Formalization of Universal Algebra in Agda

In this work we present a novel formalization of universal algebra in Agda. We show that heterogeneous signatures can be elegantly modelled in type-theory using sets indexed by arities to represent operations. We prove elementary results of heterogeneous algebras, including the proof that the term algebra is initial and the proofs of the three isomorphism theorems. We further formalize equational theory and prove soundness and completeness. At the end, we define (derived) signature morphisms, from which we get the contravariant functor between algebras; moreover, we also proved that, under some restrictions, the translation of a theory induces a contra-variant functor between models.Fil: Gunther, Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gadea, Alejandro Emilio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Pagano, Miguel Maria. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentin

Biortogonalidad para corrección de compiladores y adecuación computacional

Tesis (Doctor en Ciencias de la Computación)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2019.En esta tesis hemos estudiado en profundidad los métodos de biortogonalidad y step-indexing para probar tanto adecuación computacional como corrección de compiladores. Un primer aporte es la prueba de corrección de una semántica denotacional con respecto a una operacional para un lenguaje funcional lazy definido por John Launchbury corriegiendo ciertos ciertas irregularidades en algunas definiciones. Otra contribución es la prueba de adecuación computacional de una semántica operacional con respecto a una denotacional para un lenguaje funcional call-by-value con subtipado. Para este mismo lenguaje probamos la coincidencia entre una semántica denotacional extrínseca y una intrínseca, obteniendo como corolario la coherencia de la semántica intrínseca. Este aporte incluye la mecanización completa en Coq de todos los resultados; siendo, tanto como sabemos, la primera mecanización del teorema de bracketing propuesto por John Reynolds. Finalmente damos una prueba de corrección de un compilador para un lenguaje lazy con recursión generando código para una máquina abstracta, este aporte extiende significativamente un trabajo previo desarrollado por Leonardo Rodríguez. Incluimos también la mecanización completa en Coq.In this work we studied the techniques of biorthogonality and step-indexing for proving computational adequacy and compiler correctness. The first contribution is the proof of correction of a denotational semantics with respect to a operational semantics for a lazy language originally defined by John Launchbury fixing some definition irregularities. Another contribution is the proof of computational adequacy of the operational semantics with respect to a denotational semantics for a call-by-value functional language with subtyping. Also for this same language we prove the coincidence between an extrinsic and intrinsic denotational semantics. This contribution includes the complete mechanization in Coq of all the results; being, as far as we know, the first mechanization of Reynolds’ bracketing theorem. Finally we give a proof of the correction of a compiler for an abstract machine, this contribution significantly extends previous work developed by Leonardo Rodríguez. We also include the complete mechanization in Coq.Gadea, Alejandro Emilio. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía, Física y Computación; Argentina

Clonal chromosomal mosaicism and loss of chromosome Y in elderly men increase vulnerability for SARS-CoV-2

The pandemic caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2, COVID-19) had an estimated overall case fatality ratio of 1.38% (pre-vaccination), being 53% higher in males and increasing exponentially with age. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, we found 133 cases (1.42%) with detectable clonal mosaicism for chromosome alterations (mCA) and 226 males (5.08%) with acquired loss of chromosome Y (LOY). Individuals with clonal mosaic events (mCA and/or LOY) showed a 54% increase in the risk of COVID-19 lethality. LOY is associated with transcriptomic biomarkers of immune dysfunction, pro-coagulation activity and cardiovascular risk. Interferon-induced genes involved in the initial immune response to SARS-CoV-2 are also down-regulated in LOY. Thus, mCA and LOY underlie at least part of the sex-biased severity and mortality of COVID-19 in aging patients. Given its potential therapeutic and prognostic relevance, evaluation of clonal mosaicism should be implemented as biomarker of COVID-19 severity in elderly people. Among 9578 individuals diagnosed with COVID-19 in the SCOURGE study, individuals with clonal mosaic events (clonal mosaicism for chromosome alterations and/or loss of chromosome Y) showed an increased risk of COVID-19 lethality