In ANTLR v3, syntactic predicates could be used to solve ambiguitites, i.e., to explicitly tell ANTLR which alternative should be chosen. ANTLR4 seems to simply accept grammars with similar ambiguities, but during parsing it reports these ambiguities. It produces a parse tree, despite these ambiguities (by chosing the first alternative, according to the documentation). But what can I do, if I want it to chose some other alternative? In other words, how can I explicitly resolve ambiguities?
(For the simple case of the dangling else problem see: What to use in ANTLR4 to resolve ambiguities (instead of syntactic predicates)?)
A more complex example:
If I have a rule like this:
expr
: expr '[' expr? ']'
| ID expr
| '[' expr ']'
| ID
| INT
;
This will parse foo[4] as (expr foo (expr [ (expr 4) ])). But I may want to parse it as (expr (expr foo) [ (expr 4) ]). (I. e., always take the first alternative if possible. It is the first alternative, so according to the documentation, it should have higher precedence. So why it builds this tree?)
If I understand correctly, I have 2 solutions:
Basically implement the syntactic predicate with a semantic predicate (however, I'm not sure how, in this case).
Restructure the grammar.
For example, replace expr with e:
e : expr | pe
;
expr
: expr '[' expr? ']'
| ID expr
| ID
| INT
;
pe : '[' expr ']'
;
This seems to work, although the grammar became more complex.
I may misunderstood some things, but both of these solutions seem less elegant and more complicated than syntactic predicates. Although, I like the solution for the dangling else problem with the ?? operator. But I'm not sure how to use in this case. Is it possible?
You may be able to resolve this by placing the ID alternative above ID expr. When left-recursion is eliminated, all of your alternatives which are not left recursive are parsed before your alternatives which are left recursive.
For your example, the first non-left-recursive alternative ID expr matches the entire expression, so there is nothing left to parse afterwards.
To get this expression (expr (expr foo) [ (expr 4) ]), you can use
top : expr EOF;
expr : expr '[' expr? ']' | ID | INT ;
Related
In the following example, the order matters in terms of precedence:
grammar Precedence;
root: expr EOF;
expr
: expr ('+'|'-') expr
| expr ('*' | '/') expr
| Atom
;
Atom: [0-9]+;
WHITESPACE: [ \t\r\n] -> skip;
For example, on the expression 1+1*2 the above would produce the following parse tree which would evaluate to (1+1)*2=4:
Whereas if I changed the first and second alternations in the expr I would then get the following parse tree which would evaluate to 1+(1*2)=3:
What are the 'rules' then for when it actually matters where the ordering in an alternation occurs? Is this only relevant if it one of the 'edges' of the alternation recursively calls the expr? For example, something like ~ expr or expr + expr would matter, but something like func_call '(' expr ')' or Atom would not. Or, when is it important to order things for precedence?
If ANTLR did not have the rule to give precedence to the first alternative that could match, then either of those trees would be valid interpretations of your input (and means the grammar is technically ambiguous).
However, when there are two alternatives that could be used to match your input, then ANTLR will use the first alternative to resolve the ambiguity, in this case establishing operator precedence, so typically you would put the multiplication/division operator before the addition/subtraction, since that would be the traditional order of operations:
grammar Precedence;
root: expr EOF;
expr
: expr ('+'|'-') expr
| expr ('*' | '/') expr
| Atom
;
Atom: [0-9]+;
WHITESPACE: [ \t\r\n] -> skip;
Most grammar authors will just put them in precedence order, but things like Atoms or parenthesized exprs won’t really care about the order since there’s only a single alternative that could be used.
I could capture a parenthetical group using something like:
expr ::= "(" <something> ")"
However, sometimes it's useful to use multiple levels of nesting, and so it's (theoretically) possible to have more than one parens as long as they match. For example:
>>> (1)+1
2
>>> (((((-1)))))+2
1
>>> ((2+2)+(1+1))
6
>>> (2+2))
SyntaxError: invalid syntax
Is there a way to specify a "matching-ness" in EBNF, or how is parenthetical-matching handled by most parsers?
