README

This 'project' aims at implementing basic parsers for a very simple
grammar which describes arithmetic expressions.

Below is the grammar in BNF:

    <integer>		::= [0-9][0-9]*

    <primary-exp>	::= <integer> | "(" <exp> ")"

    <mult-exp>		::= <primary-exp>
			  | <mult-exp> "*" <primary-exp>

    <sum-exp>		::= <mult-exp>
			  | <sum-exp> "+" <mult-exp>
			  | <sum-exp> "-" <mult-exp>

    <exp>		::= <sum-exp>


Same grammar using EBNF:

   digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" ;

   integer = [ "-" ] , digit , {digit} ;

   val = '(' sum ')' | integer ;

   prod = val , { ('*'|'/'|'%'), val } ;

   sum = prod , { ('+'|'-'), prod } ;

   expr = sum



rdp.c: Implements the parser using a recursive descent parser (a
common way to program an LL parser). With many levels of precedence,
implementing this grammar with a predictive recursive-descent parser
can become inefficient. Parsing a number, for example, can require
four function calls (one for each non-terminal in the grammar, until
we reach primary-exp).

http://www.garshol.priv.no/download/text/bnf.html#id1.2.

opp.c: The operator-precedence parser can parse all LR(1) grammars
where two consecutive nonterminals never appear in the right-hand side
of any rule.

They can be written to consult an operator table at runtime, which
makes them suitable for languages that can add to or change their
operators while parsing.

The idea is that we can left associate the arithmetic operations as
long as we find operators with the same precedence, but we have to
save a temporary result to evaluate higher precedence operators.