Understanding slice notation
The answers above don't discuss slice assignment. To understand slice assignment, it's helpful to add another concept to the ASCII art:
+---+---+---+---+---+---+
| P | y | t | h | o | n |
+---+---+---+---+---+---+
Slice position: 0 1 2 3 4 5 6
Index position: 0 1 2 3 4 5
>>> p = ['P','y','t','h','o','n']
# Why the two sets of numbers:
# indexing gives items, not lists
>>> p[0]
'P'
>>> p[5]
'n'
# Slicing gives lists
>>> p[0:1]
['P']
>>> p[0:2]
['P','y']
One heuristic is, for a slice from zero to n, think: "zero is the beginning, start at the beginning and take n items in a list".
>>> p[5] # the last of six items, indexed from zero
'n'
>>> p[0:5] # does NOT include the last item!
['P','y','t','h','o']
>>> p[0:6] # not p[0:5]!!!
['P','y','t','h','o','n']
Another heuristic is, "for any slice, replace the start by zero, apply the previous heuristic to get the end of the list, then count the first number back up to chop items off the beginning"
>>> p[0:4] # Start at the beginning and count out 4 items
['P','y','t','h']
>>> p[1:4] # Take one item off the front
['y','t','h']
>>> p[2:4] # Take two items off the front
['t','h']
# etc.
The first rule of slice assignment is that since slicing returns a list, slice assignment requires a list (or other iterable):
>>> p[2:3]
['t']
>>> p[2:3] = ['T']
>>> p
['P','y','T','h','o','n']
>>> p[2:3] = 't'
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
TypeError: can only assign an iterable
The second rule of slice assignment, which you can also see above, is that whatever portion of the list is returned by slice indexing, that's the same portion that is changed by slice assignment:
>>> p[2:4]
['T','h']
>>> p[2:4] = ['t','r']
>>> p
['P','y','t','r','o','n']
The third rule of slice assignment is, the assigned list (iterable) doesn't have to have the same length; the indexed slice is simply sliced out and replaced en masse by whatever is being assigned:
>>> p = ['P','y','t','h','o','n'] # Start over
>>> p[2:4] = ['s','p','a','m']
>>> p
['P','y','s','p','a','m','o','n']
The trickiest part to get used to is assignment to empty slices. Using heuristic 1 and 2 it's easy to get your head around indexing an empty slice:
>>> p = ['P','y','t','h','o','n']
>>> p[0:4]
['P','y','t','h']
>>> p[1:4]
['y','t','h']
>>> p[2:4]
['t','h']
>>> p[3:4]
['h']
>>> p[4:4]
[]
And then once you've seen that, slice assignment to the empty slice makes sense too:
>>> p = ['P','y','t','h','o','n']
>>> p[2:4] = ['x','y'] # Assigned list is same length as slice
>>> p
['P','y','x','y','o','n'] # Result is same length
>>> p = ['P','y','t','h','o','n']
>>> p[3:4] = ['x','y'] # Assigned list is longer than slice
>>> p
['P','y','t','x','y','o','n'] # The result is longer
>>> p = ['P','y','t','h','o','n']
>>> p[4:4] = ['x','y']
>>> p
['P','y','t','h','x','y','o','n'] # The result is longer still
Note that, since we are not changing the second number of the slice (4), the inserted items always stack right up against the 'o', even when we're assigning to the empty slice. So the position for the empty slice assignment is the logical extension of the positions for the non-empty slice assignments.
Backing up a little bit, what happens when you keep going with our procession of counting up the slice beginning?
>>> p = ['P','y','t','h','o','n']
>>> p[0:4]
['P','y','t','h']
>>> p[1:4]
['y','t','h']
>>> p[2:4]
['t','h']
>>> p[3:4]
['h']
>>> p[4:4]
[]
>>> p[5:4]
[]
>>> p[6:4]
[]
With slicing, once you're done, you're done; it doesn't start slicing backwards. In Python you don't get negative strides unless you explicitly ask for them by using a negative number.
>>> p[5:3:-1]
['n','o']
There are some weird consequences to the "once you're done, you're done" rule:
>>> p[4:4]
[]
>>> p[5:4]
[]
>>> p[6:4]
[]
>>> p[6]
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
IndexError: list index out of range
In fact, compared to indexing, Python slicing is bizarrely error-proof:
>>> p[100:200]
[]
>>> p[int(2e99):int(1e99)]
[]
This can come in handy sometimes, but it can also lead to somewhat strange behavior:
>>> p
['P', 'y', 't', 'h', 'o', 'n']
>>> p[int(2e99):int(1e99)] = ['p','o','w','e','r']
>>> p
['P', 'y', 't', 'h', 'o', 'n', 'p', 'o', 'w', 'e', 'r']
Depending on your application, that might... or might not... be what you were hoping for there!
