Regular Expression String Search With Bison

Hello,

I am struggling to understand bison, and parser in general, so I hope I 
can get some help. To understand better I decided to try to create a 
program the understands simple regular expressions, and is able to show 
correct sub string matches. Here is the grammar for the language I would 
like to make:

<regex>   ::= <term> '|' <regex>
           | term
<term>    ::= <term> <factor>
           | <factor>
<factor>  ::= <base> '*'
           | <base>
<base>    ::= '(' regex ')'
           | char

I have attempted to make smaller code to explain my issue, since using 
words alone is a bit difficult. Some of it may be nonsensical:

%{
   #include <stdio.h>
   #include <string.h>
   #include <stdbool.h>

   #define BUF_MAX 31
   
   int yylex (void);
   void yyerror (char const *);

   char regxp[BUF_MAX];
   char text[BUF_MAX];
   char input[BUF_MAX]

   int i = 0;
   
   struct regxp
   {
     bool star;
     char str[BUF_MAX];
   };
%}

%parse-param {char* regex}
%define api.value.type union
%token <char> CHAR
%type  <struct regxp> regex term factor base

%%
   input:
     input line
   | %empty
   ;

   line:
     regex '\n' { printf ($1.str); }
   | error '\n' { yyerrork; }
   | '\n'
   ;

   regex:
     regex term { strncpy ($1.str, $2.str); $$ = $1; }
   | term { $$ = $1; }
   ;

   term:
     term factor { strncpy ($1.str, $2.str); $$ = $1; }
   | factor { $$ = $1; }
   ;

   factor:
     base '*' { $$ = $1; $$.star = true; }
   | base { $$ = $1; sscanf (input, "%c", &$1.str) }
   ;

   base:
     '(' regex ')' { $$ = $1; }
   | CHAR { input[++i] = $1; }
%%

int
main (int argc, char const **argv)
{
   if (argc < 3)
     return 1;
   else
     strncpy (argv[2], regxp[], BUF_MAX);
   return yypase (argv[1]);
}

What exactly happens for the semantic variables, especially $$? My 
smallest element is a character, but I have to idea how to go from a 
character to a base token in code. So I think there will have to be some 
way of passing information around to the string in the regexp type.

In my main section, I just want to get a regular expression and a string 
to test against, like ./prog ab* ababb.
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