Coenzyme Q10 deficiencies: pathways in yeast and humans.

Coenzyme Q (ubiquinone or CoQ) is an essential lipid that plays a role in mitochondrial respiratory electron transport and serves as an important antioxidant. In human and yeast cells, CoQ synthesis derives from aromatic ring precursors and the isoprene biosynthetic pathway. Saccharomyces cerevisiae coq mutants provide a powerful model for our understanding of CoQ biosynthesis. This review focusses on the biosynthesis of CoQ in yeast and the relevance of this model to CoQ biosynthesis in human cells. The COQ1-COQ11 yeast genes are required for efficient biosynthesis of yeast CoQ. Expression of human homologs of yeast COQ1-COQ10 genes restore CoQ biosynthesis in the corresponding yeast coq mutants, indicating profound functional conservation. Thus, yeast provides a simple yet effective model to investigate and define the function and possible pathology of human COQ (yeast or human gene involved in CoQ biosynthesis) gene polymorphisms and mutations. Biosynthesis of CoQ in yeast and human cells depends on high molecular mass multisubunit complexes consisting of several of the COQ gene products, as well as CoQ itself and CoQ intermediates. The CoQ synthome in yeast or Complex Q in human cells, is essential for de novo biosynthesis of CoQ. Although some human CoQ deficiencies respond to dietary supplementation with CoQ, in general the uptake and assimilation of this very hydrophobic lipid is inefficient. Simple natural products may serve as alternate ring precursors in CoQ biosynthesis in both yeast and human cells, and these compounds may act to enhance biosynthesis of CoQ or may bypass certain deficient steps in the CoQ biosynthetic pathway

A Coq-based synthesis of Scala programs which are correct-by-construction

The present paper introduces Scala-of-Coq, a new compiler that allows a Coq-based synthesis of Scala programs which are "correct-by-construction". A typical workflow features a user implementing a Coq functional program, proving this program's correctness with regards to its specification and making use of Scala-of-Coq to synthesize a Scala program that can seamlessly be integrated into an existing industrial Scala or Java application.Comment: 2 pages, accepted version of the paper as submitted to FTfJP 2017 (Formal Techniques for Java-like Programs), June 18-23, 2017, Barcelona , Spai

Computing with Classical Real Numbers

There are two incompatible Coq libraries that have a theory of the real numbers; the Coq standard library gives an axiomatic treatment of classical real numbers, while the CoRN library from Nijmegen defines constructively valid real numbers. Unfortunately, this means results about one structure cannot easily be used in the other structure. We present a way interfacing these two libraries by showing that their real number structures are isomorphic assuming the classical axioms already present in the standard library reals. This allows us to use O'Connor's decision procedure for solving ground inequalities present in CoRN to solve inequalities about the reals from the Coq standard library, and it allows theorems from the Coq standard library to apply to problem about the CoRN reals

Category Theory in Coq 8.5

We report on our experience implementing category theory in Coq 8.5. The repository of this development can be found at https://bitbucket.org/amintimany/categories/. This implementation most notably makes use of features, primitive projections for records and universe polymorphism that are new to Coq 8.5.Comment: This is the abstract for a talk accepted for a presentation at the 7th Coq Workshop, Sophia Antipolis, France on June 26, 201

Concrete Semantics with Coq and CoqHammer

The "Concrete Semantics" book gives an introduction to imperative programming languages accompanied by an Isabelle/HOL formalization. In this paper we discuss a re-formalization of the book using the Coq proof assistant. In order to achieve a similar brevity of the formal text we extensively use CoqHammer, as well as Coq Ltac-level automation. We compare the formalization efficiency, compactness, and the readability of the proof scripts originating from a Coq re-formalization of two chapters from the book

Gradual Certified Programming in Coq

Expressive static typing disciplines are a powerful way to achieve high-quality software. However, the adoption cost of such techniques should not be under-estimated. Just like gradual typing allows for a smooth transition from dynamically-typed to statically-typed programs, it seems desirable to support a gradual path to certified programming. We explore gradual certified programming in Coq, providing the possibility to postpone the proofs of selected properties, and to check "at runtime" whether the properties actually hold. Casts can be integrated with the implicit coercion mechanism of Coq to support implicit cast insertion a la gradual typing. Additionally, when extracting Coq functions to mainstream languages, our encoding of casts supports lifting assumed properties into runtime checks. Much to our surprise, it is not necessary to extend Coq in any way to support gradual certified programming. A simple mix of type classes and axioms makes it possible to bring gradual certified programming to Coq in a straightforward manner.Comment: DLS'15 final version, Proceedings of the ACM Dynamic Languages Symposium (DLS 2015

Total Haskell is Reasonable Coq

We would like to use the Coq proof assistant to mechanically verify properties of Haskell programs. To that end, we present a tool, named hs-to-coq, that translates total Haskell programs into Coq programs via a shallow embedding. We apply our tool in three case studies -- a lawful Monad instance, "Hutton's razor", and an existing data structure library -- and prove their correctness. These examples show that this approach is viable: both that hs-to-coq applies to existing Haskell code, and that the output it produces is amenable to verification.Comment: 13 pages plus references. Published at CPP'18, In Proceedings of 7th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP'18). ACM, New York, NY, USA, 201

Experience Implementing a Performant Category-Theory Library in Coq

We describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to cope with large categorical constructions without slowing proof script processing unacceptably. In this paper, we share the lessons we have learned about how to represent very abstract mathematical objects and arguments in Coq and how future proof assistants might be designed to better support such reasoning. One particular encoding trick to which we draw attention allows category-theoretic arguments involving duality to be internalized in Coq's logic with definitional equality. Ours may be the largest Coq development to date that uses the relatively new Coq version developed by homotopy type theorists, and we reflect on which new features were especially helpful.Comment: The final publication will be available at link.springer.com. This version includes a full bibliography which does not fit in the Springer version; other than the more complete references, this is the version submitted as a final copy to ITP 201