DiscreteRanges

Introduction

This package provides a type DiscreteRange{T} for types T which are isomorphic to integers, in the sense that elements of T can be thought of as evenly spaced values using some relevant arithmetic operations. All subtypes of Integer satisfy this, and also Date.

DiscreteRange(left::T, right::T) is meant to represent all values x::T such that a ≤ x ≤ b. In this sense it is very similar to a UnitRange, except that it can be defined for types other than <: Real, and extended easily (see below). Iteration, indexing and array interfaces are supported, and so are basic set operations (∪, ∩, ⊆, ∈, etc).

Comparison and conflict with IntervalSets.jl

IntervalSets.jl is a similar library serving a different purpose. Both export .., you can avoid conflicts by importing only DiscreteRange and optionally using another infix operator:

using DiscreteRanges: DiscreteRange
const ∷ = DiscreteRanges.:(..) # or pick your favorite operator
1∷2                            # DiscreteRange{Int}(1, 2)

Then comparing the two packages, keep in mind that IntervalSets.jl is better for representing intervals of real numbers, while a DiscreteRange is a collection of a finite number of objects.

The following table summarizes the differences:

	DiscreteRange	IntervalSets.ClosedInterval
3 ∈ 1..3	true	true
3.0 ∈ 1..3	true (converted first)	true (compared as is)
3.1 ∈ 1..3	throws InexactError	true
1.0..3.0	throws ArgumentError (non-discrete type)	valid
(1..2) ∪ (3..4)	1..4	throws ArgumentError (disjoint)
length(1..3)	3	3 (this may change)
width(1..3)	throws MethorError	2
(1..2) ∈ (0..10)	throws MethorError	true

Extending for custom types

To make DiscreteRange work for a type T, define isdiscrete, discrete_gap, and discrete_next. See their docstring for further information. There is an example in the unit tests.