A functional presentation of Fourier series convergence

Abstract

Understanding lengthy mathematical proofs requires strong concentration. Authors must efficiently map whole logical structures into sequential texts. One way to ease such tasks is presenting the logical structure in a functional programming style. In our method, functional proofs are implemented by a real programming language. The behavior of each function appears in the proofs as a building block ready to be visualized with concrete data. This paper contains a case study of the well-known Dirichlet's theorem on the convergence of Fourier series. It shows the relevance of our method in rigorous mathematical presentations that involve ε-δ arguments intensively.