Coq is a total dependently-typed programming language: recursive functions must be terminating and co-recursive functions must be productive. The requirement of totality is essential to ensure logical consistency, since a non-terminating function can be easily used to encode a proof of falsity. Systems based on dependent type theories, such as Coq and Agda, typically use syntactic methods, call...

The COQ2 gene in Saccharomyces cerevisiae encodes a Coq2 (p-hydroxybenzoate:polyprenyl transferase), which is required in the biosynthetic pathway of CoQ (ubiquinone). This enzyme catalyses the prenylation of p-hydroxybenzoate with an all-trans polyprenyl group. We have isolated cDNA which we believe encodes the human homologue of COQ2 from a human muscle and liver cDNA library. The clone conta...

Mitochondria are key regulators of cell viability and provide essential functions that protect against neurodegenerative disease. To develop a model for mitochondrial-dependent neurodegeneration in Caenorhabditis elegans, we used RNA interference (RNAi) and genetic ablation to knock down expression of enzymes in the Coenzyme Q (CoQ) biosynthetic pathway. CoQ is a required component of the ATP-p...

We present the rewriting toolkit CiME3. Amongst other original features, this version enjoys two kinds of engines: to handle and discover proofs of various properties of rewriting systems, and to generate COQ scripts from proofs traces input in certification proof format (CPF) (an XML format widely accepted by the certified rewriting community) in order to certify them with a skeptical proof as...

In this communication, we introduce a novel biomarker of aquatic contamination based on the xenobiotic-induced response of the hepatic coenzyme Q (CoQ) redox balance of fishes to polycyclic aromatic hydrocarbons (PAHs). The method is demonstrated by comparing changes in the liver CoQ redox balance with that measured using the CYP1A-based, 7-ethoxyresofurin-O-deethylase activity assay, on admini...

The Focal language (formerly FoC) allows one to incrementally build modules and to formally prove their correctness. In this paper, we present two formal semantics for encoding Focal constructions in the Coq proof assistant. The first one is implemented in the Focal compiler to have the correctness of Focal libraries verified with the Coq proof-checker. The second one formalizes the Focal struc...

Largely adopted by proof assistants, the conventional induction methods based on explicit induction schemas are non-reductive and local, at schema level. On the other hand, the implicit induction methods used by automated theorem provers allow for lazy and mutual induction reasoning. In this paper, we present a new tactic for the Coq proof assistant able to perform automatically implicit induct...