arXiv subjects

Raul Rojas

Publications and source records attributed to Raul Rojas.

20 records · Page 2Linked to original sources

arXiv2015

A Tutorial Introduction to the Lambda Calculus

This paper is a concise and painless introduction to the $λ$-calculus. This formalism was developed by Alonzo Church as a tool for studying the mathematical properties of effectively computable functions. The formalism became popular and has provided a strong theoretical foundation for the family of functional programming languages. This tutorial shows how to perform arithmetical and logical computations using the $λ$-calculus and how to define recursive functions, even though $λ$-calculus functions are unnamed and thus cannot refer explicitly to themselves.

cs.LO↗

arXiv2014

The straight line, the catenary, the brachistochrone, the circle, and Fermat

This paper shows that the well-known curve optimization problems which lead to the straight line, the catenary curve, the brachistochrone, and the circle, can all be handled using a unified formalism. Furthermore, from the general differential equation fulfilled by these geodesics, we can guess additional functions and the required metric. The parabola, for example, is a geodesic under a metric guessed in this way. Numerical solutions are found for the curves corresponding to geodesics in the various metrics using a ray-tracing approach based on Fermat's principle.

math.HO↗