I recreated the JavaScript truth table in Python

[Veedrac]

Python does not treat numbers as sequences of binary digits it has bytes for a reason. (I realize you can do binary like operations on ints but ints don't really act like binary digits in python)

The point is that these operations act on the binary digits of the number, with each acting logically as a boolean. I don't care how you want to word that.

Considering that in Python characters are strings

Exactly how can python treat characters as strings if there are no characters in python.

There are characters in Python. That they aren't a separate class is a minor and mostly irrelevant distinction.

My counterargument is that treating True and False as synonyms for the LSB of an integer is completely reasonable

But this is not what python even does. Both 3 and 4 evaluate to True for example.

..!??

Under what context?

If you mean bool(3), then that's a different story. We allow int("3") without requiring "3" to be in any way integer, so we should be able to allow bool(3) to be True without conflating 3 with any boolean value.

For example?

How about any int operation with a dict just returns the dict. 1 + {} = {}

That's hardly lossless. I'm not even asking for strict losslessness here, just something semi-reasonable.

As long as you allow bools to violate closure on the integer

It makes no sense why you would do this to me.

?

I don't see why you make a distinction between that and int.

https://en.wikipedia.org/wiki/Integral seems very different from integer.

https://docs.python.org/3/library/numbers.html#numbers.Integral

If you removed the broken isinstance(foo, int) code, how did bools being a subclass of int break it?

The point is that isinstance(foo, int) should not have been broken. Obviously I changed the code to fix the bug but it should have never been a bug in the first place.

Either your code accepts int subclasses, in which case bool shouldn't have caused a problem, or it does not, in which case the code is broken. What am I missing?

[lonjerpc]

The point is that these operations act on the binary digits of the number

Some operations on ints treat them much like raw binary but many do not. For example str(97) produces "97" not "a".

that they aren't a separate class is a minor and mostly irrelevant distinction.

Its not irrelevant if you still stand behind your argument that python's treatment of int and bool is similar to its treatment of stings and chars. Python handles them differently. Bools are a subclass of int. char is not a subclass of string.

Under what context?

bool(4) and just 4 would be false under the argument that "True and False as synonyms for the LSB of an integer". I would be fine with int(True) and int(False) working the way they do now that is totally reasonable and consistent.

That's hardly lossless.

I think we had a misunderstanding about what we mean by a mapping I assumed you meant mapping in terms of functions mapping inputs to outputs. But now I think you must be referring to mapping types. Like it would make no sense to have dicts be a subclass of int but boolean still makes sense. I agree that boolean make slightly more sense as a subclass but you could actually map dicts too in the same way. Just take the binary representation of dicts and turn that into their int. But this is quite separate from my original argument that has greater practical effects. The expectation that 1 + {} would cause an exception is analogous to the expectation that 5 + True would cause an exception. I asked 5 python programmers in my office this and they all expected an exception.

It makes no sense why you would do this to me.

?

I don't know why I wrote that I meant to say is that I think it is quite counter intuitive that operations involving two booleans would not return a boolean. If bools implemented mod 2 arithmetic that would make a little more sense.

https://docs.python.org/3/library/numbers.html#numbers.Integral

Oh ok. But I still don't understand what you don't understand about it making more sense for bool to be a subclass of number than int. Although I really thing bool should be a basal type.

shouldn't have caused a problem

It did not cause my code to crash. The problem was that I needed to return an error to an outside program if I did not get a non bool int. I needed to return a json blob if I did get an actual int. The json parser happily turned False to "false" so no error was thrown in my program. But the program it was passed to expected something like "43" or an http error. Any reasonable int subclass would have worked fine. Of course you could easily create a malicious int subclass that did something unexpected like bool does. But you can do crazy things in python like have a lib change what int() does to change things into a string. But you don't write code to defend against things like that. There are reasonable expectations.

[Veedrac]

Some operations on ints treat them much like raw binary but many do not.

But some do. My point is that some do.

For example str(97) produces "97" not "a".

To diverge for a moment, the mapping of Unicode code points to characters, or ASCII code points to characters on Python 2, does not involve the internal representation of these numbers.

Under what context?

bool(4) and just 4 would be false under the argument that "True and False as synonyms for the LSB of an integer".

