这些表达式的解析器语法

Question

I am trying to come up with a simple EBNF grammar for parsing the below expressions examples: ("->" isn't part of input). 'a', 'b' 'c' are multi character words which contain alphabets only.

-> a
-> (a)
-> (a | b | c)
-> (a (b | c | d))
-> (a (b | (c | d)) )
-> (a (
     b (
        c x
      | d (e | f)
      )
    )
  )

I tried coming up with several grammars (in Antlr) but all of them break for a few cases, this is what I have right now, Any help would be appreciated.

term:   '(' WORD+ options_list ')' 
    |   '(' WORD+ ('|' term)* ')'
    |   WORD+
    ;

options_list:   '(' term ('|' term)* ')' 
    ;
}

WORD    :   ('a'..'z')+ 
    ;

EDIT 1: Basically I am trying to create a hierarchical tree of words from the grammar for example in the last case the tree would look like these

     [a]
      |
     [b]
     / \
 [c,x]  [d]
        /  \
       [e]  [f] 

I don't want depend on Antlr or JavaCC for auto generating the parser for a different set of reasons, I would want to write my own simple recursive descent parser in order to do that I am first coming up with a valid grammar that works for all cases, then it would simple enough to implement from that.

EDIT2: After working some bits I have this which seems to work for

term:   WORD term?
    |   '(' term ('|' term)* ')'
    ;


WORD    :   ('a'..'z')+ 
    ;

Answer 1

The following grammar appears to parse all your provided examples.

term        : WORD+
            | '(' alt_term ')'
            ;

alt_term    : app_term
            | app_term '|' alt_term
            | app_term '|' '(' alt_term ')'
            ;

app_term    : WORD+
            | WORD+ '(' alt_term ')'
            ;

WORD        : ('a'..'z')+ 
            ;

I tested it in AntlrWorks, and all of your examples are parsed. I just added EOF recognition and skip on whitespaces.

Analysis of each case:

1. a

   1.1. term (1)

2. (a)

   2.1. term (2)

   2.2. alt_term (1)

   2.3. app_term (1)

3. (a | b | c)

   3.1. term (2)

   3.2. alt_term (2)

   3.3. app_term (1)

   3.4. alt_term (2)

   3.5. app_term (1)

   3.6. alt_term (1)

   3.7. app_term (1)

4. (a (b | c | d))

   4.1. term (2)

   4.2. alt_term (1)

   4.3. app_term (2)

   4.4. alt_term (2)

   4.5. app_term (1)

   4.6. alt_term (2)

   4.7. app_term (1)

   4.8. alt_term (1)

   4.9. app_term (1)

5. (a (b | (c | d)) )

   5.1. term (2)

   5.2. alt_term (1)

   5.3. app_term (2)

   5.4. alt_term (3)

   5.5. app_term (1)

   5.6. alt_term (2)

   5.7. app_term (1)

   5.8. alt_term (1)

   5.9. app_term (1)

6. (a (b (cx | d (e | f))))

   6.1. term (2)

   6.2. alt_term (1)

   6.3. app_term (2)

   6.4. alt_term (1)

   6.5. app_term (2)

   6.6. alt_term (2)

   6.7. app_term (1)

   6.8. alt_term (1)

   6.9. app_term (2)

   6.10. alt_term (2)

   6.11. app_term (1)

   6.12. alt_term (1)

   6.13. app_term (1)