On Sep 26, 2014, at 11:13, Ram Rachum wrote:

I agree with both the points you raised, they're both disadvantages. The question is whether the uses would be worth these two disadvantages. (`collections.Hashable` also has the second disadvantage you mentioned, and it's still in the stdlib, so there's hope.)

Hashable doesn't have that disadvantage. It checks whether the object's class or any superclass has a __hash__ method. So it's still based on the type, not on the value, and it works as expected with issubclass.

On Fri, Sep 26, 2014 at 9:10 PM, Thomas Gläßle wrote:

...

At first glance it sounds nice and straight forward. But - is a natural positive, or just non-negative? I guess, I'd have to look it up in the docs each time, since either definition is used in lots of places. Also, Natural does not correspond to the python type, but its value. So, you couldn't use it with issubclass.

Ram Rachum wrote on 09/26/2014 07:54 PM:

...

I wish the `numbers` module would include a `Natural` class that would simply check whether the number is integral and positive.

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On Sep 26, 2014, at 11:37, Ram Rachum wrote:

I checked it and you're right. So I guess `Hashable` is a bit confusing:

>>> isinstance(([3],), collections.Hashable) True

It makes sense if you think of isinstance as a type check, which is what it's supposed to be, rather than a value check. ([3],) is a tuple, and tuples are hashable as a type, even though some specific tuple values might not be. That's exactly why I think you want a type that you can check for Natural, rather than something about the value. That's what isinstance is for, and if you start subverting it to mean other things, that's when it leads to confusion.

On Fri, Sep 26, 2014 at 9:35 PM, Andrew Barnert wrote:

...

On Sep 26, 2014, at 11:13, Ram Rachum wrote:

...

I agree with both the points you raised, they're both disadvantages. The question is whether the uses would be worth these two disadvantages. (`collections.Hashable` also has the second disadvantage you mentioned, and it's still in the stdlib, so there's hope.)

Hashable doesn't have that disadvantage. It checks whether the object's class or any superclass has a __hash__ method. So it's still based on the type, not on the value, and it works as expected with issubclass.

...

On Fri, Sep 26, 2014 at 9:10 PM, Thomas Gläßle wrote:

...

At first glance it sounds nice and straight forward. But - is a natural positive, or just non-negative? I guess, I'd have to look it up in the docs each time, since either definition is used in lots of places. Also, Natural does not correspond to the python type, but its value. So, you couldn't use it with issubclass.

Ram Rachum wrote on 09/26/2014 07:54 PM:

...

I wish the `numbers` module would include a `Natural` class that would simply check whether the number is integral and positive.

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Hmm, I don't know, but I like it better. I probably had a reason and forgot it. Sorry :( On Fri, Sep 26, 2014 at 11:03 PM, David Mertz wrote:

Isn't the right answer to create an isNatural() function? Why do we need a type or class rather than just a function? It's not any easier to write 'isinstance(x, Natural)' than it is to write 'isNatural(x)'.

On Fri, Sep 26, 2014 at 11:47 AM, Andrew Barnert < abarnert@yahoo.com.dmarc.invalid> wrote:

...

On Sep 26, 2014, at 11:37, Ram Rachum wrote:

I checked it and you're right. So I guess `Hashable` is a bit confusing:

>>> isinstance(([3],), collections.Hashable) True

It makes sense if you think of isinstance as a type check, which is what it's supposed to be, rather than a value check. ([3],) is a tuple, and tuples are hashable as a type, even though some specific tuple values might not be.

That's exactly why I think you want a type that you can check for Natural, rather than something about the value. That's what isinstance is for, and if you start subverting it to mean other things, that's when it leads to confusion.

On Fri, Sep 26, 2014 at 9:35 PM, Andrew Barnert wrote:

...

On Sep 26, 2014, at 11:13, Ram Rachum wrote:

I agree with both the points you raised, they're both disadvantages. The question is whether the uses would be worth these two disadvantages. (`collections.Hashable` also has the second disadvantage you mentioned, and it's still in the stdlib, so there's hope.)

Hashable doesn't have that disadvantage. It checks whether the object's class or any superclass has a __hash__ method. So it's still based on the type, not on the value, and it works as expected with issubclass.

On Fri, Sep 26, 2014 at 9:10 PM, Thomas Gläßle wrote:

...

At first glance it sounds nice and straight forward. But - is a natural positive, or just non-negative? I guess, I'd have to look it up in the docs each time, since either definition is used in lots of places. Also, Natural does not correspond to the python type, but its value. So, you couldn't use it with issubclass.

Ram Rachum wrote on 09/26/2014 07:54 PM:

I wish the `numbers` module would include a `Natural` class that would simply check whether the number is integral and positive.

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-- Keeping medicines from the bloodstreams of the sick; food from the bellies of the hungry; books from the hands of the uneducated; technology from the underdeveloped; and putting advocates of freedom in prisons. Intellectual property is to the 21st century what the slave trade was to the 16th.

