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In this paper, we present an efficient, functional, and formally verifiedparsing algorithm for LL(1) context-free expressions based on the concept ofderivatives of formal languages. Parsing with derivatives is an elegant parsingtechnique, which, in the general case, suffers from cubic worst-case timecomplexity and slow performance in practice. We specialise the parsing withderivatives algorithm to LL(1) context-free expressions, where alternatives canbe chosen given a single token of lookahead. We formalise the notion of LL(1)expressions and show how to efficiently check the LL(1) property. Next, wepresent a novel linear-time parsing with derivatives algorithm for LL(1)expressions operating on a zipper-inspired data structure. We prove thealgorithm correct in Coq and present an implementation as a parser combinatorsframework in Scala, with enumeration and pretty printing capabilities.

LL(1) Parsing with Derivatives and Zippers