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Extra info for Flex & bison
BNF Grammars In order to write a parser, we need some way to describe the rules the parser uses to turn a sequence of tokens into a parse tree. ‡ The standard form to write down a CFG is Backus-Naur Form (BNF), created around 1960 to describe Algol 60 and named after two members of the Algol 60 committee. Fortunately, BNF is quite simple. Here’s BNF for simple arithmetic expressions enough to handle 1 * 2 + 3 * 4 + 5:
There’s a separate issue for interactive scanners related to whether the scanning process itself needs to peek ahead at the character after the one being processed, but we’ll save that for later in this chapter. Fortunately, flex generally does the right thing in that case, too. ‡ If the previous yyin was read all the way to EOF, YY_NEW_FILE isn’t strictly necessary, but it’s good to use anyway for defensive programming. This is particularly the case if a scanner or parse error might return from the scanner or parser without reading the whole file.
Why not? Would it be easier to fix this in the scanner or in the parser? 2. Make the calculator into a hex calculator that accepts both hex and decimal numbers. In the scanner add a pattern such as 0x[a-f0-9]+ to match a hex number, and in the action code use strtol to convert the string to a number that you store in yylval; then return a NUMBER token. Adjust the output printf to print the result in both decimal and hex. 3. (extra credit) Add bit operators such as AND and OR to the calculator. The obvious operator to use for OR is a vertical bar, but that’s already the unary absolute value operator.