On Sun, Oct 27, 2013 at 10:40 AM, MRAB <python@mrabarnett.plus.com> wrote:
On 27/10/2013 17:04, Guido van Rossum wrote:
In the comments of
http://python-history.blogspot.com/2013/10/why-python-uses-0-based-indexing.html
there were some complaints about the interpretation of the bounds for
negative strides, and I have to admin it feels wrong. Where did we go
wrong? For example,

"abcde"[::-1] == "edcba"

as you'd expect, but there is no number you can put as the second bound
to get the same result:

"abcde"[:1:-1] == "edc"
"abcde"[:0:-1] == "edcb"

but

"abcde":-1:-1] == ""

I'm guessing it all comes from the semantics I assigned to negative
stride for range() long ago, unthinkingly combined with the rules for
negative indices.

For a positive stride, omitting the second bound is equivalent to
length + 1:

>>> "abcde"[:6:1]
'abcde'

Actually, it is equivalent to length; "abcde"[:5:1] == "abcde" too.
 
For a negative stride, omitting the second bound is equivalent to
-(length + 1):

>>> "abcde"[:-6:-1]
'edcba'

Hm, so the idea is that with a negative stride you you should use negative indices. Then at least you get a somewhat useful invariant:

if -len(a)-1 <= j <= i <= -1:
    len(a[i:j:-1]) == i-j

which at least somewhat resembles the invariant for positive indexes and stride:

if 0 <= i <= j <= len(a):
    len(a[i:j:1]) == j-i

For negative indices and stride, we now also get back this nice theorem about adjacent slices:

if -len(a)-1 <= i <= -1:
    a[:i:-1] + a[i::-1] == a[::-1]

Using negative indices also restores the observation that a[i:j:k] produces exactly the items corresponding to the values produced by range(i, j, k).

Still, the invariant for negative stride looks less attractive, and the need to use negative indices confuses the matter. Also we end up with -1 corresponding to the position at one end and -len(a)-1 corresponding to the position at the other end. The -1 offset feels really wrong here.

I wonder if it would have been simpler if we had defined a[i:j:-1] as the reverse of a[i:j]?

What are real use cases for negative strides?

--
--Guido van Rossum (python.org/~guido)