We have the following grammar for a simple language:

  stmts^: stmt+;
  stmt: 'if'^ expr 'then'! stmts ('else'! stmts)? 'end'!
      | 'while'^ expr 'do'! stmts 'end'!
      | 'for'^ expr? ';'! expr? ';'! expr? 'do'! stmts 'done'!
      | 'break'
      | expr ';'!;

  expr: addi (('='^|'+='^|'-='^|'*='^|'/='^) expr)?;
  addi: term (('+'^|'-'^) term)*;
  term: atom (('*'^|'/'^) atom)*;
  atom: '-'^ atom | IDENT | NATURAL_LIT | '('! expr ')'!;

  IDENT: ('a'..'z'|'A'..'Z'|'_')('a'..'z'|'A'..'Z'|'_'|'0'..'9')*;
  NATURAL_LIT: ('0'..'9')+;

However, we have discovered the following problem: the expressions

• for i+=1 ; ; do ... done
• for ; ; i+=1 do ... done

generate the same AST: “for(+=(i,1), ...)”. This happens because the expr on the header of the for-loop may be missing, and in such case, nothing is included in the AST. Fix the grammar to resolve these ambiguities by making missing expressions on the header of the for-loop to appear explicitly in the AST: they should be represented by a special node named nop (no operation). For instance, the AST of the previous examples should be:

• for(+=(i,1),nop,nop,...)
• for(nop,nop,+=(i,1),...)