Lambda the Ultimate

Non-Deterministic Recursive Ascent Parsing, Renee Leermakers. 1991 conference on European chapter of the Association for Computational Linguistics.

A purely functional implementation of LR-parsers is given, together with a simple correctness proof. It is presented as a generalization of the recursive descent parser. For non-LR grammars the time-complexity of our parser is cubic if the functions that constitute the parser are implemented as memo-functions, i.e. functions that memorize the results of previous invocations. Memo-functions also facilitate a simple way to construct a very compact representation of the parse forest. For LR(0) grammars, our algorithm is closely related to the recursive ascent parsers recently discovered by Kruseman Aretz [1] and Roberts [2]. Extended CF grammars (grammars with regular expressions at the right hand side) can be parsed with a simple modification of the LR-parser for normal CF grammars.

How LR parsers worked always confused me until I learned about their presentation in terms of recursive ascent.