A Verified Earley Parser

An Earley parser is a top-down parsing technique that is capable of parsing arbitrary context-free grammars. We present a functional implementation of an Earley parser verified using the interactive theorem prover Isabelle/HOL. Our formalization builds upon Cliff Jones' extensive, refinement-based paper proof. We implement and prove soundness and completeness of a functional recognizer modeling Jay Earley’s original imperative implementation and extend it with the necessary data structures to enable the construction of parse trees following the work of Elizabeth Scott. Building upon this foundation, we develop a functional parser and prove its soundness. We round off the paper by providing an informal argument and empirical data regarding the running time and space complexity of our implementation.