From: Ben Tilly <ben_tilly@...>
Date: 2001-01-22T14:19:16+09:00
Subject: [ruby-talk:9702] Re: 101 Misconceptions About Dynamic Languages

Dave Thomas <Dave@PragmaticProgrammer.com> wrote:
>
>"Christoph Rippel" <crippel@primenet.com> writes:
>
> > try to express this in Ruby - it is going to be a nightmare.

(This having been a basic ring construction.)

>Perhaps you could help me understand the problem. The Ruby solution
>would seem to my naive eyes about half the size an considerably
>clearer. Without the need to jump through template hoops for type
>safety, most of the issues of genericity seem to go away.
>
>What am I missing?

Constructing Z/n is a special case of a generic
construction that you see in ring theory.  The general
idea is that you take a ring R (eg Z), and a subring I
(eg the multiples of 5) with the special property that
anything in R times anything in I gives you something
back in I.  You can now say that two elements x and y
are the same mod I if x-y is in I.  Each equivalence
class can now be represented by a single element in R,
and the set of equivalence classes turn out to be a new
ring R/I.

In my books a good model of Ring would be able to handle
this common and basic construction.  That would mean
(for instance) being able to handle the idea that
evaluating x=5 can be done in Q[x] (the ring of
polynomials over the rationals) by modding out by the
ideal (x-5).  (Ruby might do this, I don't know.  But
to my eyes this is a statement of the general problem
that I see in modelling concepts like Ring in an OO
hierarchy.)

Cheers,
Ben
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