An implementation of Deflate in Coq

The widely-used compression format "Deflate" is defined in RFC 1951 and is based on prefix-free codings and backreferences. There are unclear points about the way these codings are specified, and several sources for confusion in the standard. We tried to fix this problem by giving a rigorous mathematical specification, which we formalized in Coq. We produced a verified implementation in Coq which achieves competitive performance on inputs of several megabytes. In this paper we present the several parts of our implementation: a fully verified implementation of canonical prefix-free codings, which can be used in other compression formats as well, and an elegant formalism for specifying sophisticated formats, which we used to implement both a compression and decompression algorithm in Coq which we formally prove inverse to each other -- the first time this has been achieved to our knowledge. The compatibility to other Deflate implementations can be shown empirically. We furthermore discuss some of the difficulties, specifically regarding memory and runtime requirements, and our approaches to overcome them.