In order to be able to match an arbitrary amount of anything (be it parentheses, operators, list items etc.) you need recursion (EBNF also features repetition operators that can be used instead of recursion in some cases, but not for constructs that need to be matched like parentheses).
For well-matched parentheses, the proper production is simply:
expr ::= "(" expr ")"
That's in addition to productions for other types of expressions, of course, so a complete grammar might look like this:
expr ::= "(" expr ")"
expr ::= NUMBER
expr ::= expr "+" expr
expr ::= expr "-" expr
expr ::= expr "*" expr
expr ::= expr "/" expr
Or for an unambiguous grammar:
expr ::= expr "+" multExpr
expr ::= expr "-" multExpr
multExpr ::= multExpr "*" primaryExpr
multExpr ::= multExpr "/" primaryExpr
primaryExpr ::= "(" expr ")"
primaryExpr ::= NUMBER
Also, how do you usually go about 'testing' that it is correct -- is there an online tool or something that can validate a syntax?
There are many parser generators that can accept some form of BNF- or EBNF-like notation and generate a parser from it. You can use one of those and then test whether the generated parser parses what you want it to. They're usually not available as online tools though. Also note that parser generators generally need the grammar to be unambiguous or you to add precedence declarations to disambiguate it.
also wouldn't infinite loop?
No. The exact mechanics depend on the parsing algorithm used of course, but if the character at the current input position is not an opening parenthesis, then clearly this isn't the right production to use and another one needs to be applied (or a syntax error raised if none of the productions apply).
Left recursion can cause infinite recursion when using top-down parsing algorithms (though in case of parser generators it's more likely that the grammar will either be rejected or in some cases automatically rewritten than that you get an actual infinite recursion or loop), but non-left recursion doesn't cause that kind of problem with any algorithm.
I'm currently writing a simple grammar that requires operator precedence and mixed associativities in one expression. An example expression would be a -> b ?> C ?> D -> e, which should be parsed as (a -> (((b ?> C) ?> D) -> e). That is, the ?> operator is a high-precedence left-associative operator wheras the -> operator is a lower-precedence right-associative operator.
I'm prototyping the grammar in ANTLR 3.5.1 (via ANTLRWorks 1.5.2) and find that it can't handle the following grammar:
prog : expr EOF;
expr : term '->' expr
| term;
term : ID rest;
rest : '?>' ID rest
| ;
It produces rule expr has non-LL(*) decision due to recursive rule invocations reachable from alts 1,2 error.
The term and rest productions work fine in isolation when I tested it , so I assumed this happened because the parser is getting confused by expr. To get around that, I did the following refactor:
prog : expr EOF;
expr : term exprRest;
exprRest
: '->' expr
| ;
term : ID rest;
rest : DU ID rest
| ;
This works fine. However, because of this refactor I now need to check for empty exprRest nodes in the output parse tree, which is non-ideal. Is there a way to make ANTLR work around the ambiguity in the initial declaration of expr? I would of assumed that the generated parser would fully match term and then do a lookahead search for "->" and either continue parsing or return the lone term. What am I missing?
As stated, the problem is in this rule:
expr : term '->' expr
| term;
The problematic part is the term which is common to both alternatives.
LL(1) grammar doesn't allow this at all (unless term only matches zero tokens - but such rules would be pointless), because it cannot decide which alternative to use with only being able to see one token ahead (that's the 1 in LL(1)).
LL(k) grammar would only allow this if the term rule could match at most k - 1 tokens.
LL(*) grammar which ANTLR 3.5 uses does some tricks that allows it to handle rules that match any number of tokens (ANTLR author calls this "variable look-ahead").
However, one thing that these tricks cannot handle is if the rule is recursive, i.e. if it or any rules it invokes reference itself in any way (direct or indirect) - and that is exactly what your term rule does:
term : ID rest;
rest : '?>' ID rest
| ;
- the rule rest, referenced from term, recursively references itself. Thus, the error message
rule expr has non-LL(*) decision due to recursive rule invocations ...
