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In Python 2.6, socket.error was changed to be a child class of IOError
[1]. IOError derives from EnvironmentError [2], and EnvironmentError
accepts a 2-tuple used to set the values of the errno and strerror
attributes respectively [3].
Apparently the IOError raised by the socket module are instantiated
passing (always?) 'socket error' as first arg and an instance of
socket.gaierror, socket.timeout or socket.herror (and maybe others) as
second arg.
The errno attributes ends up being a string (and not a number) and the
strerror another exception (and not a str):
>>> import socket
>>> from urllib import urlopen
>>> socket.setdefaulttimeout(0.01)
>>> try: urlopen('http://www.python.org')
... except Exception, e: err1 = e
...
>>> err1
IOError('socket error', timeout('timed out',))
>>> err1.errno
'socket error'
>>> err1.strerror
timeout('timed out',)
>>> err1.strerror.errno
>>> err1.strerror.strerror
>>>
>>> try: urlopen('http://www.pythonfoobarbaz.org')
... except Exception, e: err2 = e
...
>>> err2
IOError('socket error', gaierror(11001, 'getaddrinfo failed'))
>>> err1.errno
'socket error'
>>> err1.strerror
timeout('timed out',)
>>> err1.strerror.errno
>>> err2.errno
'socket error'
>>> err2.strerror
gaierror(11001, 'getaddrinfo failed')
>>> err2.strerror.errno
11001
>>> err2.strerror.strerror
'getaddrinfo failed'
The 'socket error' strings doesn't provide any useful information
(herror, gaierror and timeout are already subclasses of socket.error)
and it results in confusing messages like:
IOError: [Errno socket error] [Errno 11001] getaddrinfo failed
The relevant information is not accessible directly on the error but it
is in err.strerror/err.args[1].
IMHO the first arg should be the errno (if it's available) and the
second the message (e.g. 'getaddrinfo failed' or 'timed out').
The doc of socket.error [1] should be also changed because it says:
"The accompanying value is either a string telling what went wrong or a
pair (errno, string) representing an error returned by a system call,
similar to the value accompanying os.error." (and this is actually what
I'd like it to be, but right now it's something different.)
[1]: http://docs.python.org/library/socket.html#socket.error
[2]: http://docs.python.org/library/exceptions.html#exceptions.IOError
[3]:
http://docs.python.org/library/exceptions.html#exceptions.EnvironmentError 

No, it seems that 2.5 has the same problem. The 'socket error' message is 
raised in urllib.py. The socket module is innocent to me...
It appears that this file routinely raises IOErrors, passing various 
arguments, which are not stored properly in the IOError object. IMO it 
should raise subclasses of IOError.
In this particular case of "socket error", it should let the exception 
propagate. Other occurrences need more thinking.

Yes, it looks to me like urllib is intentionally putting the 'socket
error' or 'url error' into the errno position in the IOError arguments.
 Now that socket.error is an IOError, that at least seems wrong.

Can this be fixed without breaking compatibility?
It also affects Python2.7 and maybe also Python 3.x (there the error is different and might be intentional).
Copy/pastable snippet to reproduce the error on 2.x:
from urllib import urlopen
try:
 urlopen('http://www.pythonfoobarbaz.org')
except Exception, err:
 print 'err:', err
 print 'repr(err):', repr(err)
 print 'err.errno:', err.errno
 print 'err.strerror:', err.strerror
 print 'err.strerror.errno:', err.strerror.errno
 print 'err.strerror.strerror:', err.strerror.strerror
Result on 2.7:
err: [Errno socket error] [Errno -2] Name or service not known
repr(err): IOError('socket error', gaierror(-2, 'Name or service not known'))
err.errno: socket error
err.strerror: [Errno -2] Name or service not known
err.strerror.errno: -2
err.strerror.strerror: Name or service not known
Copy/pastable snippet to reproduce the error on 3.x:
from urllib.request import urlopen
try:
 urlopen('http://www.pythonfoobarbaz.org')
except Exception as exc:
 err = exc
 print('err:', err)
 print('repr(err):', repr(err))
 print('err.errno:', err.errno)
 print('err.strerror:', err.strerror)
 print('err.reason:', err.reason)
 print('err.reason.errno:', err.reason.errno)
 print('err.reason.strerror:', err.reason.strerror)
Result on 3.2:
err: <urlopen error [Errno -2] Name or service not known>
repr(err): URLError(gaierror(-2, 'Name or service not known'),)
err.errno: None
err.strerror: None
err.reason: [Errno -2] Name or service not known
err.reason.errno: -2
err.reason.strerror: Name or service not known

It's very hard to tell what ought to be done here, since Lib/urllib/request.py throws URLErrors with a great variety of order and number of arguments, and it's not clear how URLError (in Lib/urllib/error.py) intends to handle them.
However, in this case, AbstractHTTPHandler.do_open is instantiating URLError with another exception instance, and that exception contains .errno and .strerror. URLError puts the entire error instance into ``reason``, where the information is hidden away as .reason.strno and .reason.strerror. 
In the name of keeping this information available rather than hiding it, I'm attaching a patch that adds to URLError.__init__:
 if hasattr(reason, "errno"):
 self.errno = reason.errno
 if hasattr(reason, "strerror"):
 self.strerror = reason.strerror
Again, I'm not sure this is the most logical approach because I can't find a consistent pattern in the ways URLError is instantiated.

This is an interesting idea and should at least improve matters. I'm wondering, though...I seem to remember writing code that fished the wrapped error out using one of those attributrs...but I'm not at a computer where I can try to check on that. Hopefully I can check on it this weekend.

> I seem to remember writing code that fished the wrapped error
> out using one of those attributrs...
That would be err.reason:
from urllib.request import urlopen
try:
 urlopen('http://www.pythonfoobarbaz.org')
except Exception as exc:
 print('err:', err)
 print('repr(err):', repr(err))
 print('err.reason:', err.reason)
 print('repr(err.reason):', repr(err.reason))
prints:
err: <urlopen error [Errno -2] Name or service not known>
repr(err): URLError(gaierror(-2, 'Name or service not known'),)
err.reason: [Errno -2] Name or service not known
repr(err.reason): gaierror(-2, 'Name or service not known')

Ah, of course. I should have reread the whole issue :)
The backward compatibility is the big concern here. Regardless of what we do about that, we should at least fix this in 3.4.

Reproduced on 3.11:
>>> from urllib.request import urlopen
>>> try:
... urlopen('http://www.pythonfoobarbaz.org')
... except Exception as exc:
... err = exc
... print('err:', err)
... print('repr(err):', repr(err))
... print('err.errno:', err.errno)
... print('err.strerror:', err.strerror)
... print('err.reason:', err.reason)
... print('err.reason.errno:', err.reason.errno)
... print('err.reason.strerror:', err.reason.strerror)
... 
err: <urlopen error [Errno 8] nodename nor servname provided, or not known>
repr(err): URLError(gaierror(8, 'nodename nor servname provided, or not known'))
err.errno: None
err.strerror: None
err.reason: [Errno 8] nodename nor servname provided, or not known
err.reason.errno: 8
err.reason.strerror: nodename nor servname provided, or not known