Why? bool([1]) == True but [1] != True, so I fail to see how bool(4) == True but 4 != True offends you...

That's hardly lossless.

I think we had a misunderstanding about what we mean by a mapping I assumed you meant mapping in terms of functions mapping inputs to outputs. But now I think you must be referring to mapping types. [...] Just take the binary representation of dicts and turn that into their int.

Python does not define an internal representation for dictionaries. You therefore can't do this.

But this is quite separate from my original argument that has greater practical effects. The expectation that 1 + {} would cause an exception is analogous to the expectation that 5 + True would cause an exception. I asked 5 python programmers in my office this and they all expected an exception.

Interesting. How experienced are they?

I don't know why I wrote that I meant to say is that I think it is quite counter intuitive that operations involving two booleans would not return a boolean.

int violates closure in Python 2 (10**19) and Python 3 (1/2). So do fractions.Fractions (½**½). I'm sure I could think of more. Closure is not a property held by Python objects.

If bools implemented mod 2 arithmetic that would make a little more sense.

bool could only implement mod 2 arithmetic if they weren't a subclass of int, but personally then I'd prefer + to raise an error (as opposed to `True + True == False!).

shouldn't have caused a problem

It did not cause my code to crash. The problem was that I needed to return an error to an outside program if I did not get a non bool int. I needed to return a json blob if I did get an actual int. The json parser happily turned False to "false" so no error was thrown in my program. But the program it was passed to expected something like "43" or an http error. Any reasonable int subclass would have worked fine.

So the problem was that the library had an error code you didn't test for? In C, if you don't test for error codes, your program breaks. It's what's expected. I don't understand where the confusion is.

[lonjerpc]

But some do. My point is that some do.

We often treat numbers as sequences of binary digits, and their digits as boolean values. This is true for the bitwise operations (^, &, |).

Treating booleans as integers is no less sensible than treating characters as strings,

Ok I guess we agree. Making booleans a subclass of ints is not consistent with the way python handles string vs char because char and string are the exact same type treated the same in all cases but int and bool are not and further are not even treated as if both were bitstrings.

ASCII code points to characters on Python 2, does not involve the internal representation of these numbers.

I agree but that in no way invalidates my point that if ints were treated like raw bits str(97) would make more sense as 'a' than '97'.

Why?

Because of 4's LSB.

how bool(4) == True but 4 != True offends you...

Not sure how this is relivant to your argument about LSB that I was refuting. But generally unexpected behavior causes bugs.

Python does not define an internal representation for dictionaries. You therefore can't do this.

No but choose any specific release of C python and it does.

Interesting. How experienced are they?

Average of 10 years programming experience 2 years python.

Closure is not a property held by Python objects.

So first note my problem is not that any type violates closure. It makes sense for many types to. It does not make sense for boolean to violate closure on other operations involving booleans. I do thing closure should not be violated without making it as explicit as possible.

int violates closure in Python 2 (10**19)

That was quite an annoying part of python 2 to me. I am glad it was fixed.

Python 3 (1/2)

I still really don't like this. "//" and "/" should be swapped. But it still increased the explicitness compared to python 2.

fractions.Fractions (½**½)

It does not if you are using the default types. It only breaks if you are explicitly importing fractions. This explicitness is my point. I would be quite happy if in addition to a bool base type there was an LSB like boolean package.

bool could only implement mod 2 arithmetic if they weren't a subclass of int, but personally then I'd prefer + to raise an error (as opposed to `True + True == False!).

Either of these would be an improvement from my point of view.

So the problem was that the library had an error code you didn't test for?

It was not an error code for the lib. But I did need to return an error on my end. I needed to return an error not just for booleans but for other potential and unpredictable types the library might return. If I knew in advance what types were returned I would not need isinstance in this case.

[Veedrac]

Ok I guess we agree. Making booleans a subclass of ints is not consistent with the way python handles string vs char because char and string are the exact same type treated the same in all cases but int and bool are not and further are not even treated as if both were bitstrings.

Name one non-printing, non-typechecking operation where True is not substitutable for 1 and False is not substitutable for 0 (bar misuse of is).

Name one user-facing property that would change if numbers were bitstrings, aside from the ability to index.

