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On Wed, Sep 14, 2016 at 2:32 AM,  <> wrote:
> I am new to lua and I want to understand the language. According book (Programming in Lua, 3rd edition):
> "More precisely, a sequence is a table where the numeric keys comprise a set 1, . . . , n for some n." (page 24)
> So table {10, nil, 30, 40} contains sequence {10} (n=1), which length is 1. Is there any other definition?
> It is very confusing and operator # can be unusable for tables, because in many cases I need to check sequences and I cannot trust this operator. It should return or 1 (book definition) or if holes in sequence break the sequence, it should return 0. Otherwise I will be pushed for every sequence check to check all array fields manually in some kind of loop.

It behaves the way it does for efficiency.

The length algorithm, as I understand it (from previous explanations
on this list), does not and should not check every key-value pair in
the table, as you suggest, to determine whether or not a valid
sequence is present. That would be an O(n) operation, and nobody wants
that. The actual algorithm is (I think) closer to O(log n), and checks
pairs of positive integer keys according to a sensible pattern until
it finds an `n` where `t[n]` is not nil and `t[n+1]` is nil. It then
returns `n` as the length.

Thus, the length of a table is defined if and only it is a sequence,
since with a non-sequence, getting the length could result in any
non-negative integer `n` where `t[n]` is non-nil and `t[n+1]` is nil.
The length operator guarantees only that.

So what exactly is a sequence? A sequence, as you quoted from PiL, is
"a table where the numeric keys comprise a set 1, . . . , n for some
n." "Comprise" means that all of the numeric keys have to participate
in that, but even that is not perfectly accurate. Let me tweak and
expand the wording of PiL to be even more precise:

"A sequence is a table where the set of all positive integer keys that
do not correspond to a nil value is exactly equal to the set {1..n}
where n is the highest positive integer key that does not correspond
with a nil value."

So what is the table {10, nil, 30, 40} (to use your example)? It
cannot be a sequence of length 4, because the key 2 is nil. It also
cannot be a sequence of length 1 because keys 3 and 4 have values.
Specifically, the set of all positive integer keys is {1, 3, 4}, but
the set of all integers {1..n}, where n is the highest integer key in
the table, is {1, 2, 3, 4}. As those set are not identical, it is
therefore not a sequence at all, and the length of the table is

The bottom line is that if you want to work with sequences, you CANNOT
use nil as a value in those sequences.

P.S. In the explanation above, I repeatedly stated "positive integer
keys" rather than "numeric keys" or simply "keys". Why? Because (and
this is an important point) zero, negative, non-integer (float) and
non-numeric keys are completely irrelevant to whether a table is a
sequence. When determining whether a table is a sequence, ONLY
positive integer keys matter. All other keys are ignored for that
purpose. So, for example, the table

{10, 20, 30, 40, [math.pi] = 3.14, [0] = 'foo', [-4] = 'bar', ignore = 'me'}

is a valid sequence of length 4.