From: Massimiliano Mirra <list@...>
Date: 2002-07-04T21:10:41+09:00
Subject: Range thoughts (was: Re: (0..3) == (0...4) returning false?)

On Thu, Jul 04, 2002 at 01:38:44AM +0900, Yukihiro Matsumoto wrote:
> |I think you are right in your surprise.  The confusion comes when one group 
> |sees a range of integers as a set of integers and another group sees a range 
> |as a continuum of floats.  The "correct" answer depends of first determining 
> |the definition of a range: (1) a collection or (2) a single continuum.
> 
> That's the point.  My guess is a Range should work as both, depending
> on a method called.  I think I have to define useful / natural set of
> method names for each definition of a range.

And your guess is usually right. :-)

Take this as just thinking out loud:

FiniteSet < OrderedSet < DiscreteRange

InfiniteSet < Continuum

FiniteSet holds a finite number of elements, OrderedSet does the same
but they are sorted, DiscreteRange does the same but all the items
between the maximum and the minimum are present and at a fixed step
from the previous one and the next one.

InfiniteSet would hold an infinite number of elements (not really
useful), Continuum holds all the elements between a minimum and a
maximum.


Another thought:

Continuum < DiscreteRange

DiscreteRange adds a condition to Continuum.  While Continuum is all
the numbers between a minimum and a maximum, DiscreteRange is all the
numbers between a minimum and a maximum *such that* n % 1 == 0 (or n %
2 == 0 for the range to include only even numbers, and so on).
DiscreteRange#include?(n) is true when n satisfies the condition.

A block could be used for building the range (and an exception thrown
when the return value of the block does not match the rule):

min, max, step = 0, 10, 1
range = DiscreteRange.new(min, max) do |index| # index takes on 0,1,2...
  min + step*index
end
range.include?(5)    # true
range.include?(1.5)  # false
range.include?(11)   # false


It wouldn't be limited to uniformly stepped ranges.  Acceleration
against space, for example...

mix, max, acceleration = 0, 100, 9.81

space_travelled = DiscreteRange.new(min, max) do |time|
  acceleration * time ** 2
end
range.include?(39.24)  # true
range.include?(40)     # false
range.include?(245.25) # false


Again, just thinking out loud...



Massimiliano