On 09/26/2014 01:27 PM, Ian Cordasco wrote:

The only motivations I can think of for making this a type (not that they're good ones) is you could do something like:

if isinstance(x, (Natural, Complex, Real)): # elif isinstance(x, Rational): # else: raise ValueError

Which is naturally (no pun intended) slightly nicer than

if isinstance(x, (Complex, Real)) or isNatural(x): #

The Good Reason for having a Natural type would be not having to always check for illegal values -- if one is (attempted to be) created, an exception is raised on the spot. n5 = Natural(5) n7 = Natural(7) n5 - n7 Traceback... -- ~Ethan~

On Fri, Sep 26, 2014 at 1:27 PM, Ian Cordasco wrote:

The only motivations I can think of for making this a type (not that they're good ones) is you could do something like:

if isinstance(x, (Natural, Complex, Real)): # elif isinstance(x, Rational): # else: raise ValueError

This code seems a bit broken, given:

...

...

issubclass(numbers.Rational, numbers.Real) Out[3]: True

def isNatural(x): return isinstance(x, int) and x > 0

I think the original desired behavior is this different one-liner: isNatural = lambda x: int(x)==x and x>0 -- Keeping medicines from the bloodstreams of the sick; food from the bellies of the hungry; books from the hands of the uneducated; technology from the underdeveloped; and putting advocates of freedom in prisons. Intellectual property is to the 21st century what the slave trade was to the 16th.

David Mertz wrote on 09/26/2014 10:38 PM:

On Fri, Sep 26, 2014 at 1:27 PM, Ian Cordasco mailto:graffatcolmingov@gmail.com> wrote:

The only motivations I can think of for making this a type (not that they're good ones) is you could do something like:

if isinstance(x, (Natural, Complex, Real)): # elif isinstance(x, Rational): # else: raise ValueError

This code seems a bit broken, given:

...

...

...

issubclass(numbers.Rational, numbers.Real) Out[3]: True

def isNatural(x): return isinstance(x, int) and x > 0

I think the original desired behavior is this different one-liner:

isNatural = lambda x: int(x)==x and x>0

Not sure about the original desired behaviour. I would have guessed the former function as well, as it more closely resembles the isinstance checks with the numbers types: >>> isinstance(1.0, (numbers.Rational, numbers.Integral)) False (one might argue, that 1.0 is a rational value, as is true for most float values, but the type has a different intention)

-- Keeping medicines from the bloodstreams of the sick; food from the bellies of the hungry; books from the hands of the uneducated; technology from the underdeveloped; and putting advocates of freedom in prisons. Intellectual property is to the 21st century what the slave trade was to the 16th.

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On Fri, Sep 26, 2014 at 1:57 PM, Thomas Gläßle wrote

And more importantly: you wouldn't expect isNatural(3.5) to return True.

That's not a problem with my one-liner, nor Ian's:

...

...

isNatural = lambda x: int(x)==x and x>0 isNatural(3.5) False

However, my correction to avoid crashing on some inputs is still wrong, given:

...

...

isinstance(0j, numbers.Number) True int(0j) TypeError

So I think I really need a couple lines: def isNatural(x): try: return int(x)==x and x>0 except (TypeError, ValueError): return False Of course... if you don't want that behavior, you need to write a different function :-). -- Keeping medicines from the bloodstreams of the sick; food from the bellies of the hungry; books from the hands of the uneducated; technology from the underdeveloped; and putting advocates of freedom in prisons. Intellectual property is to the 21st century what the slave trade was to the 16th.

David Mertz writes:

Isn't the right answer to create an isNatural() function?

No, the right answer (by PEP 8) is to create an ‘is_natural’ or ‘isnatural’ function :-)

Why do we need a type or class rather than just a function?

Less facetiously: I suspect what is being asked for here is a type which will *ensure* the values are natural numbers. That is a good use of types, IMO: they enforce a domain of values. I'm not convinced there is a pressing need to add such a type to the standard type hierarchy though. -- \ “I find the whole business of religion profoundly interesting. | `\ But it does mystify me that otherwise intelligent people take | _o__) it seriously.” —Douglas Adams | Ben Finney

On Sep 26, 2014, at 17:01, David Mertz wrote:

Well, yeah. I think I lost that discussion in the type annotation thread though. I'd love types to include predicates, but Guido wouldn't 😏. An 'is_natural()' function--by whichever spelling--needs to contain a test which isn't in the type system, whichever result one chooses for 'is_natural(1.0)'.

It is (or should be) in the type system for any application which has a good use for a natural number type. That's pretty much why Python has classes in the first place. Anyway, the only time I remember ever writing a Natural class in a language that didn't have one was to demonstrate Peano arithmetic, so in Python I'd be inheriting from or encapsulating a frozenset, not an int. I can imagine doing something similar (but more useful) in a symbolic math package. I could even see a Natural type being useful for the same kinds of things C uses unsigned for, but not if it was defined as 1.. instead of 0.. Do people have an actual use case for the type we're talking about here?

FWIW, I want 'isNatural(0j+1) == True'. But I'm on the losing end of at least three arguments there.... Unless I just roll my own in 5-8 lines of code.[*]

What about something that's one denornal bit of rounding error away from 0j+1?