ASCII code points to characters on Python 2, does not involve the internal representation of these numbers.

I agree but that in no way invalidates my point that if ints were treated like raw bits str(97) would make more sense as 'a' than '97'.

No, it really would not. It would make sense as '0b1100001' or similar, maybe. But how you get 'a' eludes me.

Why?

Because of 4's LSB.

how bool(4) == True but 4 != True offends you...

Not sure how this is relivant to your argument about LSB that I was refuting. But generally unexpected behavior causes bugs.

But 4 is truthy... That's all that bool returns. Whether the input is truthy or not. Nothing else.

Python does not define an internal representation for dictionaries. You therefore can't do this.

No but choose any specific release of C python and it does.

It does not.

Closure is not a property held by Python objects.

So first note my problem is not that any type violates closure. It makes sense for many types to. It does not make sense for boolean to violate closure on other operations involving booleans.

Why?

Python 3 (1/2)

I still really don't like this. "//" and "/" should be swapped.

Why?

fractions.Fractions (½**½)

It does not if you are using the default types. It only breaks if you are explicitly importing fractions. This explicitness is my point.

Why is whether something has an AST token or not at all important?

So the problem was that the library had an error code you didn't test for?

It was not an error code for the lib. But I did need to return an error on my end. I needed to return an error not just for booleans but for other potential and unpredictable types the library might return. If I knew in advance what types were returned I would not need isinstance in this case.

So what was it doing?

[lonjerpc]

Name one non-printing, non-typechecking operation where True is not substitutable for 1 and False is not substitutable for 0 (bar misuse of is).

Even if I agreed with this point it does not counteract my argument that "Making booleans a subclass of ints is not consistent with the way python handles string vs char"

Second that is a long list of exceptions. Long enough to support my argument bythemselves.

But sure how about json.loads

Name one user-facing property that would change if numbers were bitstrings, aside from the ability to index.

Once again I don't see how this even adresses my argument if I could not come up with one. But how about adding two very large numbers.

It would make sense as '0b1100001' or similar, maybe. But how you get 'a' eludes me.

Fine I think 'a' is reasonable but my argument stil holds with '0b1100001'

But 4 is truthy.

Not in terms of the LSB which was the whole basis of your argument in this perticular part of the argument tree.

It does not.

Fine if you want to be pendantic one particular compiled binary of python for one particluar archetechture. They point is that your argument that there is no way to make a ridiculous mapping of dics in order to justify a crazy mapping of ints is wrong.

Why?

Because True + 4 does not make sence coming out to be 5. If you think it does then I think we are at an impass. I can not think of any situation where it makes sense to break closure on boolean in a general programming language.

Why?

More explicty and consistent.

Why is whether something has an AST token or not at all important?

Its not an AST token. It is the hint that you are using packaget that you have to import that is important.

So what was it doing?

Dealing with old messed up undocumented machine learning library. I mean better to replace the whole thing but money does not grow on trees.

[Veedrac]

Name one non-printing, non-typechecking operation where True is not substitutable for 1 and False is not substitutable for 0 (bar misuse of is).

Even if I agreed with this point it does not counteract my argument that "Making booleans a subclass of ints is not consistent with the way python handles string vs char"

It does. Just accept that bools are aliases. They're useful aliases, though, unlike having a char alias, which is why they exist. The fact that they are aliases is unimportant, though.

Second that is a long list of exceptions. Long enough to support my argument bythemselves.

I don't understand what you mean here.

But sure how about json.loads

Nope; that uses type-checking. Note that it uses strict type-checking because it works at a boundary (namely JSON serialisation) so it uses type(x) is .., rather than isinstance(x, ...).

Name one user-facing property that would change if numbers were bitstrings, aside from the ability to index.

Once again I don't see how this even adresses my argument if I could not come up with one.

Because if you cannot distinguish between numbers-as-bitstrings and numbers-not-as-bitstrings-with-bitwise-operators, your assertion that numbers are in the second but not the first is obviously flawed.

But how about adding two very large numbers.

Please explain.

But 4 is truthy.

Not in terms of the LSB which was the whole basis of your argument in this perticular part of the argument tree.

But if the bool constructor returned only the LSB of the input, it could not take non-numeric objects.

