Antlr4: Another "No Viable Alternative Error" - parsing

Question

I have checked similar questions surrounding this issue but none seems to provide a solution to my version of the problem.
I just started Antlr4 recently and all has been going nicely until I hit this particular roadblock.
My grammar is a basic math expression grammar but for some reason I noticed the generated parser(?) is unable to walk from paser-rule "equal" to paser-rule "expr", in order to reach lexer-rule "NAME".
grammar MathCraze;
NUM : [0-9]+ ('.' [0-9]+)?;
WS : [ \t]+ -> skip;
NL : '\r'? '\n' -> skip;
NAME: [a-zA-Z_][a-zA-Z_0-9]*;
ADD: '+';
SUB : '-';
MUL : '*';
DIV : '/';
POW : '^';
equal
: add # add1
| NAME '=' equal # assign
;
add
: mul # mul1
| add op=('+'|'-') mul # addSub
;
mul
: exponent # power1
| mul op=('*'|'/') exponent # mulDiv
;
exponent
: expr # expr1
| expr '^' exponent # power
;
expr
: NUM # num
| NAME # name
| '(' add ')' # parens
;
If I pass a word as input, sth like "variable", the parser throws the error above, but if I pass a number as input (say "78"), the parser walks the tree successfully (i.e, from rule "equal" to "expr").
equal equal
| |
add add
| |
mul mul
| |
exponent exponent
| |
expr expr
| |
NUM NAME
| |
"78" # No Error "variable" # Error! Tree walk doesn't reach here.
I've checked for every type of ambiguity I know of, so I'm probably missing something here.
I'm using Antlr5.6 by the way and I will appreciate if this problem gets solved. Thanks in advance.

Answer 1

Your style of expression hierarchy is the one we use in parsers written by hand or in ANTLR v3, from low to high precedence.
As Raven said, ANTLR 4 is much more powerful. Note the <assoc = right> specification in the power rule, which is usually right-associative.
grammar Question;
question
: line+ EOF
;
line
: expr NL
| assign NL
;
assign
: NAME '=' expr # assignSingle
| NAME '=' assign # assignMulti
;
expr // from high to low precedence
: <assoc = right> expr '^' expr # power
| expr op=( '*' | '/' ) expr # mulDiv
| expr op=( '+' | '-' ) expr # addSub
| '(' expr ')' # parens
| atom_r # atom
;
atom_r
: NUM
| NAME
;
NAME: [a-zA-Z_][a-zA-Z_0-9]*;
NUM : [0-9]+ ('.' [0-9]+)?;
WS : [ \t]+ -> skip;
NL : [\r\n]+ ;
Run with the -gui option to see the parse tree :
$ echo $CLASSPATH
.:/usr/local/lib/antlr-4.6-complete.jar
$ alias grun
alias grun='java org.antlr.v4.gui.TestRig'
$ grun Question question -gui data.txt
and this data.txt file :
variable
78
a + b * c
a * b + c
a = 8 + (6 * 9)
a ^ b
a ^ b ^ c
7 * 2 ^ 5
a = b = c = 88
.
Added
Using your original grammar and starting with the equal rule, I have the following error :
$ grun Q2 equal -tokens data.txt
[#0,0:7='variable',<NAME>,1:0]
[#1,9:10='78',<NUM>,2:0]
...
[#41,89:88='<EOF>',<EOF>,10:0]
line 2:0 no viable alternative at input 'variable78'
If I start with rule expr, there is no error :
$ grun Q2 expr -tokens data.txt
[#0,0:7='variable',<NAME>,1:0]
...
[#41,89:88='<EOF>',<EOF>,10:0]
$
Run grun with the -gui option and you'll see the difference :
running with expr, the input token variable is catched in NAME, rule expr is satisfied and terminates;
running with equal it's all in error. The parser tries the first alternative equal -> add -> mul -> exponent -> expr -> NAME => OK. It consumes the token variable and tries to do something with the next token 78. It rolls back in each rule, see if it can do something with the alt of rule, but each alt requires an operator. Thus it arrives in equal and starts again with the token variable, this time using the alt | NAME '='. NAME consumes the token, then the rule requires '=', but the input is 78 and does not satisfies it. As there is no other choice, it says there is no viable alternative.
$ grun Q2 equal -tokens data.txt
[#0,0:7='variable',<NAME>,1:0]
[#1,8:7='<EOF>',<EOF>,1:8]
line 1:8 no viable alternative at input 'variable'
If variable is the only token, same reasoning : first alternative equal -> add -> mul -> exponent -> expr -> NAME => OK, consumes variable, back to equal, tries the alt which requires '=', but the input is at EOF. That's why it says there is no viable alternative.
$ grun Q2 equal -tokens data.txt
[#0,0:1='78',<NUM>,1:0]
[#1,2:1='<EOF>',<EOF>,1:2]
If 78 is the only token, do the same reasoning : first alternative equal -> add -> mul -> exponent -> expr -> NUM => OK, consumes 78, back to equal. The alternative is not an option. Satisfied ? oops, what about EOF.
Now let's add a NUM alt to equal :
equal
: add # add1
| NAME '=' equal # assign
| NUM '=' equal # assignNum
;
$ grun Q2 equal -tokens data.txt
[#0,0:1='78',<NUM>,1:0]
[#1,2:1='<EOF>',<EOF>,1:2]
line 1:2 no viable alternative at input '78'
First alternative equal -> add -> mul -> exponent -> expr -> NUM => OK, consumes 78, back to equal. Now there is also an alt for NUM, starts again, this time using the alt | NUM '='. NUM consumes the token 78,
then the parser requires '=', but the input is at EOF, hence the message.
Now let's add a new rule with EOF and let's run the grammar from all :
all : equal EOF ;
$ grun Q2 all -tokens data.txt
[#0,0:1='78',<NUM>,1:0]
[#1,2:1='<EOF>',<EOF>,1:2]
$ grun Q2 all -tokens data.txt
[#0,0:7='variable',<NAME>,1:0]
[#1,8:7='<EOF>',<EOF>,1:8]
The input corresponds to the grammar, and there is no more message.

Answer 2

Although I can't answer your question about why the parser can't reach NAME in expr I'd like to point out that with Antlr4 you can use direct left recursion in your rule specification which makes your grammar more compact and omproves readability.
With that in mind your grammar could be rewritten as
math:
assignment
| expression
;
assignment:
ID '=' (assignment | expression)
;
expression:
expression '^' expression
| expression ('*' | '/') expression
| expression ('+' | '-') expression
| NAME
| NUM
;
That grammar hapily takes a NAME as part of an expression so I guess it would solve your problem.
If you're really interested in why it didn't work with your grammar then I'd first check if the lexer has matched the input into the expected tokens. Afterwards I would have a look at the parse tree to see what the parser is making of the given token sequence and then trying to do the parsing manually accoding to your grammar and during that you should be able to find the point at which the parser does something different from what you'd expect it to do.