From: Daniel Carrera <dcarrera@...>
Date: 2002-12-01T05:55:42+09:00
Subject: Re: Ruby ++, the one element and generators


[snip]
> In algebra, the one element is a particularly important element (along with
> zero) because you can generate all values by systematically adding the one
> element to the previous result, starting with the zero element.

Their importance is not that 0 is the additive identity, and if we have a
ring, then there is a multiplicative identity 1.

[snip]
> It appears to me that all the talk about why ++ is not valid due to
> anti-shoe-box behaviour is beside the point, because the would also be true
> for += :

The anti-shoe-box explanation, as I understand it, is that assignment (ie.
"=") is distinctly different from object methods (e.g. +).  This explains
why += cannot be a method.  Indeed, it is not a method.

The analogy does not say that we cannot have a '++'.  It only explains
why, if we did, it would not be a method either.

[snip]
> The point, is that whatever problems there are with ++ and object
> modifications applies equally to += and the next, next! method, and these
> problems have been solved.

True.  Maybe the difference is that '+=' has an '=', so it looks like a
binding operator.  Maybe Matz feels that '++' is just not "The Ruby way".

[snip]
> Note that integers do not have a next! operation and float do not have
> a next method at all - this makes perfect sense:
>
> In algebraic terms, there is no 'one' element for Real numbers, while
> natural numbers (integers) do have a one element.

Please don't call it "one".  There is a multiplicative identity, it's
just 1.  It just happens that 1 is not an additive generator.  Call it
"generator".

[snip]
> a++ as a synonym for
> a = a.next
[snip]
> a++! as a synom for
> a.next!

Perhaps we can make 'a++' a synonym for 'a.next' (i.e. no inplace change)
and 'a++!' a synonym for 'a.next!' (i.e. inplace change).  Maybe Matz will
like that.


Daniel.