It’s been 45 years since Stephen Johnson wrote Yacc (Yet another compiler-compiler), a parser generator that made it possible for anyone to write fast, efficient parsers. Yacc, and its many derivatives, quickly became popular and were included in many Unix distributions. You would imagine that in 45 years we would have further perfected the art of creating parsers and would have standardized on a single tool. A lot of progress has been made, but there are still annoyances and problems affecting every tool out there.

This is great, even just for the overview of parsing.

The CYK algorithm (named after Cocke–Younger–Kasami) is in my opinion of great theoretical importance when it comes to parsing context-free grammars. CYK will parse all context-free parsers in O(n3), including the “simple” grammars that LL/LR can parse in linear time. It accomplishes this by converting parsing into a different problem: CYK shows that parsing context-free languages is equivalent to doing a boolean matrix multiplication. Matrix multiplication can be done naively in cubic time, and as such parsing context-free languages can be done in cubic time. It’s a very satisfying theoretical result, and the actual algorithm is small and easy to understand.

source: trivium