List Comprehension question

[Mark Elston]

I recently stumbled over List Comprehension while reading the
Python Cookbook.  I have not kept up with the What's New
sections in the online docs. :)

Anyway,  I thought I was following the discussions of List
Comprehension (LC) until I got to Recipe 1.16.  In this recipe
we have the following:

    	arr = [[1,2,3], [4,5,6], [7,8,9], [10,11,12]]
    	print [[r[col] for r in arr] for col in range(len(arr[0]))]
    	   -> [[1, 4, 7, 10], [2, 5, 8, 11], [3, 6, 9, 12]]

For all the previous LC examples (and in the What's New
writeup for 2.0) it was stated (or implied) that code of the form:

    	[ expression for expr in sequence1 
                   for expr2 in sequence2 ...
                   for exprN in sequenceN
                   if condition ]

was equivalent to:

    for expr1 in sequence1:
        for expr2 in sequence2:
        ...
            for exprN in sequenceN:
                 if (condition):
                      # Append the value of 
                      # the expression to the 
                      # resulting list.

I thought I understood this until I got to the above recipe.  Here
it looks like the order of evaluation is reversed.  That is, instead
of translating to:

    for r[col] in arr:
        for col in range(len(arr[0])):
            ...

we actually have

    for col in range(len(arr[0])):
        for r[col] in arr:
            ...

And all of this due to a placement of '[ ... ]' around the 'inner'
loop.

The reference documentation doesn't explain this either.  The grammar 
page on List Displays doesn't seem to give any insight.

While I don't really understand it I may have some kind of rationale.
Please let me know if this is correct.

The print... command is a LC with a single expression and a single 'for'
construct.  The expression, itself, is also a LC.  When the command is
executed 'col' is set to 0 (the first value in the range) and this is
'passed' to the expression for evaluation.  This evaluation results in 
a list generated by the 'inner' LC which iterates over each row in the
array and, therefore, generates the list: [1, 4, 7, 10].

The next step is to go back to 'col' and extract the next value (1) and
generate the next list, etc.

Well, hmmmmm.  OK.  Maybe I do understand it.  It just wasn't apparent
at first.

Am I close, or did I guess wrong?

Mark