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

A Certified Extension of the Krivine Machine for a Call-by-Name Higher-Order Imperative Language

In this paper we present a compiler that translates programs from an imperative higher-order language into a sequence of instructions for an abstract machine. We consider an extension of the Krivine machine for the call-by-name lambda calculus, which includes strict operators and imperative features. We show that the compiler is correct with respect to the big-step semantics of our language, both for convergent and divergent programs

The formal verification of the ctm approach to forcing

We discuss some highlights of our computer-verified proof of the construction, given a countable transitive set-model $M$ of $\mathit{ZFC}$, of generic extensions satisfying $\mathit{ZFC}+\neg\mathit{CH}$ and $\mathit{ZFC}+\mathit{CH}$. Moreover, let $\mathcal{R}$ be the set of instances of the Axiom of Replacement. We isolated a 21-element subset $\Omega\subseteq\mathcal{R}$ and defined $\mathcal{F}:\mathcal{R}\to\mathcal{R}$ such that for every $\Phi\subseteq\mathcal{R}$ and $M$-generic $G$, $M\models \mathit{ZC} \cup \mathcal{F}\text{``}\Phi \cup \Omega$ implies $M[G]\models \mathit{ZC} \cup \Phi \cup \{ \neg \mathit{CH} \}$, where $\mathit{ZC}$ is Zermelo set theory with Choice. To achieve this, we worked in the proof assistant Isabelle, basing our development on the Isabelle/ZF library by L. Paulson and others.Comment: 20pp + 14pp in bibliography & appendices, 2 table

A certified extension of the Krivine machine for a call-by-name higher-order imperative language

In this paper we present a compiler that translates programs from an imperative higher-order language into a sequence of instructions for an abstract machine. We consider an extension of the Krivine machine for the call-by-name lambda calculus, which includes strict operators and imperative features. We show that the compiler is correct with respect to the big-step semantics of our language, both for convergent and divergent programs.http://drops.dagstuhl.de/opus/volltexte/2014/4634publishedVersionFil: Rodríguez, Leonardo Matías. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Fridlender, Daniel Edgardo. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Pagano, Miguel María. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Ciencias de la Computació

First steps towards a formalization of forcing

We lay the ground for an Isabelle/ZF formalization of Cohen's technique of forcing. We formalize the definition of forcing notions as preorders with top, dense subsets, and generic filters. We formalize a version of the principle of Dependent Choices and using it we prove the Rasiowa-Sikorski lemma on the existence of generic filters. Given a transitive set M, we define its generic extension M[G], the canonical names for elements of M, and finally show that if M satisfies the axiom of pairing, then M[G] also does. We also prove that M[G] is transitive.Fil: Gunther, Emmanuel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física. Sección Ciencias de la Computación; 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. Sección Ciencias de la Computación; ArgentinaFil: Sanchez Terraf, Pedro Octavio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomia y Física. Sección Matemática; Argentin

Adaptative mechanisms of cellulose synthesis under stress conditions

Cellulose is the main structural compound of the plant cell wall and the most abundant biopolymer on Earth (Bar‐On et al 2018). The essential role of cellulose in plant development and defence highlights the importance of understanding how its synthesis is regulated and will provide new tools to improve crop tolerance to biotic and abiotic stresses. We identified that Tetratricopeptide Thioredoxin‐Like (TTL) proteins function as scaffold components of brassinosteroid signalling components (Amorim‐Silva et al 2019) and as new components of the Cellulose Synthase Complex (CSC) and describe its unique dynamic association with the CSC under cellulose‐deficient conditions (Kesten, García‐Moreno, Amorim‐Silva et al 2022). The TTL‐CESA interaction at the plasma membrane significantly increased under conditions that cause reduced cellulose content, such as salt stress and structural alterations of the CSCs. The relocalization of cytosolic TTLs to the active CSCs allows cellulose synthesis, mediated by a stress‐resilient cortical microtubule array and the stabilization of the CSCs at the plasma membrane. TTLs carry this out by interacting with Cellulose Synthase 1 and promoting the polymerization of microtubules, thus maintaining the stability and integrity of the complex. We propose that TTLs act as bridges connecting stress‐mediated cell wall modification with the regulation of cellulose biosynthesis. We are currently investigating novel components involved in TTL function and how this protein family is regulated. Recently, we have identified the 14‐3‐3 proteins as interactors of TTL3. The 14‐3‐3s are a family of proteins conserved in eukaryotes that target a wide number of proteins (Huang et al 2022). An Arabidopsis line overexpressing 14‐3‐3λ present phenotypes under stress consistent with defects in cellulose biosynthesis. This study will elucidate a possible role of 14‐3‐3 proteins in TTL regulation and cellulose biosynthesis.This work was funded by the Spanish Ministry for Science and Innovation (MCIN/AEI/10.1 0 9/ 011000110 ) and the Andalusian Research Plan cofinanced by the European Union(PAI I 2020-PY20_0008 and UMA20- E ERJA-02 ) to M.A.B.; V.A.-S. was supported by an Emerging Investigator research project (UMA20- E ERJA-007) and cofinanced by the “Programa Operativo E ER 201 -2020” and by the “Consejeria de Economia y Conocimiento de la Junta de Andalucia”. R.P.M. was supported by the Andalusian PRE OC_01 fellowship. A.M. was supported by Shanghai Center for Plant Stress Biology. Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

FUN: una herramienta didáctica para la derivación de programas funcionales

En este trabajo se describe la utilización de una herramienta desarrollada para la enseñanza de lógica y programación. En la sección 2 se presentan el contexto de utilización de la herramienta y se aborda la perspectiva didáctica; en la sección 3 se describen los conceptos básicos a enseñar con esta herramienta. En la sección 4 se describe la utilización de la herramienta con ejemplos. En la sección 5 cerramos con las conclusiones de nuestro trabajo.WIEI - II Workshop de innovación en educación en informáticaRed de Universidades con Carreras en Informática (RedUNCI