New submission from Géry <[email protected]>:
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 `(x<y or x==y)` does not imply `x<=y`.**
*Note.* — These union relationships are always valid, contrary to the following
relationships which are only valid for [total
orders](https://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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Python tracker <[email protected]>
<https://bugs.python.org/issue39862>
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