| java.lang.Object org.antlr.analysis.NFAToDFAConverter
NFAToDFAConverter | public class NFAToDFAConverter (Code) | | Code that embodies the NFA conversion to DFA.
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Field Summary | |
public static boolean | SINGLE_THREADED_NFA_CONVERSION Should ANTLR launch multiple threads to convert NFAs to DFAs?
With a 2-CPU box, I note that it's about the same single or
multithreaded. | protected NFAContext[] | contextTrees While converting NFA, we must track states that
reference other rule's NFAs so we know what to do
at the end of a rule. | public static boolean | debug | protected DFA | dfa | protected List | work |
Method Summary | |
protected DFAState | addDFAStateToWorkList(DFAState d) Add a new DFA state to the DFA if not already present.
If the DFA state uniquely predicts a single alternative, it
becomes a stop state; don't add to work list. | protected void | addPredicateTransitions(DFAState d) for each NFA config in d, look for "predicate required" sign set
during nondeterminism resolution.
Add the predicate edges sorted by the alternative number; I'm fairly
sure that I could walk the configs backwards so they are added to
the predDFATarget in the right order, but it's best to make sure.
Predicates succeed in the order they are specifed. | protected static int | addTransition(DFAState d, Label label, DFAState targetState, Map targetToLabelMap) Add a transition from state d to targetState with label in normal case.
if COLLAPSE_ALL_INCIDENT_EDGES, however, try to merge all edges from
d to targetState; this means merging their labels. | public void | closure(DFAState d) For all NFA states (configurations) merged in d,
compute the epsilon closure; that is, find all NFA states reachable
from the NFA states in d via purely epsilon transitions. | public void | closure(NFAState p, int alt, NFAContext context, SemanticContext semanticContext, DFAState d, boolean collectPredicates) Where can we get from NFA state p traversing only epsilon transitions?
Add new NFA states + context to DFA state d. | public static boolean | closureIsBusy(DFAState d, NFAConfiguration proposedNFAConfiguration) A closure operation should abort if that computation has already
been done or a computation with a conflicting context has already
been done. | protected DFAState | computeStartState() From this first NFA state of a decision, create a DFA.
Walk each alt in decision and compute closure from the start of that
rule, making sure that the closure does not include other alts within
that same decision. | public void | convert() | protected DFAState | convertToAcceptState(DFAState d, int alt) | protected void | convertToEOTAcceptState(DFAState d) Walk the configurations of this DFA state d looking for the
configuration, c, that has a transition on EOT. | protected void | findNewDFAStatesAndAddDFATransitions(DFAState d) From this node, add a d--a-->t transition for all
labels 'a' where t is a DFA node created
from the set of NFA states reachable from any NFA
state in DFA state d. | protected static int | getMinAlt(DFAState d) | protected static int | getMinAlt(Set nondeterministicAlts) | protected Map | getPredicatesPerNonDeterministicAlt(DFAState d, Set nondeterministicAlts) Return a mapping from nondeterministc alt to combined list of predicates.
If both (s|i|semCtx1) and (t|i|semCtx2) exist, then the proper predicate
for alt i is semCtx1||semCtx2 because you have arrived at this single
DFA state via two NFA paths, both of which have semantic predicates.
We ignore deterministic alts because syntax alone is sufficient
to predict those. | protected static SemanticContext | getUnionOfPredicates(Map altToPredMap) OR together all predicates from the alts. | protected void | initContextTrees(int numberOfAlts) | public static int | max(Set s) | public DFAState | reach(DFAState d, Label label) Given the set of NFA states in DFA state d, find all NFA states
reachable traversing label arcs. | protected int | resolveByChoosingFirstAlt(DFAState d, Set nondeterministicAlts) | protected int | resolveByPickingExitAlt(DFAState d, Set nondeterministicAlts) Resolve state d by choosing exit alt, which is same value as the
number of alternatives. | protected int | resolveByPickingMinAlt(DFAState d, Set nondeterministicAlts) Turn off all configurations associated with the
set of incoming nondeterministic alts except the min alt number. | public void | resolveNonDeterminisms(DFAState d) If > 1 NFA configurations within this DFA state have identical
NFA state and context, but differ in their predicted
TODO update for new context suffix stuff 3-9-2005
alternative then a single input sequence predicts multiple alts.
