On Sat, 31 Oct 2009 14:12:40 -0400, Terry Reedy wrote:

> alex23 wrote:

>> Terry Reedy <(E-Mail Removed)> wrote:

>>> alex23 wrote:

>>>> You're completely wrong. Immutability has nothing to do with

>>>> identity,

> ...

> > I'm honestly not getting your point here.

>

> Let me try again, a bit differently.

>

> I claim that the second statement, and therefor the first, can be seen

> as wrong. I also claim that (Python) programmers need to understand why.

>

> In mathematics, we generally have immutable values whose 'identity' is

> their value. There is, for example, only one, immutable, empty set.
I think it's more than that -- I don't think pure mathematics makes any

distinction at all between identity and equality. There are no instances

at all, so you can't talk about individual values. It's not that the

empty set is a singleton, because the empty set isn't a concrete object-

with-existence at all. It's an abstraction, and as such, questions of

"how many separate empty sets are there?" are meaningless.

There are an infinite number of empty sets that differ according to their

construction:

The set of all American Presidents called Boris Nogoodnik.

The set of all human languages with exactly one noun and one verb.

The set of all fire-breathing mammals.

The set of all real numbers equal to sqrt(-1).

The set of all even prime numbers other than 2.

The set of all integers between 0 and 1 exclusive.

The set of all integers between 1 and 2 exclusive.

The set of all positive integers between 2/5 and 4/5.

The set of all multiples of five between 26 and 29.

The set of all non-zero circles in Euclidean geometry where the radius

equals the circumference.

....

I certainly wouldn't say all fire-breathing mammals are integers between

0 and 1, so those sets are "different", and yet clearly they're also "the

same" in some sense. I think this demonstrates that the question of how

many different empty sets is meaningless -- it depends on what you mean

by different and how many.

> In informatics, and in particular in Python, in order to have

> mutability, we have objects with value and an identity that is separate

> from their value.
I think you have this backwards. We have value and identity because of

the hardware we use -- we store values in memory locations, which gives

identity. Our universe imposes the distinction between value and

identity. To simulate immutability and singletons is hard, and needs to

be worked at.

Nevertheless, it would be possible to go the other way. Given

hypothetical hardware which only supported mutable singletons, we could

simulate multiple instances. It would be horribly inefficient, but it

could be done. Imagine a singleton-mutable-set implementation, something

like this:

class set:

def __init__(id):

return singleton

def add(id, obj):

singleton.elements.append((id, obj))

def __contains__(id, element)

return (id, obj) in singleton.elements

and so forth.

You might notice that this is not terribly different from how one might

define non-singleton sets. The difference being, Python sets have

identity implied by storage in distinct memory locations, while this

hypothetical singleton-set has to explicitly code for identity.

> There can be, for example, multiple mutable empty

> sets. Identity is important because we must care about which empty set

> we add things to. 'Identity' is only needed because of 'mutability', so

> it is mistaken to say they have nothing to do with each other.
True, but it is not a mistake to say that identity and mutability are

independent: there are immutable singletons, and mutable singletons, and

immutable non-singletons, and mutable non-singletons. Clearly, knowing

that an object is mutable doesn't tell you whether it is a singleton or

not, and knowing it is a singleton doesn't tell you whether it is

immutable or not.

E.g. under normal circumstances modules are singletons, but they are

mutable; frozensets are immutable, but they are not singletons.

> Ideally, from both a conceptual and space efficiency view, an

> implementation would allow only one copy for each value of immutable

> classes.
Ideally, from a complexity of implementation view, an implementation

would allow an unlimited number of copies of each value of immutable

classes.

> This is what new programmers assume when they blithely use 'is'

> instead of '==' (as would usually be correct in math).
Nah, I think you're crediting them with far more sophistication than they

actually have. I think most people in general, including many new

programmers, simply don't have a good grasp of the conceptual difference

between equality and identity. In plain language, "is" and its

grammatical forms "be", "are", "am" etc. have many meanings:

(1) Set membership testing:

Socrates is a man.

This is a hammer.

(2) Existence:

There is a computer language called Python.

There is a monster under the bed.

(3) Identity:

Iron Man is Tony Stark.

The butler is the murderer.

(4) Mathematical equality:

If x is 5, and y is 11, then y is 2x+1.

(5) Equivalence:

The winner of this race is the champion.

The diameter of a circle is twice the radius.

(6) Metaphoric equivalence:

Kali is death.

Life is like a box of chocolates.

(7) Testing of state:

My ankle is sore.

Fred is left-handed.

(

Consequence

If George won the lottery, he would say he is happy.

(9) Cost

A cup of coffee is $3.

Only two of these usages work at all in any language I know of: equality

and identity testing, although it would be interesting to consider a

language that allowed type testing:

45 is an int -> returns True

"abc" is a float -> returns False

Some languages, like Hypertalk (by memory) and related languages, make

"is" a synonym for equals.

> However, for time efficiency reasons, there is no unique copy guarantee,

> so one must use '==' instead of 'is', except in those few cases where

> there is a unique copy guarantee, either by the language spec or by

> one's own design, when one must use 'is' and not '=='. Here 'must'

> means 'must to be generally assured of program correctness as intended'.

>

> We obviously agree on this guideline.
Yes.

--

Steven