfig#alt alt} # map hash/equals uses s and x, not
	 * alt and not pred
	 * </pre>
	 */
	public static Collection<BitSet> getConflictingAltSubsets(ATNConfigSet configs) {
		AltAndContextMap configToAlts = new AltAndContextMap();
		for (ATNConfig c : configs) {
			BitSet alts = configToAlts.get(c);
			if ( alts==null ) {
				alts = new BitSet();
				configToAlts.put(c, alts);
			}
			alts.set(c.alt);
		}
		return configToAlts.values();
	}

	
Get a map from state to alt subset from a configuration set. For each configuration c in configs: 
map[c.state] U= c.alt 


/**
	 * Get a map from state to alt subset from a configuration set. For each
	 * configuration {@code c} in {@code configs}:
	 *
	 * <pre>
	 * map[c.{@link ATNConfig#state state}] U= c.{@link ATNConfig#alt alt}
	 * </pre>
	 */
	public static Map<ATNState, BitSet> getStateToAltMap(ATNConfigSet configs) {
		Map<ATNState, BitSet> m = new HashMap<ATNState, BitSet>();
		for (ATNConfig c : configs) {
			BitSet alts = m.get(c.state);
			if ( alts==null ) {
				alts = new BitSet();
				m.put(c.state, alts);
			}
			alts.set(c.alt);
		}
		return m;
	}

	public static boolean hasStateAssociatedWithOneAlt(ATNConfigSet configs) {
		Map<ATNState, BitSet> x = getStateToAltMap(configs);
		for (BitSet alts : x.values()) {
			if ( alts.cardinality()==1 ) return true;
		}
		return false;
	}

	public static int getSingleViableAlt(Collection<BitSet> altsets) {
		BitSet viableAlts = new BitSet();
		for (BitSet alts : altsets) {
			int minAlt = alts.nextSetBit(0);
			viableAlts.set(minAlt);
			if ( viableAlts.cardinality()>1 ) { // more than 1 viable alt
				return ATN.INVALID_ALT_NUMBER;
			}
		}
		return viableAlts.nextSetBit(0);
	}

}