The NFA decision is therefore syntactically indistinguishable
from the left edge upon at least one input sequence. | protected boolean | tryToResolveWithSemanticPredicates(DFAState d, Set nondeterministicAlts) See if a set of nondeterministic alternatives can be disambiguated
with the semantic predicate contexts of the alternatives.
Without semantic predicates, syntactic conflicts are resolved
by simply choosing the first viable alternative. | protected static void | turnOffOtherAlts(DFAState d, int min, Set nondeterministicAlts) |
SINGLE_THREADED_NFA_CONVERSION | public static boolean SINGLE_THREADED_NFA_CONVERSION(Code) | | Should ANTLR launch multiple threads to convert NFAs to DFAs?
With a 2-CPU box, I note that it's about the same single or
multithreaded. Both CPU meters are going even when single-threaded
so I assume the GC is killing us. Could be the compiler. When I
run java -Xint mode, I get about 15% speed improvement with multiple
threads.
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contextTrees | protected NFAContext[] contextTrees(Code) | | While converting NFA, we must track states that
reference other rule's NFAs so we know what to do
at the end of a rule. We need to know what context invoked
this rule so we can know where to continue looking for NFA
states. I'm tracking a context tree (record of rule invocation
stack trace) for each alternative that could be predicted.
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debug | public static boolean debug(Code) | | |
dfa | protected DFA dfa(Code) | | We are converting which DFA?
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work | protected List work(Code) | | A list of DFA states we still need to process during NFA conversion
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NFAToDFAConverter | public NFAToDFAConverter(DFA dfa)(Code) | | |
addDFAStateToWorkList | protected DFAState addDFAStateToWorkList(DFAState d)(Code) | | Add a new DFA state to the DFA if not already present.
If the DFA state uniquely predicts a single alternative, it
becomes a stop state; don't add to work list. Further, if
there exists an NFA state predicted by > 1 different alternatives
and with the same syn and sem context, the DFA is nondeterministic for
at least one input sequence reaching that NFA state.
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addPredicateTransitions | protected void addPredicateTransitions(DFAState d)(Code) | | for each NFA config in d, look for "predicate required" sign set
during nondeterminism resolution.
Add the predicate edges sorted by the alternative number; I'm fairly
sure that I could walk the configs backwards so they are added to
the predDFATarget in the right order, but it's best to make sure.
Predicates succeed in the order they are specifed. Alt i wins
over alt i+1 if both predicates are true.
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addTransition | protected static int addTransition(DFAState d, Label label, DFAState targetState, Map targetToLabelMap)(Code) | | Add a transition from state d to targetState with label in normal case.
if COLLAPSE_ALL_INCIDENT_EDGES, however, try to merge all edges from
d to targetState; this means merging their labels. Another optimization
is to reduce to a single EOT edge any set of edges from d to targetState
where there exists an EOT state. EOT is like the wildcard so don't
bother to test any other edges. Example:
NUM_INT
: '1'..'9' ('0'..'9')* ('l'|'L')?
| '0' ('x'|'X') ('0'..'9'|'a'..'f'|'A'..'F')+ ('l'|'L')?
| '0' ('0'..'7')* ('l'|'L')?
;
The normal decision to predict alts 1, 2, 3 is:
if ( (input.LA(1)>='1' && input.LA(1)<='9') ) {
alt7=1;
}
else if ( input.LA(1)=='0' ) {
if ( input.LA(2)=='X'||input.LA(2)=='x' ) {
alt7=2;
}
else if ( (input.LA(2)>='0' && input.LA(2)<='7') ) {
alt7=3;
}
else if ( input.LA(2)=='L'||input.LA(2)=='l' ) {
alt7=3;
}
else {
alt7=3;
}
}
else error
Clearly, alt 3 is predicted with extra work since it tests 0..7
and [lL] before finally realizing that any character is actually
ok at k=2.
A better decision is as follows:
if ( (input.LA(1)>='1' && input.LA(1)<='9') ) {
alt7=1;
}
else if ( input.LA(1)=='0' ) {
if ( input.LA(2)=='X'||input.LA(2)=='x' ) {
alt7=2;
}
else {
alt7=3;
}
}
The DFA originally has 3 edges going to the state the predicts alt 3,
but upon seeing the EOT edge (the "else"-clause), this method
replaces the old merged label (which would have (0..7|l|L)) with EOT.
