Pragmatic Quotient Types in Coq

Certified Programming with Dependent Types - A Pragmatic Introduction to the Coq Proof Assistant

Universal Algebra in Type Theory

We present a development of Universal Algebra inside Type Theory, formalized using the proof assistant Coq. We define the notion of a signature and of an algebra over a signature. We use setoids, i.e. types endowed with an arbitrary equivalence relation, as carriers for algebras. In this way it is possible to define the quotient of an algebra by a congruence. Standard constructions over algebra...

Coq as a Metatheory for Nuprl with Bar Induction

These past few years, we have been experimenting in Nuprl with versions of Brouwer’s Bar Induction principle. Until recently we had no formal proof that these rules are valid Nuprl reasoning principles. Thanks to our formalization of Nuprl’s metatheory in Coq, we can now rigorously check whether these principles are consistent with Nuprl. In this paper we present a proof, using our Coq framewor...

Ëøóöý Ó Ö Áòù Blockinøóò Ò Aeùôöð Îò Blockinòø Êðð 1⋆¸ååö Óö 2 ¸ Òò Êóöø ĺ Óò×øøøðð 2

Abstra t. In order to turn Nuprl's logi into a fully intuitionisti logi , we are urrently experimenting with versions of Brouwer's bar indu tion prin iple. Using our formalization of Nuprl's metatheory in Coq, we have proved the lassi al validity of two su h prin iples: one for sequen es of numbers that involved little hanges to the system, and a more general one for sequen es of losed terms wi...

A Novel Hybrid Approach to Analyze Cost of Quality: Balanced Scorecard and Fuzzy Logic

In this paper, a new methodology in the area of cost of quality (COQ) is proposed to determine the optimal investment allocation to all costs. The goal is to minimize costs involved in achieving a required level of quality. The contribution of this paper is fourfold: (I) considering two types of weights for each part of COQ, in which the first type is determined by the cost volume and the secon...