SRFI 231: Intervals and Generalized Arrays

by Bradley J. Lucier

status: final (2022-09-25)

keywords: Data Structure, Numbers

Abstract

This SRFI specifies an array mechanism for Scheme. Arrays as defined here are quite general; at their most basic, an array is simply a mapping, or function, from multi-indices of exact integers $i_0,\ldots,i_{d-1}$ to Scheme values. The set of multi-indices $i_0,\ldots,i_{d-1}$ that are valid for a given array form the domain of the array. In this SRFI, each array's domain consists of the cross product of intervals of exact integers $[l_0,u_0)\times[l_1,u_1)\times\cdots\times[l_{d-1},u_{d-1})$ of $\mathbb Z^d$, $d$-tuples of integers. Thus, we introduce a data type called $d$-intervals, or more briefly intervals, that encapsulates this notion. (We borrow this terminology from, e.g., Elias Zakon's Basic Concepts of Mathematics.) Specialized variants of arrays provide portable programs with efficient representations for common use cases.

This is a revised and improved version of SRFI 179.