The code generator then leaves alt 3 predicted with a simple else-
clause. :)
The only time the EOT optimization makes no sense is in the Tokens
rule. We want EOT to truly mean you have matched an entire token
so don't bother actually rewinding to execute that rule unless there
are actions in that rule. For now, since I am not preventing
backtracking from Tokens rule, I will simply allow the optimization.
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closure | public void closure(DFAState d)(Code) | | For all NFA states (configurations) merged in d,
compute the epsilon closure; that is, find all NFA states reachable
from the NFA states in d via purely epsilon transitions.
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closure | public void closure(NFAState p, int alt, NFAContext context, SemanticContext semanticContext, DFAState d, boolean collectPredicates)(Code) | | Where can we get from NFA state p traversing only epsilon transitions?
Add new NFA states + context to DFA state d. Also add semantic
predicates to semantic context if collectPredicates is set. We only
collect predicates at hoisting depth 0, meaning before any token/char
have been recognized. This corresponds, during analysis, to the
initial DFA start state construction closure() invocation.
There are four cases of interest (the last being the usual transition):
1. Traverse an edge that takes us to the start state of another
rule, r. We must push this state so that if the DFA
conversion hits the end of rule r, then it knows to continue
the conversion at state following state that "invoked" r. By
construction, there is a single transition emanating from a rule
ref node.
2. Reach an NFA state associated with the end of a rule, r, in the
grammar from which it was built. We must add an implicit (i.e.,
don't actually add an epsilon transition) epsilon transition
from r's end state to the NFA state following the NFA state
that transitioned to rule r's start state. Because there are
many states that could reach r, the context for a rule invocation
is part of a call tree not a simple stack. When we fall off end
of rule, "pop" a state off the call tree and add that state's
"following" node to d's NFA configuration list. The context
for this new addition will be the new "stack top" in the call tree.
3. Like case 2, we reach an NFA state associated with the end of a
rule, r, in the grammar from which NFA was built. In this case,
however, we realize that during this NFA->DFA conversion, no state
invoked the current rule's NFA. There is no choice but to add
all NFA states that follow references to r's start state. This is
analogous to computing the FOLLOW(r) in the LL(k) world. By
construction, even rule stop state has a chain of nodes emanating
from it that points to every possible following node. This case
is conveniently handled then by the 4th case.
4. Normal case. If p can reach another NFA state q, then add
q to d's configuration list, copying p's context for q's context.
If there is a semantic predicate on the transition, then AND it
with any existing semantic context.
Current state p is always added to d's configuration list as it's part
of the closure as well.
When is a closure operation in a cycle condition? While it is
very possible to have the same NFA state mentioned twice
within the same DFA state, there are two situations that
would lead to nontermination of closure operation:
o Whenever closure reaches a configuration where the same state
with same or a suffix context already exists. This catches
the IF-THEN-ELSE tail recursion cycle and things like
a : A a | B ;
the context will be $ (empty stack).
We have to check
larger context stacks because of (...)+ loops. For
example, the context of a (...)+ can be nonempty if the
surrounding rule is invoked by another rule:
a : b A | X ;
b : (B|)+ ; // nondeterministic by the way
The context of the (B|)+ loop is "invoked from item
a : . b A ;" and then the empty alt of the loop can reach back
to itself. The context stack will have one "return
address" element and so we must check for same state, same
context for arbitrary context stacks.
Idea: If we've seen this configuration before during closure, stop.
We also need to avoid reaching same state with conflicting context.
Ultimately analysis would stop and we'd find the conflict, but we
should stop the computation. Previously I only checked for
exact config. Need to check for same state, suffix context
not just exact context.
o Whenever closure reaches a configuration where state p
is present in its own context stack. This means that
p is a rule invocation state and the target rule has
been called before. NFAContext.MAX_RECURSIVE_INVOCATIONS
(See the comment there also) determines how many times
it's possible to recurse; clearly we cannot recurse forever.
Some grammars such as the following actually require at
least one recursive call to correctly compute the lookahead:
a : L ID R
| b
;
b : ID
| L a R
;
Input L ID R is ambiguous but to figure this out, ANTLR
needs to go a->b->a->b to find the L ID sequence.
Do not allow closure to add a configuration that would
allow too much recursion.
