Decidability of Univariate Real Algebra with Predicates for Rational and Integer Powers

We prove decidability of univariate real algebra extended with predicates for rational and integer powers, i.e., $(x^n \in \mathbb{Q})$ and $(x^n \in \mathbb{Z})$. Our decision procedure combines computation over real algebraic cells with the rational root theorem and witness construction via algebraic number density arguments.Comment: To appear in CADE-25: 25th International Conference on Automated Deduction, 2015. Proceedings to be published by Springer-Verla

Machine-Checked Proofs For Realizability Checking Algorithms

Virtual integration techniques focus on building architectural models of systems that can be analyzed early in the design cycle to try to lower cost, reduce risk, and improve quality of complex embedded systems. Given appropriate architectural descriptions, assume/guarantee contracts, and compositional reasoning rules, these techniques can be used to prove important safety properties about the architecture prior to system construction. For these proofs to be meaningful, each leaf-level component contract must be realizable; i.e., it is possible to construct a component such that for any input allowed by the contract assumptions, there is some output value that the component can produce that satisfies the contract guarantees. We have recently proposed (in [1]) a contract-based realizability checking algorithm for assume/guarantee contracts over infinite theories supported by SMT solvers such as linear integer/real arithmetic and uninterpreted functions. In that work, we used an SMT solver and an algorithm similar to k-induction to establish the realizability of a contract, and justified our approach via a hand proof. Given the central importance of realizability to our virtual integration approach, we wanted additional confidence that our approach was sound. This paper describes a complete formalization of the approach in the Coq proof and specification language. During formalization, we found several small mistakes and missing assumptions in our reasoning. Although these did not compromise the correctness of the algorithm used in the checking tools, they point to the value of machine-checked formalization. In addition, we believe this is the first machine-checked formalization for a realizability algorithm.Comment: 14 pages, 1 figur

A Formalization of the Theorem of Existence of First-Order Most General Unifiers

This work presents a formalization of the theorem of existence of most general unifiers in first-order signatures in the higher-order proof assistant PVS. The distinguishing feature of this formalization is that it remains close to the textbook proofs that are based on proving the correctness of the well-known Robinson's first-order unification algorithm. The formalization was applied inside a PVS development for term rewriting systems that provides a complete formalization of the Knuth-Bendix Critical Pair theorem, among other relevant theorems of the theory of rewriting. In addition, the formalization methodology has been proved of practical use in order to verify the correctness of unification algorithms in the style of the original Robinson's unification algorithm.Comment: In Proceedings LSFA 2011, arXiv:1203.542

Hypercalcemia in a patient with disseminated paracoccidioidomycosis: a case report

<p>Abstract</p> <p>Introduction</p> <p>Hypercalcemia is well described in various granulomatous disorders, such as sarcoidosis, tuberculosis, berylliosis, leprosy and fungal infections. However, the association of <it>Paracoccidioides brasiliensis </it>and hypercalcemia is rare: to the best of our knowledge, only two cases have previously been reported, and neither had a clear documentation of the etiology of the hypercalcemia.</p> <p>Case presentation</p> <p>We report the case of a 22-year-old man in whom disseminated infection with paracoccidioidomycosis was associated with hypercalcemia. The patient had a high normal serum level of 1,25-dihydroxyvitamin D and a suppressed parathyroid hormone value, an indication that the hypercalcemia was not mediated by parathyroid hormone and might be associated with 1,25-dihydroxyvitamin D.</p> <p>Conclusion</p> <p>The episode resolved readily with administration of corticosteroids, an outcome suggesting that this is an effective treatment of hypercalcemia of this origin. On follow-up, while receiving antifungal therapy for <it>P. brasiliensis </it>the patient's calcium values remained normal.</p

Evolução na utilização e nos gastos de uma operadora de saúde

Brazil’s aging population and the rising number of people reliant upon the country’s supplementary healthcare system have elicited the concern of public and private managers regarding the increase in healthcare costs. In this paper, the costs per gender, per type of medical expenses and per age group of a major Brazilian self-managed healthcare provider between 2007 and 2013 were analyzed. This healthcare provider is of interest because, besides portraying a single condition of revenue growth restricted to the existing contributors, it also replicates the demographic profile expected for Brazil in 2050, when approximately one-third of its population will be over 60 years of age. The analyses confirm the current literature as they show an increase in healthcare plan usage by the elderly and the difference between admission rates by gender. They also reveal an increase in average length of stay in hospital and the increase in medical costs far above inflation, especially for materials and medicines. It is hoped that this study will help scholars and others interested in comparisons of medical expense trends, especially by age and sex, and that it encourages further collaboration on the sustainability of health insurance providers in Brazil

Friends with benefits: implementing corecursion in foundational proof assistants

We introduce AmiCo, a tool that extends a proof assistant, Isabelle/HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As new friends are registered, corecursion benefits by becoming more expressive. We describe this process and its implementation, from the user’s specification to the synthesis of a higher-order definition to the registration of a friend. We show some substantial case studies where our approach makes a difference