A Derivative-based Parser Generator for Visibly Pushdown Grammars

In this article, we present a derivative-based, functional recognizer and parser generator for visibly pushdown grammars. The generated parser accepts ambiguous grammars and produces a parse forest containing all valid parse trees for an input string in linear time. Each parse tree in the forest can then be extracted also in linear time. Besides the parser generator, to allow more flexible forms of the visibly pushdown grammars, we also present a translator that converts a tagged CFG to a visibly pushdown grammar in a sound way, and the parse trees of the tagged CFG are further produced by running the semantic actions embedded in the parse trees of the translated visibly pushdown grammar. The performance of the parser is compared with popular parsing tools, including ANTLR, GNU Bison, and other popular hand-crafted parsers. The correctness and the time complexity of the core parsing algorithm are formally verified in the proof assistant Coq.