This case also catches infinite left recursion.
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closureIsBusy | public static boolean closureIsBusy(DFAState d, NFAConfiguration proposedNFAConfiguration)(Code) | | A closure operation should abort if that computation has already
been done or a computation with a conflicting context has already
been done. If proposed NFA config's state and alt are the same
there is potentially a problem. If the stack context is identical
then clearly the exact same computation is proposed. If a context
is a suffix of the other, then again the computation is in an
identical context. ?$ and ??$ are considered the same stack.
We have to walk configurations linearly doing the comparison instead
of a set for exact matches.
We cannot use a set hash table for this lookup as contexts that are
suffixes could be !equal() but their hashCode()s would be different;
that's a problem for a HashSet. This costs a lot actually, it
takes about 490ms vs 355ms for Java grammar's analysis phase when
I moved away from hash lookup. Argh! Still it's small. For newbie
generated grammars though this really speeds things up because it
avoids chasing its tail during closure operations on highly left-
recursive grammars.
Ok, backing this out to use exact match again for speed. We will
always detect the conflict later when checking for context suffixes...
I was just trying to prevent unnecessary closures for random crap
submitted by newbies. Instead now I check for left-recursive stuff
and terminate before analysis obviates the need to do this more
expensive computation.
If the semantic context is different, then allow new computation.
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computeStartState | protected DFAState computeStartState()(Code) | | From this first NFA state of a decision, create a DFA.
Walk each alt in decision and compute closure from the start of that
rule, making sure that the closure does not include other alts within
that same decision. The idea is to associate a specific alt number
with the starting closure so we can trace the alt number for all states
derived from this. At a stop state in the DFA, we can return this alt
number, indicating which alt is predicted.
If this DFA is derived from an loop back NFA state, then the first
transition is actually the exit branch of the loop. Rather than make
this alternative one, let's make this alt n+1 where n is the number of
alts in this block. This is nice to keep the alts of the block 1..n;
helps with error messages.
I handle nongreedy in findNewDFAStatesAndAddDFATransitions
when nongreedy and EOT transition. Make state with EOT emanating
from it the accept state.
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convert | public void convert()(Code) | | |
convertToEOTAcceptState | protected void convertToEOTAcceptState(DFAState d)(Code) | | Walk the configurations of this DFA state d looking for the
configuration, c, that has a transition on EOT. State d should
be converted to an accept state predicting the c.alt. Blast
d's current configuration set and make it just have config c.
TODO: can there be more than one config with EOT transition?
That would mean that two NFA configurations could reach the
end of the token with possibly different predicted alts.
Seems like that would be rare or impossible. Perhaps convert
this routine to find all such configs and give error if >1.
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findNewDFAStatesAndAddDFATransitions | protected void findNewDFAStatesAndAddDFATransitions(DFAState d)(Code) | | From this node, add a d--a-->t transition for all
labels 'a' where t is a DFA node created
from the set of NFA states reachable from any NFA
state in DFA state d.
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getMinAlt | protected static int getMinAlt(Set nondeterministicAlts)(Code) | | |
getPredicatesPerNonDeterministicAlt | protected Map getPredicatesPerNonDeterministicAlt(DFAState d, Set nondeterministicAlts)(Code) | | Return a mapping from nondeterministc alt to combined list of predicates.
If both (s|i|semCtx1) and (t|i|semCtx2) exist, then the proper predicate
for alt i is semCtx1||semCtx2 because you have arrived at this single
DFA state via two NFA paths, both of which have semantic predicates.
We ignore deterministic alts because syntax alone is sufficient
to predict those. Do not include their predicates.
Alts with no predicate are assumed to have {true}? pred.
When combining via || with "true", all predicates are removed from
consideration since the expression will always be true and hence
not tell us how to resolve anything. So, if any NFA configuration
in this DFA state does not have a semantic context, the alt cannot
be resolved with a predicate.
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getUnionOfPredicates | protected static SemanticContext getUnionOfPredicates(Map altToPredMap)(Code) | | OR together all predicates from the alts. Note that the predicate
for an alt could itself be a combination of predicates.
