Tail recursive parser

A Tail Recursive Parser is on that uses a tail recursive parsing technique, it is an alternative to complex bottom-up parsers. Tail Recursive Parsing is a method of parsing a CFG, it is usually used in a Compiler for semantic analysis of a source program. Tail Recursive parsers are typically used because they can be easily written (given their closeness to Recursive descent parsers), and use little stack space. Given a EBNF Grammar such as the following:

E: T
T: T ('+' F)* | F
F: I ('*' I)* | I
I: <identifier>

A simple tail recursive parser can be written much like a recursive descent parser. The typical algorithm for parsing a grammar like this using an Abstract syntax tree is:

Parse the next level of the grammar and get its output tree, designate it the first tree, F
While there is terminating token, T, that can be put as the parent of this node:
1. Allocate a new node, N
2. Set N's current operator as the current input token
3. Advance the input one token
4. Set N's left subtree as F
5. Parse another level down again and store this as the next tree, X
6. Set N's right subtree as X
7. Set F to N
Return N

An C programming language implementation of this parser is shown here:

exptree *parse_e(void) {
    return parse_t();
}

exptree *parse_t(void) {
    exptree *first_f = parse_f();
    
    while(cur_token() == '+') {
        exptree *replace_tree = alloc_tree();
        replace_tree->token = cur_token();
        replace_token->left = first_f;
        next_token();
        replace_token->right = parse_f();
        first_f = replace_token;
    }

    return first_f;
}

exptree *parse_f(void) {
    exptree *first_i = parse_i();
    
    while(cur_token() == '*') {
        exptree *replace_tree = alloc_tree();
        replace_tree->token = cur_token();
        replace_tree->left = first_i;
        next_token();
        replace_tree->right = parse_i();
        first_i = replace_tree;
    }
    
    return first_i;
}

exptree *parse_i(void) {
    exptree *i = alloc_tree();
    exptree->left = exptree->right = NULL;
    exptree->token = cur_token();
    next_token();
}

Further reading