[*] I'd want the non-PEP8 spelling because "Natural" in mathematics is always capitalized. That's why we have the built-in 'isGuido(BDFL)' rather than 'is_guido()'.

Wouldn't is\N{ELEMENT}\N{DOUBLE_N} or something like that (sorry, don't know how to type the actual Unicode on my phone, do know how to look up the right names but too lazy to do so) be better if "in mathematics" is what you really want? In math textbooks and papers, the symbols are usually translated to "is a natural number", not "is a Natural number", so I don't think violating PEP 8 is warranted here.

On Sep 26, 2014 4:42 PM, "Ben Finney" wrote:

...

David Mertz writes:

...

Isn't the right answer to create an isNatural() function?

No, the right answer (by PEP 8) is to create an ‘is_natural’ or ‘isnatural’ function :-)

...

Why do we need a type or class rather than just a function?

Less facetiously: I suspect what is being asked for here is a type which will *ensure* the values are natural numbers.

That is a good use of types, IMO: they enforce a domain of values.

I'm not convinced there is a pressing need to add such a type to the standard type hierarchy though.

-- \ “I find the whole business of religion profoundly interesting. | `\ But it does mystify me that otherwise intelligent people take | _o__) it seriously.” —Douglas Adams | Ben Finney

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---

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I've mentioned before that I used vim-cute-python ( https://github.com/ehamberg/vim-cute-python), but customized myself ( http://gnosis.cx/bin/.vim/after/syntax/python.vim). I do not utilize U+2115 'DOUBLE-STRUCK CAPITAL N' anywhere, but it is an elegant character. I use others such as: syntax match pyNiceOperator "\" conceal cchar=∈ syntax match pyNiceOperator "\" conceal cchar=∨ syntax match pyNiceOperator "\" conceal cchar=∧ syntax match pyNiceOperator "\" conceal cchar=∉ syntax keyword pyNiceOperator sum conceal cchar=∑ syntax keyword pyNiceBuiltin all conceal cchar=∀ syntax keyword pyNiceBuiltin any conceal cchar=∃ syntax keyword pyNiceStatement int conceal cchar=ℤ syntax keyword pyNiceStatement float conceal cchar=ℝ syntax keyword pyNiceStatement complex conceal cchar=ℂ And contentiously, but it makes sense to me: syntax keyword pyNiceStatement None conceal cchar=ℵ In my mind, since aleph-naught is the first inaccessible cardinal, and 'None' can similarly not be "reached" by operations on values of other types, there is a bit of an analogy. The fact aleph visually resembles capital-N(one) add to the appeal. So onscreen I see something like: for x ∈ it: if isinstance(x, (ℤ, ℝ, ℂ)): y = (x ∨ z) ∧ w I could easily define something to use ℕ but still have the actual source spelling of "Natural", just displayed in a fancy way. On Fri, Sep 26, 2014 at 10:04 PM, Chris Angelico wrote:

On Sat, Sep 27, 2014 at 11:13 AM, Andrew Barnert wrote:

...

Wouldn't is\N{ELEMENT}\N{DOUBLE_N} or something like that (sorry, don't know how to type the actual Unicode on my phone, do know how to look up the right names but too lazy to do so) be better if "in mathematics" is what you really want? In math textbooks and papers, the symbols are usually translated to "is a natural number", not "is a Natural number", so I don't think violating PEP 8 is warranted here.

Assuming the characters you're after are U+2208 'ELEMENT OF' and U+2115 'DOUBLE-STRUCK CAPITAL N', your name would be is∈ℕ(). I'd prefer isℕ() for two reasons: firstly, ∈ is a symbol, so it's not valid in a name (though you could open the other can of worms and ask for it to be an operator - then you could spell it "x ∈ ℕ" instead of "isℕ(x)"), and secondly because it's much more common to ask "is natural?" than "is element-of natural?" in function names. But I think this has long gone into crazyland.

ChrisA _______________________________________________ Python-ideas mailing list Python-ideas@python.org https://mail.python.org/mailman/listinfo/python-ideas Code of Conduct: http://python.org/psf/codeofconduct/

-- Keeping medicines from the bloodstreams of the sick; food from the bellies of the hungry; books from the hands of the uneducated; technology from the underdeveloped; and putting advocates of freedom in prisons. Intellectual property is to the 21st century what the slave trade was to the 16th.

On Sun, Sep 28, 2014 at 12:13:43AM -0400, random832@fastmail.us wrote:

On Sat, Sep 27, 2014, at 01:04, Chris Angelico wrote:

...

Assuming the characters you're after are U+2208 'ELEMENT OF' and U+2115 'DOUBLE-STRUCK CAPITAL N', your name would be is∈ℕ(). [...] Speaking of the other can of worms... we already _have_ that operator, it is spelled "in". What we don't have is infinite sets.

Guys, a reminder please: Python is a general purpose programming language with a general-purpose notation, not Mathematica. The most specialised the task, or the notation, the less likely it is to belong in Python the language or the standard library. But feel free to create your own libraries, or even your own parser for a mini-language capable of interpreting things like x ∈ ℕ. Or help contribute to Sage. http://www.sagemath.org -- Steven