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initContextTrees | protected void initContextTrees(int numberOfAlts)(Code) | | |
reach | public DFAState reach(DFAState d, Label label)(Code) | | Given the set of NFA states in DFA state d, find all NFA states
reachable traversing label arcs. By definition, there can be
only one DFA state reachable by an atom from DFA state d so we must
find and merge all NFA states reachable via label. Return a new
DFAState that has all of those NFA states with their context (i.e.,
which alt do they predict and where to return to if they fall off
end of a rule).
Because we cannot jump to another rule nor fall off the end of a rule
via a non-epsilon transition, NFA states reachable from d have the
same configuration as the NFA state in d. So if NFA state 7 in d's
configurations can reach NFA state 13 then 13 will be added to the
new DFAState (labelDFATarget) with the same configuration as state
7 had.
This method does not see EOT transitions off the end of token rule
accept states if the rule was invoked by somebody.
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resolveByChoosingFirstAlt | protected int resolveByChoosingFirstAlt(DFAState d, Set nondeterministicAlts)(Code) | | |
resolveByPickingExitAlt | protected int resolveByPickingExitAlt(DFAState d, Set nondeterministicAlts)(Code) | | Resolve state d by choosing exit alt, which is same value as the
number of alternatives. Return that exit alt.
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resolveByPickingMinAlt | protected int resolveByPickingMinAlt(DFAState d, Set nondeterministicAlts)(Code) | | Turn off all configurations associated with the
set of incoming nondeterministic alts except the min alt number.
There may be many alts among the configurations but only turn off
the ones with problems (other than the min alt of course).
If nondeterministicAlts is null then turn off all configs 'cept those
associated with the minimum alt.
Return the min alt found.
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resolveNonDeterminisms | public void resolveNonDeterminisms(DFAState d)(Code) | | If > 1 NFA configurations within this DFA state have identical
NFA state and context, but differ in their predicted
TODO update for new context suffix stuff 3-9-2005
alternative then a single input sequence predicts multiple alts.
The NFA decision is therefore syntactically indistinguishable
from the left edge upon at least one input sequence. We may
terminate the NFA to DFA conversion for these paths since no
paths emanating from those NFA states can possibly separate
these conjoined twins once interwined to make things
deterministic (unless there are semantic predicates; see below).
Upon a nondeterministic set of NFA configurations, we should
report a problem to the grammar designer and resolve the issue
by aribitrarily picking the first alternative (this usually
ends up producing the most natural behavior). Pick the lowest
alt number and just turn off all NFA configurations
associated with the other alts. Rather than remove conflicting
NFA configurations, I set the "resolved" bit so that future
computations will ignore them. In this way, we maintain the
complete DFA state with all its configurations, but prevent
future DFA conversion operations from pursuing undesirable
paths. Remember that we want to terminate DFA conversion as
soon as we know the decision is deterministic *or*
nondeterministic.
[BTW, I have convinced myself that there can be at most one
set of nondeterministic configurations in a DFA state. Only NFA
configurations arising from the same input sequence can appear
in a DFA state. There is no way to have another complete set
of nondeterministic NFA configurations without another input
sequence, which would reach a different DFA state. Therefore,
the two nondeterministic NFA configuration sets cannot collide
in the same DFA state.]
Consider DFA state {(s|1),(s|2),(s|3),(t|3),(v|4)} where (s|a)
is state 's' and alternative 'a'. Here, configuration set
{(s|1),(s|2),(s|3)} predicts 3 different alts. Configurations
(s|2) and (s|3) are "resolved", leaving {(s|1),(t|3),(v|4)} as
items that must still be considered by the DFA conversion
algorithm in DFA.findNewDFAStatesAndAddDFATransitions().
Consider the following grammar where alts 1 and 2 are no
problem because of the 2nd lookahead symbol. Alts 3 and 4 are
identical and will therefore reach the rule end NFA state but
predicting 2 different alts (no amount of future lookahead
will render them deterministic/separable):
a : A B
| A C
| A
| A
;
Here is a (slightly reduced) NFA of this grammar:
(1)-A->(2)-B->(end)-EOF->(8)
| ^
(2)-A->(3)-C----|
| ^
(4)-A->(5)------|
| ^
(6)-A->(7)------|
where (n) is NFA state n. To begin DFA conversion, the start
state is created:
{(1|1),(2|2),(4|3),(6|4)}
Upon A, all NFA configurations lead to new NFA states yielding
new DFA state:
{(2|1),(3|2),(5|3),(7|4),(end|3),(end|4)}
where the configurations with state end in them are added
during the epsilon closure operation. State end predicts both
alts 3 and 4. An error is reported, the latter configuration is
flagged as resolved leaving the DFA state as:
{(2|1),(3|2),(5|3),(7|4|resolved),(end|3),(end|4|resolved)}
As NFA configurations are added to a DFA state during its
construction, the reachable set of labels is computed. Here
reachable is {B,C,EOF} because there is at least one NFA state
in the DFA state that can transition upon those symbols.
