[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Géry]

Géry  added the comment:

Alright @rhettinger, here is the post: 
https://discuss.python.org/t/add-missing-default-implementations-of-le-and-ge/5327

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Raymond Hettinger]

Raymond Hettinger  added the comment:

This issue is more of a question or objection than a bug report, so I'm going 
to mark this as closed.  

Feel free to continue the discussion on python-ideas or ask more about it on 
StackOverflow.

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resolution:  -> not a bug
stage:  -> resolved
status: open -> closed

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Irit Katriel]

Irit Katriel  added the comment:

The PEP that Raymond linked to says:

"Further smarts could have been added to the comparison mechanism, but this 
limited set of allowed "swaps" was chosen because it doesn't require the 
infrastructure to do any processing (negation) of return values. The choice of 
six special methods was made over a single (e.g. __richcmp__) method to allow 
the dispatching on the opcode to be performed at the level of the C 
implementation rather than the user-defined method."


The pseudo code you suggested assumes that the results of comparisons can be 
interpreted as booleans, which not always correct and makes your suggestion 
under-specified.  It is not easy to devise a sound and intuitive composition of 
boolean expressions whose semantics are user-defined. 


As an aside, I think for the boolean case it is enough that one of them is not 
NotImplemented, so your pseudo code should have been:

def __le__(self, other):
result_1 = self.__lt__(other)
result_2 = self.__eq__(other)
if result_1 is NotImplemented and result_2 is NotImplemented:
return NotImplemented
return result_1 or result_2

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Géry]

Géry  added the comment:

More precisely:

The following relationships are always valid and therefore implemented by 
default in Python (_except for the union relationships, which seems arbitrary 
and is the reason of this Python issue_):

- 2 [complementary](https://en.wikipedia.org/wiki/Binary_relation#Complement) 
relationships: "= and ≠ are each other’s complement";
- 6 [converse](https://en.wikipedia.org/wiki/Binary_relation#Converse) 
relationships*: "= is the converse of itself", "≠ is the converse of itself", 
"< and > are each other’s converse", and "≤ and ≥ are each other’s converse";
- 2 [union](https://en.wikipedia.org/wiki/Binary_relation#Union) relationships: 
"≤ is the union < and =" and "≥ is the union of > and ≤".

The following relationships are only valid for [total 
orders](https://en.wikipedia.org/wiki/Binary_relation#Properties) and therefore 
not implemented by default in Python (but users can conveniently implement them 
when they are valid with the 
[`functools.total_ordering`](https://docs.python.org/3/library/functools.html#functools.total_ordering)
 class decorator provided by the Python standard library):

- 4 [complementary](https://en.wikipedia.org/wiki/Binary_relation#Complement) 
relationships: "< and ≥ are each other’s complement" and "> and ≤ are each 
other’s complement".



\* Converse relationships are implemented in Python through the 
[`NotImplemented` 
protocol](https://docs.python.org/3/reference/datamodel.html#the-standard-type-hierarchy).

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Géry]

Géry  added the comment:

Note that other relationships are always valid _and already implemented by 
default in the interpreter (through the `NotImplemented` return value 
protocol)_: = is the 
[converse](https://en.wikipedia.org/wiki/Binary_relation#Converse) of itself, ≠ 
is the converse of itself, < and > are each other’s converse, ≤ and ≥ as each 
other’s converse. ("converse" is loosely called "reflected" in the Python 
documentation.)

Which also makes me think that the last sentence of this documentation 
paragraph is incorrect:

> By default, `__ne__()` delegates to `__eq__()` and inverts the result
> unless it is `NotImplemented`. There are no other implied
> relationships among the comparison operators, for example, the truth
> of `(x are each 
other’s converse, and ≤ and ≥ are each other’s converse.

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Géry]

Géry  added the comment:

Thanks for the reference @Raymond. I could not find any mention of the union 
relationships for ≤ and ≥ though. Since they are always valid for Boolean 
values, in the same way that ≠ is always the complement of = for Boolean values 
and default implemented as such in the interpreter, what do you think of 
default implementing these union relationships in the interpreter?

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Raymond Hettinger]

Raymond Hettinger  added the comment:

See https://www.python.org/dev/peps/pep-0207/

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[issue39862] Why are the union relationships not implemented by default for ≤ and ≥?

[Géry]

New submission from Géry :

Mathematically, the [binary 
relation](https://en.wikipedia.org/wiki/Binary_relation) ≤ is the 
[union](https://en.wikipedia.org/wiki/Binary_relation#Union) of the binary 
relations < and =, while the binary relation ≥ is the union of the binary 
relations > and =. So is there a reason why Python does not implement `__le__` 
in terms of `__lt__` and `__eq__` by default, and `__ge__` in terms of `__gt__` 
and `__eq__` by default?

The default implementation would be like this (but probably in C for 
performance, like `__ne__`):

```python
def __le__(self, other):
result_1 = self.__lt__(other)
result_2 = self.__eq__(other)
if result_1 is not NotImplemented and result_2 is not NotImplemented:
return result_1 or result_2
return NotImplemented

def __ge__(self, other):
result_1 = self.__gt__(other)
result_2 = self.__eq__(other)
if result_1 is not NotImplemented and result_2 is not NotImplemented:
return result_1 or result_2
return NotImplemented
```

This would save users from implementing these two methods all the time.

Here is the relevant paragraph in the [Python 
documentation](https://docs.python.org/3/reference/datamodel.html#object.__lt__)
 (emphasis mine):

> By default, `__ne__()` delegates to `__eq__()` and inverts the result
> unless it is `NotImplemented`. There are no other implied
> relationships among the comparison operators, **for example, the truth
> of `(xhttps://en.wikipedia.org/wiki/Binary_relation#Properties) (also called 
connex orders) and therefore not implemented by default: < is the 
[complement](https://en.wikipedia.org/wiki/Binary_relation#Complement) of ≥, 
and > is the complement of ≤. These complementary relationships can be easily 
implemented by users when they are valid with the 
[`functools.total_ordering`](https://docs.python.org/3/library/functools.html#functools.total_ordering)
 class decorator provided by the Python standard library.

--
components: Interpreter Core
messages: 363426
nosy: maggyero
priority: normal
severity: normal
status: open
title: Why are the union relationships not implemented by default for ≤ and ≥?
type: enhancement
versions: Python 3.9

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