Validating complex user input (using normalized context-free grammars and CYK)

Validating complex user input (using normalized context-free grammars and CYK)
Here I am again, presenting to you another 'OH MI GOD, SO MUCH MATH' article. TL; DR; I made a simple JavaScript library that allows you to validate complex user input whenever regular expressions can't help you (validating formulae for example). Unfortunately, due to the algorithm's generality it ain't the quickest. Go to last section ...