The way to solve this limitation of LL grammars is called left-factoring:
expr : term
( '->' expr )?
;
What I did here is said "match term first" (since you want to match it in both alternatives, there's no point in deciding which one to match it in), then decide whether to match '->' expr (this can be decided just by looking at the very next token - if it's ->, use it - so this is even LL(1) decision).
This is very similar to what you came to as well, but the parse tree should look very much like you intended with the original grammar.
I'm writing a grammar for a toy language in Yacc (the one packaged with Go) and I have an expected shift-reduce conflict due to the following pseudo-issue. I have to distilled the problem grammar down to the following.
start:
stmt_list
expr:
INT | IDENT | lambda | '(' expr ')' { $$ = $2 }
lambda:
'(' params ')' '{' stmt_list '}'
params:
expr | params ',' expr
stmt:
/* empty */ | expr
stmt_list:
stmt | stmt_list ';' stmt
A lambda function looks something like this:
map((v) { v * 2 }, collection)
My parser emits:
conflicts: 1 shift/reduce
Given the input:
(a)
It correctly parses an expr by the '(' expr ')' rule. However given an input of:
(a) { a }
(Which would be a lambda for the identity function, returning its input). I get:
syntax error: unexpected '{'
This is because when (a) is read, the parser is choosing to reduce it as '(' expr ')', rather than consider it to be '(' params ')'. Given this conflict is a shift-reduce and not a reduce-reduce, I'm assuming this is solvable. I just don't know how to structure the grammar to support this syntax.
EDIT | It's ugly, but I'm considering defining a token so that the lexer can recognize the ')' '{' sequence and send it through as a single token to resolve this.
EDIT 2 | Actually, better still, I'll make lambdas require syntax like ->(a, b) { a * b} in the grammar, but have the lexer emit the -> rather than it being in the actual source code.
Your analysis is indeed correct; although the grammar is not ambiguous, it is impossible for the parser to decide with the input reduced to ( <expr> and with lookahead ) whether or not the expr should be reduced to params before shifting the ) or whether the ) should be shifted as part of a lambda. If the next token were visible, the decision could be made, so the grammar LR(2), which is outside of the competence of go/yacc.
If you were using bison, you could easily solve this problem by requesting a GLR parser, but I don't believe that go/yacc provides that feature.
There is an LR(1) grammar for the language (there is always an LR(1) grammar corresponding to any LR(k) grammar for any value of k) but it is rather annoying to write by hand. The essential idea of the LR(k) to LR(1) transformation is to shift the reduction decisions k-1 tokens forward by accumulating k-1 tokens of context into each production. So in the case that k is 2, each production P: N → α will be replaced with productions TNU → Tα U for each T in FIRST(α) and each U in FOLLOW(N). [See Note 1] That leads to a considerable blow-up of non-terminals in any non-trivial grammar.
Rather than pursuing that idea, let me propose two much simpler solutions, both of which you seem to be quite close to.
First, in the grammar you present, the issue really is simply the need for a two-token lookahead when the two tokens are ){. That could easily be detected in the lexer, and leads to a solution which is still hacky but a simpler hack: Return ){ as a single token. You need to deal with intervening whitespace, etc., but it doesn't require retaining any context in the lexer. This has the added bonus that you don't need to define params as a list of exprs; they can just be a list of IDENT (if that's relevant; a comment suggests that it isn't).
The alternative, which I think is a bit cleaner, is to extend the solution you already seem to be proposing: accept a little too much and reject the errors in a semantic action. In this case, you might do something like:
start:
stmt_list
expr:
INT
| IDENT
| lambda
| '(' expr_list ')'
{ // If $2 has more than one expr, report error
$$ = $2
}
lambda:
'(' expr_list ')' '{' stmt_list '}'
{ // If anything in expr_list is not a valid param, report error
$$ = make_lambda($2, $4)
}
expr_list:
expr | expr_list ',' expr
stmt:
/* empty */ | expr
stmt_list:
stmt | stmt_list ';' stmt
Notes
That's only an outline; the complete algorithm includes the mechanism to recover the original parse tree. If k is greater than 2 then T and U are strings the the FIRSTk-1 and FOLLOWk-1 sets.