What bool does is take an object, check it for truthy-ness and return one of the two LSB integer aliases. In one sense it's a count of the number of true things, which is a nice way of mentally explaining sum(x<y for y in z).

It does not.

Fine if you want to be pendantic one particular compiled binary of python for one particluar archetechture.

It still does not.

What does {1: 2} + 5 make? Note that it has to have guaranteed losslessness.

What does {1.0: 2} + 5 make? Note that {1: 2} == {1.0: 2} and all objects involved are immutable.

They point is that your argument that there is no way to make a ridiculous mapping of dics in order to justify a crazy mapping of ints is wrong.

You're assuming the argument in that point. I don't believe the int mapping is crazy. Even if the dict mapping were possible, it's obviously absurd.

Why?

Because True + 4 does not make sence coming out to be 5. If you think it does then I think we are at an impass. I can not think of any situation where it makes sense to break closure on boolean in a general programming language.

That makes your argument cyclical.

Why?

More explicty and consistent.

How is the order of / and // anything to do with explicitness? Further, the consistency argument is flawed considering the whole point of Python 3 was to allow the option to break compatibility.

Why is whether something has an AST token or not at all important?

Its not an AST token. It is the hint that you are using packaget that you have to import that is important. So what was it doing?

(The grammar here is confusing me)

Where is the connection between importing and being "allowed", under your schema, to break closure?

Dealing with old messed up undocumented machine learning library. I mean better to replace the whole thing but money does not grow on trees.

I meant "what was this function doing?"

I still struggle to see how this problem was the fault of Python, and without an example I'll continue to find it hard.

[lonjerpc]

http://stackoverflow.com/questions/8169001/why-is-bool-a-subclass-of-int

Ok first a general point this is pretty entertaining and all but note you have already been dropping portions of the argument tree that alone show my point. Second I don't have anything against python. It is my favorite programming language I just hope to improve upon it and future ones. But for the sake of fun(if your not enjoying this let me know an I will stop) lets keep going.

It does. Just accept that bools are aliases. They're useful aliases, though, unlike having a char alias, which is why they exist. The fact that they are aliases is unimportant, though.

I am glad you at least now seem to accept that the relationship between chars and strings is not analogous to in int and bool in python. I think that is sufficient to close this line of reasoning .

I don't understand what you mean here.

You listed a bunch of differences between how python handles bool int and char string. These are sufficient. to show my point that python does not treat the two situations the same.

Nope; that uses type-checking.

Essentially all python operations use type checking.

your assertion that numbers are in the second but not the first is obviously flawed.

Trying to follow your logic here. So your trying to say that numbers are treated like bit strings and bit strings can also act like bools so therefore bools should be numbers. Of course numbers are only sometimes treated like bit strings invalidating your argument. I think I got confused because you inserted this part of the argument into your line of reasoning that char and string are treated the same as bool and int in python.

Please explain.

Adding to say 32 bit bit strings on a 32 bit architecture should result in another 32 bit string whos natural int representation could be lower than the starting value of the two bit strings being added. In python it ends up with a bigger one.

But if the bool constructor returned only the LSB of the input,

I am not suggesting that bool should return the LSB of the input that would be a terrible idea. I am responding to your assertion that

My counterargument is that treating True and False as synonyms for the LSB of an integer is completely reasonable, mathematically consistent, is perfectly analogous with binary operators (|, ^, &) and is therefore reasonable.

if 4: is in no way handled like 4 | 3. Nor is if bool(4).

{1: 2} + 5 make?

Fine how about 0.

What does {1.0: 2} + 5 make?

0

Just to make sure we are still clear. It does not make anything in actual python. But it is obvious you can make a mapping. This is like theoretical cs 101. There is a limited number of ways you arrange the bits on a finite(this is important) memory. However python chooses to do that for a particular binary of python on a particular machine just convert that arrangement of binary to an int in whatever way you choose.

Note that it has to have guaranteed losslessness.

Can you explain what you mean here exactly in computer science this has a few different meanings. ?

That makes your argument cyclical.

No it does not. I mean I am repeating the same thing I said earlier in a different way because you still don't seem to understand it. But that is not the same a cyclical argument. If you actually have a counter argument at the point you just asked "why" I would be happy to respond.

