Total Haskell is Reasonable Coq

We would like to use the Coq proof assistant to mechanically verify properties of Haskell programs. To that end, we present a tool, named hs-to-coq, that translates total Haskell programs into Coq programs via a shallow embedding. We apply our tool in three case studies -- a lawful Monad instance, "Hutton's razor", and an existing data structure library -- and prove their correctness. These examples show that this approach is viable: both that hs-to-coq applies to existing Haskell code, and that the output it produces is amenable to verification.Comment: 13 pages plus references. Published at CPP'18, In Proceedings of 7th ACM SIGPLAN International Conference on Certified Programs and Proofs (CPP'18). ACM, New York, NY, USA, 201

Who is afraid of constructivism? (¿Quién tiene miedo del constructivismo?)

Both generative and constructivist researchers agree that children are able to form abstractions and produce novel grammatically patterned utterances. Both approaches are able to explain such abilities, and hence their existence does not entail an innate Universal Grammar. However, generativists and constructivists differ in their views on the nature of early generalisations: while generative researchers assume that adult-like linguistic representations are present from the very beginning, constructivists argue that children begin with relatively specific, low level schemas and gradually extract more abstract patterns. There is considerable empirical evidence for the latter position. Moreover, constructivist theories provide a better explanation for principled behaviour -not just the observed patterns, but also the absence of certain constructions in children's early productions and various developmental asynchronies. Tanto los investigadores generativistas como constructivistas coinciden en que los niños son capaces de formar abstracciones y de producir emisiones novedosas gramaticalmente estructuradas. Ambos enfoques son capaces de explicar tales habilidades, y por eso su existencia no implica una Gramática Universal innata. Sin embargo, los investigadores generativistas y constructivistas difieren en su visión sobre la naturaleza de las generalizaciones tempranas: mientras que los investigadores generativistas asumen que las representaciones lingüísticas parecidas a las adultas están presentes desde edades tempranas, los constructivistas argumentan que los niños comienzan con esquemas de bajo nivel, relativamente específicos, y que gradualmente extraen esquemas más abstractos. Existe considerable evidencia empírica en apoyo de esta segunda posición. Además, las teorías constructivistas proporcionan una mejor explicación de las conductas basadas en reglas; no sólo de los patrones observados, sino también de la ausencia de ciertas construcciones en las producciones verbales tempranas de los niños y de diversas asincronías evolutivas

The foundations of computable general equilibrium theory

general equilibrium theory,CGE models,mathematical economics,computability,constructivity

Varieties of Mathematics in Economics- A Partial View

Real analysis, founded on the Zermelo-Fraenkel axioms, buttressed by the axiom of choice, is the dominant variety of mathematics utilized in the formalization of economic theory. The accident of history that led to this dominance is not inevitable, especially in an age when the digital computer seems to be ubiquitous in research, teaching and learning. At least three other varieties of mathematics, each underpinned by its own mathematical logic, have come to be used in the formalization of mathematics in more recent years. To set theory, model theory, proof theory and recursion theory correspond, roughly speaking, real analysis, non-standard analysis, constructive analysis and computable analysis. These other varieties, we claim, are more consistent with the intrinsic nature and ontology of economic concepts. In this paper we discuss aspects of the way real analysis dominates the mathematical formalization of economic theory and the prospects for overcoming this dominance.