Below is the text of my original answer. It has been useful to many people, so I didn't want to delete it.
>>> r=[1,2,3,4]
>>> r[1:1]
[]
>>> r[1:1]=[9,8]
>>> r
[1, 9, 8, 2, 3, 4]
>>> r[1:1]=['blah']
>>> r
[1, 'blah', 9, 8, 2, 3, 4]
This may also clarify the difference between slicing and indexing.
The Python tutorial talks about it (scroll down a bit until you get to the part about slicing).
The ASCII art diagram is helpful too for remembering how slices work:
+---+---+---+---+---+---+
| P | y | t | h | o | n |
+---+---+---+---+---+---+
0 1 2 3 4 5 6
-6 -5 -4 -3 -2 -1
One way to remember how slices work is to think of the indices as pointing between characters, with the left edge of the first character numbered 0. Then the right edge of the last character of a string of n characters has index n.
Enumerating the possibilities allowed by the grammar for the sequence x:
>>> x[:] # [x[0], x[1], ..., x[-1] ]
>>> x[low:] # [x[low], x[low+1], ..., x[-1] ]
>>> x[:high] # [x[0], x[1], ..., x[high-1]]
>>> x[low:high] # [x[low], x[low+1], ..., x[high-1]]
>>> x[::stride] # [x[0], x[stride], ..., x[-1] ]
>>> x[low::stride] # [x[low], x[low+stride], ..., x[-1] ]
>>> x[:high:stride] # [x[0], x[stride], ..., x[high-1]]
>>> x[low:high:stride] # [x[low], x[low+stride], ..., x[high-1]]
Of course, if (high-low)%stride != 0, then the end point will be a little lower than high-1.
If stride is negative, the ordering is changed a bit since we're counting down:
>>> x[::-stride] # [x[-1], x[-1-stride], ..., x[0] ]
>>> x[high::-stride] # [x[high], x[high-stride], ..., x[0] ]
>>> x[:low:-stride] # [x[-1], x[-1-stride], ..., x[low+1]]
>>> x[high:low:-stride] # [x[high], x[high-stride], ..., x[low+1]]
Extended slicing (with commas and ellipses) are mostly used only by special data structures (like NumPy); the basic sequences don't support them.
>>> class slicee:
... def __getitem__(self, item):
... return repr(item)
...
>>> slicee()[0, 1:2, ::5, ...]
'(0, slice(1, 2, None), slice(None, None, 5), Ellipsis)'
The syntax is:
a[start:stop] # items start through stop-1
a[start:] # items start through the rest of the array
a[:stop] # items from the beginning through stop-1
a[:] # a copy of the whole array
There is also the step value, which can be used with any of the above:
a[start:stop:step] # start through not past stop, by step
The key point to remember is that the :stop value represents the first value that is not in the selected slice. So, the difference between stop and start is the number of elements selected (if step is 1, the default).
The other feature is that start or stop may be a negative number, which means it counts from the end of the array instead of the beginning. So:
a[-1] # last item in the array
a[-2:] # last two items in the array
a[:-2] # everything except the last two items
Similarly, step may be a negative number:
a[::-1] # all items in the array, reversed
a[1::-1] # the first two items, reversed
a[:-3:-1] # the last two items, reversed
a[-3::-1] # everything except the last two items, reversed
Python is kind to the programmer if there are fewer items than you ask for. For example, if you ask for a[:-2] and a only contains one element, you get an empty list instead of an error. Sometimes you would prefer the error, so you have to be aware that this may happen.
Relationship with the slice object
A slice object can represent a slicing operation, i.e.:
a[start:stop:step]
is equivalent to:
a[slice(start, stop, step)]
Slice objects also behave slightly differently depending on the number of arguments, similarly to range(), i.e. both slice(stop) and slice(start, stop[, step]) are supported.
To skip specifying a given argument, one might use None, so that e.g. a[start:] is equivalent to a[slice(start, None)] or a[::-1] is equivalent to a[slice(None, None, -1)].
While the :-based notation is very helpful for simple slicing, the explicit use of slice() objects simplifies the programmatic generation of slicing.