Abstract: We present a novel parsing algorithm for all context-free languages. The algorithm features a clean mathematical formulation: parsing is expressed as a series of standard operations on regular languages and relations. Parsing complexity w.r.t. input length matches the state of the art: it is worst-case cubic, quadratic for unambiguous grammars, and linear for LR-regular grammars. What distinguishes our approach is that parsing can be implemented using only immutable, acyclic data structures. We also propose a parsing optimization technique called context-free memoization. It allows handling an overwhelming majority of input symbols using a simple stack and a lookup table, similarly to the operation of a deterministic LR(1) parser. This allows our proof-of-concept implementation to outperform the best current implementations of common generalized parsing algorithms (Earley, GLR, and GLL). Tested on a large Java source corpus, parsing is 3–5 times faster, while recognition—35 times faster.