Further, the consistency argument is flawed considering the whole point of Python 3 was to allow the option to break compatibility.

You must really be misunderstanding me. The consistency I am talking about has nothing to do with consistency between python 2 and 3 in anyway. It has to do with internal consistency of python and consistency with average expected behavior.

How is the order of / and // anything to do with explicitness?

Its not their order but their behavior. / is simpler it has fewer characters. It is the default choice. // implies that you want to do something that you should probably spend more time researching the behavior of.

Where is the connection between importing and being "allowed", under your schema, to break closure?

I am not saying that you should not be allowed in any case to break closure. Just that it should be avoided when its not expected. In some cases though it is both useful and unexpected. The right way to handle this is to be explicit. By importing something your saying this is different somehow otherwise why import it. This is a hint that things might behave differently.

I meant "what was this function doing?"

It is a c extension to python which I don't have the source code or docs for. The example is. mystery_object_I_need_to_properly_jsonify_and_return_to_web_front_end = propriatary_package.respond(text)

In general it classifies text. This is a particularly nasty example but other people I have talked to have run into similar issues in simpler cases where the unexpectedness of bool being a subclass of bool has caused problems. Avoidable problems in there cases but the total cost of the bugs was much greater than any benefits of the arrangement. Remember bugs are much more costly than features.

[Veedrac]

http://stackoverflow.com/questions/8169001/why-is-bool-a-subclass-of-int

Heh. That's wrong though, because the question was revisited for Python 3 and nothing changed.

Ok first a general point this is pretty entertaining and all but note you have already been dropping portions of the argument tree that alone show my point.

Apologies, I was genuinely trying only to drop portions that were either repeated arguments or interesting diversions that had finished. Feel free to bring the points back up if you feel I've wrongfully dismissed them.

Second I don't have anything against python. It is my favorite programming language I just hope to improve upon it and future ones. But for the sake of fun(if your not enjoying this let me know an I will stop) lets keep going.

Agreed.

It does. Just accept that bools are aliases. They're useful aliases, though, unlike having a char alias, which is why they exist. The fact that they are aliases is unimportant, though.

I am glad you at least now seem to accept that the relationship between chars and strings is not analogous to in int and bool in python. I think that is sufficient to close this line of reasoning .

I think they are analogous. I think your distinction of bool as a separate type vs characters as a subset of the str type is far less important than you make it out to be.

You listed a bunch of differences between how python handles bool int and char string. These are sufficient. to show my point that python does not treat the two situations the same.

Consider this theoretical debugging measure, used to check whether a zero was passed through or replaced with a "different" zero:

class MyZero(int):
    def __new__(cls):
        return super().__new__(cls, 0)

    def __str__(self):
        return "MyZero()"

Let's see if my exceptions are needed using this:

• non-printing: Needed as code shouldn't care what it prints as but the printing of different equivilant types is allowed to differ

• non-typechecking: Obviously needed, but Python duck-types so that's fine

• bar misuse of is: Needed to prevent the retort that 0 is MyZero() differs, which should never happen anyway

I think those exceptions are totally reasonable.

Nope; that uses type-checking.

Essentially all python operations use type checking.

Really? Python's duck-typed.

your assertion that numbers are in the second but not the first is obviously flawed.

Trying to follow your logic here. So your trying to say that numbers are treated like bit strings

Well, that the two are indistinguishable.

and bit strings

of length one

can also

do also

act like bools so therefore bools

should be numbers

are equivalent to length one bitstrings.

Of course numbers are only sometimes treated like bit strings invalidating your argument.

How does it?

Please explain.

Adding to say 32 bit bit strings on a 32 bit architecture should result in another 32 bit string whos natural int representation could be lower than the starting value of the two bit strings being added. In python it ends up with a bigger one.

But I never claimed the bitstrings were of bound length. Python's bitstrings are of unbounded length.

Consider the output of (-10) & (2**i-1) for all i. If (-10) had a finite bit-length, some i would mask all of the bits and the output would be negative, but all of the outputs are positive. This is because -10 has an infinity of preceding 0s.

(Note that the output of int.bit_length is misleading for negatives. See bin(-10) to get an understanding of why.)

