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An identity function is sometimes useful in functional-style programming as a dummy or default value.
For example, we can sometimes see a pattern like this (e.g. in itertools.groupby):
def f(params, key=None):
 if key is None:
 key = lambda x: x
 ...
However, if we had a canonical itentity function:
def identity(x):
 return x
we could instead write:
def f(params, key=identity):
 ...
and the intended use of the function f and it's functioning would be more obvious simply from it's signature, while also saving a little code. 
As zen of Python says: Explicit is better than implicit.
Of course, we can now write:
def f(params, key=lambda x: x):
 ...
but the reason why is not used is probably that it feels a bit awkward to more people than just me.

I had a work mate make this exact same point literally yesterday. He asked me if Python had an identity function, and when I suggested just using `lambda x: x` he grouched that this wasn't sufficiently obvious enough as "identity" is self-explanatory.
(Perhaps for English speakers with a background in mathematics or functional programming.)
I'm not really convinced. Its easier to just write a lambda than to `from functools import identity`, and despite what my workmate thinks, "identity" is not self-evident. Consider that identity could also be a function that returns a person's identifying information. Think about the English usage of "identity theft" and "secret identity", rather than the mathematical meaning.
So I'm at best +0 on this suggestion.

Just in case anyone else thinks this is a good idea, here's a patch.

Java offers an identity function:
https://docs.oracle.com/javase/8/docs/api/java/util/function/Function.html
2016年08月25日 14:10 GMT+02:00 Steven D'Aprano <report@bugs.python.org>:
>
> Steven D'Aprano added the comment:
>
> Just in case anyone else thinks this is a good idea, here's a patch.
>
> ----------
> keywords: +patch
> Added file: https://bugs.python.org/file44218/identity.patch
>
> _______________________________________
> Python tracker <report@bugs.python.org>
> <https://bugs.python.org/issue27858>
> _______________________________________
>

I agree with Steven, I don't think this is really worth it, but I wouldn't vote -1. I suspect it won't get added, though, since a function I do want ('first') got rejected :)

I believe this has been previously discussed and declined.

See issue1673203, issue11011.