Computing Integer Sequences: Filtering vs Generation (Functional Pearl)

TL;DR

This paper compares filtering and generation strategies for computing integer sequences using Haskell, illustrating their differences and efficiencies, and discusses analogous C implementations to foster cross-paradigm insights.

Contribution

It introduces a comparative analysis of filtering versus generation methods for sequence computation in functional programming, with insights applicable across programming paradigms.

Findings

Filtering and generation approaches have distinct performance trade-offs.

Cross-paradigm considerations enhance understanding of sequence computation.

Haskell and C implementations illustrate different algorithmic strategies.

Abstract

As a report of a teaching experience, we analyse Haskell programs computing two integer sequences: the Hamming sequence and the Ulam sequence. For both of them, we investigate two strategies of computation: the first is based on filtering out those natural numbers that do not belong to the sequence, whereas the second is based on the direct generation of num- bers that belong to the sequence. Advocating cross-fertilisation among ideas emerging when programming in different programming paradigms, in the background, we sketch out some considerations about corresponding C programs solving the same two problems.