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 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 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.

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).

Parameters

configs:ATNConfigSet

the configuration set to test

Returns:boolean

true if all configurations in configs are in a RuleStopState, otherwise false

Determines if every alternative subset in altsets contains more than one alternative.

Parameters

altsets:Collection<BitSet>

a collection of alternative subsets

Returns:boolean

true if every BitSet in altsets has cardinality > 1, otherwise false

Determines if every alternative subset in altsets is equivalent.

Parameters

altsets:Collection<BitSet>

a collection of alternative subsets

Returns:boolean

true if every member of altsets is equal to the others, otherwise false

Gets the complete set of represented alternatives for a collection of alternative subsets. This method returns the union of each BitSet in altsets.

Parameters

altsets:Collection<BitSet>

a collection of alternative subsets

Returns:BitSet

the set of represented alternatives in altsets

Get union of all alts from configs.

Since

4.5.1

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

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

map[c.state] U= c.alt

Returns the unique alternative predicted by all alternative subsets in altsets. If no such alternative exists, this method returns ATN#INVALID_ALT_NUMBER.

Parameters

altsets:Collection<BitSet>

a collection of alternative subsets

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).

Parameters

configs:ATNConfigSet

the configuration set to test

Returns:boolean

true if any configuration in configs is in a RuleStopState, otherwise false

Determines if any single alternative subset in altsets contains more than one alternative.

Parameters

altsets:Collection<BitSet>

a collection of alternative subsets

Returns:boolean

true if altsets contains a BitSet with cardinality > 1, otherwise false

Determines if any single alternative subset in altsets contains exactly one alternative.

Parameters

altsets:Collection<BitSet>

a collection of alternative subsets

Returns:boolean

true if altsets contains a BitSet with cardinality 1, otherwise false

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.

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...