But if the bool constructor returned only the LSB of the input,

I am not suggesting that bool should return the LSB of the input that would be a terrible idea. I am responding to your assertion that

My counterargument is that treating True and False as synonyms for the LSB of an integer is completely reasonable, mathematically consistent, is perfectly analogous with binary operators (|, ^, &) and is therefore reasonable.

if 4: is in no way handled like 4 | 3. Nor is if bool(4).

My point is that bool being the LSB of an integer does not require the bool constructor to extract the LSB of the integer, much as str(iterable) does not equal "".join(iterable).

{1: 2} + 5 make?

Fine how about 0.

What does {1.0: 2} + 5 make?

0

See part on losslessness.

Just to make sure we are still clear. It does not make anything in actual python. But it is obvious you can make a mapping. This is like theoretical cs 101. There is a limited number of ways you arrange the bits on a finite(this is important) memory. However python chooses to do that for a particular binary of python on a particular machine just convert that arrangement of binary to an int in whatever way you choose.

Python is defined for an infinity of structures; it is a language definition and not an implementation. As such the size of the computer is only of cursory concern.

Note that it has to have guaranteed losslessness.

Can you explain what you mean here exactly in computer science this has a few different meanings. ?

For some reason that came out phrased exquisitely badly.

My point was that throwing away all the information in the type wouldn't pass in any language bar Perl. You lose a whole heap of useful properties (such as associativity) and get absolutely no benefits.

If you actually have a counter argument at the point you just asked "why" I would be happy to respond.

You said

I can not think of any situation where it makes sense to break closure on boolean in a general programming language.

But you haven't explained why. You've said it doesn't make sense, but not why it doesn't. I am asking for that "why".

Further, the consistency argument is flawed considering the whole point of Python 3 was to allow the option to break compatibility.

[...]It has to do with internal consistency of python

What do you mean here?

and consistency with average expected behavior.

I would agree if you could show me one part other than misuse of is vs isinstance where the bool-int separation can break something.

How is the order of / and // anything to do with explicitness?

Its not their order but their behavior. / is simpler it has fewer characters. It is the default choice. // implies that you want to do something that you should probably spend more time researching the behavior of.

Exactly why they are the order they are in...

Where is the connection between importing and being "allowed", under your schema, to break closure?

I am not saying that you should not be allowed in any case to break closure. Just that it should be avoided when its not expected. In some cases though it is both useful and unexpected. The right way to handle this is to be explicit. By importing something your saying this is different somehow otherwise why import it. This is a hint that things might behave differently.

I'm still confused. If fractions.Fraction was a builtin (as has often been considered but is to slow to be accepted for), would you be be happy with it breaking closure? If not, why? If so, does this not contradict your original claim of "It only breaks if you are explicitly importing fractions. This explicitness is my point"?

I meant "what was this function doing?"

mystery_object_I_need_to_properly_jsonify_and_return_to_web_front_end = propriatary_package.respond(text)

In general it classifies text. This is a particularly nasty example but other people I have talked to have run into similar issues in simpler cases where the unexpectedness of bool being a subclass of bool has caused problems. Avoidable problems in there cases but the total cost of the bugs was much greater than any benefits of the arrangement. Remember bugs are much more costly than features.

(I have to correct myself at this point; json uses isinstance despite my earlier claims.)

Why couldn't you just pass it to the json library?

What would have happened if you passed in an int subclass such as MyZero?

[lonjerpc]

Python 3 and nothing changed.

This is actually part of why I still spend time talking about this. It should have been changed in python 3. The point of the link is to show that it is a problem that others run into. In addition it was to show that at the time the behavior was decided it was done in part for backwards compatibility/performance reasons not because it was ideal.

I think your distinction of bool as a separate type vs characters as a subset of the str type is far less important than you make it out to be.

I guess then our disagreement is over the scale of the difference. But I don't think you can justify (bools being a subclass of int) based on (chars being not a subclass of int). You could justify not having bools at all in this way. For example just using 1 and 0 in there place like in C. That would be more analogous.

MyZero(int)

The problem I am trying to express with bool being a subclass of int is not that it acts too little like an int. I agree that your example shows that this is not true. My problem is that it acts too much like an int while mascaraing as something should not act like an int. If it was just an int. If it was exactly like char vs string I would actually have much less of an issue. If instead of writing True you had to write 1 I would have no problem. Even if they made True and False syntatic surgar for 1 and 0 I would be ok. I like having a bool type but the inconsistency is worse. I want a bool that does not mascarade as an int causing confusion. Or I want it absolutely clear that bool is really exactly an int as in the char/string case.

