We describe our experience implementing a broad categorytheory 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...

In a city like Dubai, where one of the biggest and fastest growing construction markets in the world exists, the need to estimate the cost of quality in the construction projects becomes a vital task. This research used the prevention–appraisal–failure (PAF) model to evaluate the cost of quality (CoQ) and to determine its optimum value – the level of quality that minimizes the total CoQ – for t...

PROD id="i32" type Definition id="i0" MUTIND uri="cic:Coq/init/Datatypes/nat.ind" notype="0" id="i33" source apply xref="i34" apply xref="i37" times definitionURL= "cic/Coq/Init/Peano/mult.con" xref="i38" 0 definitionURL= "cic:/Coq/Init/Datatypes/nat.ind" cn xref="i41" 0 definitionURL= xref="i40" "cic:/Coq/Init/Datatypes/nat.ind" cn eq xref="i35" "cic:/Coq/Init/Logic/Equality/eq.ind" definition...

One of the biologically active quinones, coenzyme Q (CoQ), is widely distributed in nature and primarily localized in the mitochondria of animal cells (1, 2). There is con siderable evidence to support the fact that CoQ may be an important carrier for mediating between flavoprotein and cytochrome chains in mitochondria (3, 4). On the other hand, there is considerable literature on the pharm...

Coenzyme Q (CoQ) is a key component for many essential metabolic and antioxidant activities in cells mitochondria cell membranes. Mitochondrial dysfunction one of the hallmarks aging age-related diseases. Deprivation CoQ during can be cause or consequence this mitochondrial dysfunction. In any case, it seems clear that aging-associated deprivation accelerates these Non-genetic prolongevity inte...

ML4PG is an extension of the Proof General interface of Coq, allowing the user to invoke machine-learning algorithms and find proof similarities in Coq/SSReflect libraries. In this talk, we will show the recent ML4PG features in action, using examples from the standard SSReflect library and HoTT library. We will compare ML4PG with traditional Coq searching tools and dependency graphs.

CertiCoq is a mechanically verified, optimizing compiler for Coq that bridges the gap between certified high-level programs and their translation to machine language. We outline its design as well as the main foundational and engineering challenges involved in building and certifying a compiler for Coq in Coq.

We report on an extendable implementation of the communication interface connecting Coq proof assistant to the computational algebra system GAP using the Symbolic Computation Software Composability Protocol (SCSCP). It allows Coq to issue OpenMath requests to a local or remote GAP instances and represent server responses as Coq terms.

Coq is a tool allowing to certify proofs. This paper describes a Coq library for certifying termination proofs.

We consider refinement types in which base types can be refined by constraints expressible in some decidable logic. Such refinement types have been applied in many settings, such as certification of security policies [1, 10], and reasoning precisely about heap updates [9, 10]. A lot of work has been done on extensions of the basic idea of refinements, including inference in liquid types [8], or...