From: GOTO Kentaro <gotoken@...>
Date: 2002-09-11T02:40:22+09:00
Subject: Re: Larry Wall's comments on Ruby

At Wed, 11 Sep 2002 01:14:23 +0900,
Giuseppe Bilotta wrote:
> > I find that highly unnatural because we've been learning since grade school 
> > that a + b = b + a.
> > 
> > If the objects don't satisfy that property they should be using a different 
> > symbol.
> 
> No way. For example, product is commutative only up to complex 
> numbers. If you move on to quaternions, you get a noncommutative 
> product. And as for noncommutative sum ... think for example about 
> strings. "a" + "b" != "b" + "a"

Well, we often choose `+' for commutative operation in algebra indeed.
Several years ago, I proposed to define String#* as concatination
because `*' can read as product and String is sometimes regarded as
semigroup which has product defined as concatination in theoretical
computer science.  String#* could give some merit:

 - Product may be noncommutative and a*b != b*a doesn't surprise us
   not so much.
 - Repeatation would be naturally replaced with String#** and it looks
   clearly noncommutative.  
 - A user could define 1+"2" and "2"+1 as 3 like Perl. 

I proposed also Array#*.  But those proposals were rejected because
`*' looked strange for many people (including matz).

However I think that decision was not bad because I can use for
Enumerable#* for direct product now.  For example:

  require 'product'
  for i,j,k in (1..2)*(3..4)*(2..3)
    puts "#{i}+#{j}+#{k} = #{i+j+k}"
  end

generates:

  1+3+2 = 6
  1+3+3 = 7
  1+4+2 = 7
  1+4+3 = 8
  2+3+2 = 7
  2+3+3 = 8
  2+4+2 = 8
  2+4+3 = 9

http://www.ruby-lang.org/en/raa-list.rhtml?name=product

-- Gotoken