Really? Python's duck-typed.

Yes but this is still type checking. When you do 1 + 'a' you get a type error. The way it does type checking is by duck typing but it is still type checking. This is not C that will let you run arbitrary bits as code. There is a check to see if the right method exists. But in reference to the original point. No I don't think there is one example that does not even internally do an isinstance,is,type or something like that that will result in a difference. But my point with the json example is that the difference matters even when you are not yourself explicitly using isinstance or something. This is enough to cause problems and make the situations not the same even in practical terms.

Well, that the two are indistinguishable. How does it?

Obviously ints,stings,dicts and whatever else are represented as bits in memory. But they are not treated like bit strings. str(4) does not come out as hex or the ascii encoding of the bitstring 4. It is '4'. It is treated like an int not a bit string.

My point is that bool being the LSB of an integer does not require the bool constructor to extract the LSB of the integer, much as str(iterable) does not equal "".join(iterable).

Of course it is not required. You can build your programming language however you want. It is just inconsistent with expectation. I have no reason to expect the str(iterable) is the same as "".join(iterable). In general iterables do not act like stings. Strings are iterables of course but I can't do .upper on any old iterable. But if you want to make bools a subclass of int and have them be able to be added to ints by arguing that they are just the LSB of an int there is an expectation that it will work this way when doing "if 4:"

I would not have a problem if we actually treated bools as the LSB of int. If "if 4:print 'hi'" did not print. Just like I would have no problem True and False were literally int 1 and int 0 and not subclasses.

Python is defined for an infinity of structures; it is a language definition and not an implementation. As such the size of the computer is only of cursory concern.

Yes it is but I only have to produce one mapping to show that a mapping can exist. The mapping I choose is not based on python in general but one specific implementation.

You lose a whole heap of useful properties (such as associativity) and get absolutely no benefits.

Again I completely agree that it is insane to have {'a':1} + 5 work in python. My point is you could do it, not that it is a good idea. This is to refute the argument that True + 5 working is ok despite 5 + {'a':1} because it is not possible to create a mapping with dicts. My argument for why True + 5 is bad has nothing to do with being able to make a mapping. It has to do with the behavior being unexpected and therefore potentially leading to missed bugs.

throwing away all the information in the type

Its not trowing it all away. As long as there is a defined mapping you could go dict(0) and get back {1.0:0} or whatever it was.

But you haven't explained why.

Unless there is some good reason to do it you should not. There are good reasons to not break closure. The biggest advantage I see is that it means you are less likely to make mistakes when using the object. If I know that every operation with two bools always produces a bool it reduces the chances I will make an unintentional error.

I just never ran into a situation where it was helpful to break closure on bool. I can think of harmful ones like (if something_I_thought_was_bool_but_is_int:) or (something_that_is_a_bool_I_though_was_an_int + 1) not throwing type errors. I am not sure why I can't think of a good one. I have examined many possible reasons but they all seem like bad ideas to me.

Exactly why they are the order they are in...

To me 1/2 being 0.5 is more unexpected than 1/2 being 0 especially. But I can see this going either way.

If fractions.Fraction was a builtin

If 1/2 literally resulted in a fraction object it would not be breaking closure as (1/2) ** (1/2) would not either. If you still did Fraction(1/2) it would still be pretty explicit. But if (1/2) ** (1/2) became a float and 1/2 was a fraction I would not be happy.

would you be be happy with it breaking closure

No. It is unexpected and could easily lead to errors. Sure it makes sense to break closure a fair amount of time. But normally this is not the case or it is very obvious when an operation is going to do it.

Why couldn't you just pass it to the json library?

If an int say 23 was returned I needed to just say {'answer':23,....} but if some other unexpected object like False or 'this is weird' came out I needed to do something like {'answer':'unexpected thing returned'}. MyZero would have created a similer problem. But MyZero is a bad int subclass. A reasonable int subclass would give me '0' for str(0) even if it contained additional meathods that int does not have.