The final DFA looks like:
{(1|1),(2|2),(4|3),(6|4)}
|
v
{(2|1),(3|2),(5|3),(7|4),(end|3),(end|4)} -B-> (end|1)
| |
C ----EOF-> (8,3)
|
v
(end|2)
Upon AB, alt 1 is predicted. Upon AC, alt 2 is predicted.
Upon A EOF, alt 3 is predicted. Alt 4 is not a viable
alternative.
The algorithm is essentially to walk all the configurations
looking for a conflict of the form (s|i) and (s|j) for i!=j.
Use a hash table to track state+context pairs for collisions
so that we have O(n) to walk the n configurations looking for
a conflict. Upon every conflict, track the alt number so
we have a list of all nondeterministically predicted alts. Also
track the minimum alt. Next go back over the configurations, setting
the "resolved" bit for any that have an alt that is a member of
the nondeterministic set. This will effectively remove any alts
but the one we want from future consideration.
See resolveWithSemanticPredicates()
AMBIGUOUS TOKENS
With keywords and ID tokens, there is an inherit ambiguity in that
"int" can be matched by ID also. Each lexer rule has an EOT
transition emanating from it which is used whenever the end of
a rule is reached and another token rule did not invoke it. EOT
is the only thing that can be seen next. If two rules are identical
like "int" and "int" then the 2nd def is unreachable and you'll get
a warning. We prevent a warning though for the keyword/ID issue as
ID is still reachable. This can be a bit weird. '+' rule then a
'+'|'+=' rule will fail to match '+' for the 2nd rule.
If all NFA states in this DFA state are targets of EOT transitions,
(and there is more than one state plus no unique alt is predicted)
then DFA conversion will leave this state as a dead state as nothing
can be reached from this state. To resolve the ambiguity, just do
what flex and friends do: pick the first rule (alt in this case) to
win. This means you should put keywords before the ID rule.
If the DFA state has only one NFA state then there is no issue:
it uniquely predicts one alt. :) Problem
states will look like this during conversion:
DFA 1:{9|1, 19|2, 14|3, 20|2, 23|2, 24|2, ...}-->5:{41|3, 42|2}
Worse, when you have two identical literal rules, you will see 3 alts
in the EOT state (one for ID and one each for the identical rules).
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tryToResolveWithSemanticPredicates | protected boolean tryToResolveWithSemanticPredicates(DFAState d, Set nondeterministicAlts)(Code) | | See if a set of nondeterministic alternatives can be disambiguated
with the semantic predicate contexts of the alternatives.
Without semantic predicates, syntactic conflicts are resolved
by simply choosing the first viable alternative. In the
presence of semantic predicates, you can resolve the issue by
evaluating boolean expressions at run time. During analysis,
this amounts to suppressing grammar error messages to the
developer. NFA configurations are always marked as "to be
resolved with predicates" so that
DFA.findNewDFAStatesAndAddDFATransitions() will know to ignore
these configurations and add predicate transitions to the DFA
after adding token/char labels.
During analysis, we can simply make sure that for n
ambiguously predicted alternatives there are at least n-1
unique predicate sets. The nth alternative can be predicted
with "not" the "or" of all other predicates. NFA configurations without
predicates are assumed to have the default predicate of
"true" from a user point of view. When true is combined via || with
another predicate, the predicate is a tautology and must be removed
from consideration for disambiguation:
a : b | B ; // hoisting p1||true out of rule b, yields no predicate
b : {p1}? B | B ;
This is done down in getPredicatesPerNonDeterministicAlt().
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turnOffOtherAlts | protected static void turnOffOtherAlts(DFAState d, int min, Set nondeterministicAlts)(Code) | | turn off all states associated with alts other than the good one
(as long as they are one of the nondeterministic ones)
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