It was recently discovered that the aarF gene in Providencia stuartii is required for coenzyme Q (CoQ) biosynthesis. Here we report that yigR, the Escherichia coli homologue of aarF, is ubiB, a gene required for the first monooxygenase step in CoQ biosynthesis. Both the P. stuartii aarF and E. coli ubiB (yigR) disruption mutant strains lack CoQ and accumulate octaprenylphenol. Octaprenylphenol ...

Using Coq, we mechanize Wegener’s proof of Kosaraju’s linear-time algorithm for computing the strongly connected components of a directed graph. Furthermore, also in Coq, we define an executable and terminating depth-first search algorithm.

We present a Coq reflexive tactic for deciding equalities or inequalities in Kleene algebras. This tactic is part of a larger project, whose aim is to provide tools for reasoning about binary relations in Coq: binary relations form a Kleene algebra, where the star operation is the reflexive transitive closure. Our tactic relies on an initiality theorem, whose proof goes by replaying finite auto...

We report on three different approaches to use hash-consing in programs certified with the Coq system, using binary decision diagrams (BDD) as running example. The use cases include execution inside Coq, or execution of the extracted OCaml code. There are different trade-offs between faithful use of pristine extracted code, and code that is fine-tuned to make use of OCaml programming constructs...

This paper describes SEPIA, a tool for automated proof generation in Coq. SEPIA combines model inference with interactive theorem proving. Existing proof corpora are modelled using state-based models inferred from tactic sequences. These can then be traversed automatically to identify proofs. The SEPIA system is described and its performance evaluated on three Coq datasets. Our results show tha...