  In this paper, we present an efficient, functional, and formally verified
parsing algorithm for LL(1) context-free expressions based on the concept of
derivatives of formal languages. Parsing with derivatives is an elegant parsing
technique, which, in the general case, suffers from cubic worst-case time
complexity and slow performance in practice. We specialise the parsing with
derivatives algorithm to LL(1) context-free expressions, where alternatives can
be 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, we
present a novel linear-time parsing with derivatives algorithm for LL(1)
expressions operating on a zipper-inspired data structure. We prove the
algorithm correct in Coq and present an implementation as a parser combinators
framework in Scala, with enumeration and pretty printing capabilities.
