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The following lines run infinitely:
b = [1]
import itertools
b += itertools.chain.from_iterable([c] for c in b)
In my opinion this is a bug. Clearly you could say that this is an implementation detail. But afaik this is not documented and very misleading.
BTW: In PyPy b would be [1, 1].

I don't think this is a bug. `b += iter(b)` and `for c in b: b.append(c)` work the same way. Also, the tutorial makes it clear that you should duplicate the list if you modify it inside a loop; in this case, this can be done either by iterating over `b[:]` instead of just `b` or using a list comprehension instead of a generator.

Yes, the behavior here is "undefined" at the language level. And as pyos says, technically it is documented: if you mutate the object over which you are iterating inside the iteration context (a for loop is just one example of same), the behavior is explicitly undefined. I agree that it is not *obvious* that that applies to chain.from_iterable in this context, but I'm not sure how we'd improve the docs to cover it.

This isn't a bug. It is an intended feature that chain.from_iterable evaluates lazily (and is documented as such). The pure python equivalent in the docs behaves the same as the C version does.
Also, it is a long standing feature of lists that you can loop over them while mutating them (I've seen more than a few pieces of code that take advantage of that feature).

If it is a feature, then is it documented in the language reference and is this actually a bug in PyPy (it sounds like it is)?

It looks to me as though this has nothing to do with itertools In CPython 2.7:
Python 2.7.3 |EPD 7.3-1 (32-bit)| (default, Apr 12 2012, 11:28:34) 
[GCC 4.0.1 (Apple Inc. build 5493)] on darwin
Type "credits", "demo" or "enthought" for more information.
>>> b = [1]
>>> b += (x for x in b) # runs until Ctrl-C
^CTraceback (most recent call last):
 File "<stdin>", line 1, in <module>
 File "<stdin>", line 1, in <genexpr>
KeyboardInterrupt
In PyPy:
Python 2.7.2 (341e1e3821fff77db3bb5cdb7a4851626298c44e, Jun 09 2012, 14:24:15)
[PyPy 1.9.0] on darwin
Type "help", "copyright", "credits" or "license" for more information.
And now for something completely different: ``the world doesn't want us to
know''
>>>> b = [1]
>>>> b += (x for x in b) # Returns immediately.
>>>> b
[1, 1]
So it seems that PyPy is building the RHS before appending it to b. That looks like a bug in PyPy to me.

And here's a non-infinite example where CPython and PyPy differ.
Python 2.7.3 |EPD 7.3-1 (32-bit)| (default, Apr 12 2012, 11:28:34) 
[GCC 4.0.1 (Apple Inc. build 5493)] on darwin
Type "credits", "demo" or "enthought" for more information.
>>> b = [1]
>>> b += (x+1 for x in b if x < 5)
>>> b
[1, 2, 3, 4, 5]
>>> 
iwasawa:cpython mdickinson$ pypy-c
-bash: pypy-c: command not found
iwasawa:cpython mdickinson$ /opt/local/bin/pypy-c
Python 2.7.2 (341e1e3821fff77db3bb5cdb7a4851626298c44e, Jun 09 2012, 14:24:15)
[PyPy 1.9.0] on darwin
Type "help", "copyright", "credits" or "license" for more information.
And now for something completely different: ``'that's definitely a case of
"uh????"'''
>>>> b = [1]
>>>> b += (x+1 for x in b if x < 5)
>>>> b
[1, 2]

Opened https://bugs.pypy.org/issue1355 for this.