If it really is a shift-reduce conflict, and you want only the shift behavior, your parser generator may give you a way to prefer a shift vs. a reduce. This is classically how the conflict for grammar rules for "if-then-stmt" and "if-then-stmt-else-stmt" is resolved, when the if statement can also be a statement.
See http://www.gnu.org/software/bison/manual/html_node/Shift_002fReduce.html
You can get this effect two ways:
a) Count on the accidental behavior of the parsing engine.
If an LALR parser handles shifts first, and then reductions if there are no shifts, then you'll get this "prefer shift" for free. All the parser generator has to do is built the parse tables anyway, even if there is a detected conflict.
b) Enforce the accidental behavior. Design (or a get a) parser generator to accept "prefer shift on token T". Then one can supress the ambiguity. One still have to implement the parsing engine as in a) but that's pretty easy.
I think this is easier/cleaner than abusing the lexer to make strange tokens (and that doesn't always work anyway).
Obviously, you could make a preference for reductions to turn it the other way. With some extra hacking, you could make shift-vs-reduce specific the state in which the conflict occured; you can even make it specific to the pair of conflicting rules but now the parsing engine needs to keep preference data around for nonterminals. That still isn't hard. Finally, you could add a predicate for each nonterminal which is called when a shift-reduce conflict is about to occur, and it have it provide a decision.
The point is you don't have to accept "pure" LALR parsing; you can bend it easily in a variety of ways, if you are willing to modify the parser generator/engine a little bit. This gives a really good reason to understand how these tools work; then you can abuse them to your benefit.
Let's imagine I want to be able to parse values like this (each line is a separate example):
x
(x)
((((x))))
x = x
(((x))) = x
(x) = ((x))
I've written this YACC grammar:
%%
Line: Binding | Expr
Binding: Pattern '=' Expr
Expr: Id | '(' Expr ')'
Pattern: Id | '(' Pattern ')'
Id: 'x'
But I get a reduce/reduce conflict:
$ bison example.y
example.y: warning: 1 reduce/reduce conflict [-Wconflicts-rr]
Any hint as to how to solve it? I am using GNU bison 3.0.2
Reduce/reduce conflicts often mean there is a fundamental problem in the grammar.
The first step in resolving is to get the output file (bison -v example.y produces example.output). Bison 2.3 says (in part):
state 7
4 Expr: Id .
6 Pattern: Id .
'=' reduce using rule 6 (Pattern)
')' reduce using rule 4 (Expr)
')' [reduce using rule 6 (Pattern)]
$default reduce using rule 4 (Expr)
The conflict is clear; after the grammar reads an x (and reduces that to an Id) and a ), it doesn't know whether to reduce the expression as an Expr or as a Pattern. That presents a problem.
I think you should rewrite the grammar without one of Expr and Pattern:
%%
Line: Binding | Expr
Binding: Expr '=' Expr
Expr: Id | '(' Expr ')'
Id: 'x'
Your grammar is not LR(k) for any k. So you either need to fix the grammar or use a GLR parser.
Suppose the input starts with:
(((((((((((((x
Up to here, there is no problem, because every character has been shifted onto the parser stack.
But now what? At the next step, x must be reduced and the lookahead is ). If there is an = somewhere in the future, x is a Pattern. Otherwise, it is an Expr.
You can fix the grammar by:
getting rid of Pattern and changing Binding to Expr | Expr '=' Expr;
getting rid of all the definitions of Expr and replacing them with Expr: Pattern
The second alternative is probably better in the long run, because it is likely that in the full grammar which you are imagining (or developing), Pattern is a subset of Expr, rather than being identical to Expr. Factoring Expr into a unit production for Pattern and the non-Pattern alternatives will allow you to parse the grammar with an LALR(1) parser (if the rest of the grammar conforms).
Or you can use a GLR grammar, as noted above.