Re: More on lists and sets
From: paul c <toledobythesea_at_oohay.ac>
Date: Thu, 23 Mar 2006 03:44:33 GMT
Message-ID: <BQoUf.172164$sa3.69546_at_pd7tw1no>
>
>
> A label doesn't define list node identity. Otherwise, characters
> strings can't be represented as lists.
>
> Also the informal defintion above is too sketchy. Let A(x) and B(x) be
> lists. Convert them to relations A(x,y) and B(x,z) where attributes y
> and z are orderings. In the
> example we have
>
> A(x,y)
> -------
> 1 0
> 2 1
> 1 2
>
> B(x,z)
> -------
> 2 0
> 1 1
> 2 2
>
> Join the relations
>
> A(x,y)&&B(y,z)
> -------------
> 2 1 0
> 1 0 1
> 1 2 1
> 2 1 2
>
> Make the list of values x ordered by z*100+y (where the magic constant
> 100
> is the greatest y in B). Project away the ordering columns y and z.
>
> This definition should be equipped with a proposition that proves
> independence from the choice of auxiliary ordering columns.
>
Date: Thu, 23 Mar 2006 03:44:33 GMT
Message-ID: <BQoUf.172164$sa3.69546_at_pd7tw1no>
Mikito Harakiri wrote:
> paul c wrote:
>
>>Mikito Harakiri wrote: >> >>>... >>>Definition. List intersection is a cartesian product with equijoin of >>>the list nodes and lexicographic order. Example: 1->2->1 /\ 2->1->2 = >>>2->1->1->2 >>>... >> >>I'm struggling with the definition. If 1 and 2 stand for nodes, aren't >>the two lists circular? If that's so, aren't there multiple answers? >>(or one answer comprising two lists?)
>
>
> A label doesn't define list node identity. Otherwise, characters
> strings can't be represented as lists.
>
> Also the informal defintion above is too sketchy. Let A(x) and B(x) be
> lists. Convert them to relations A(x,y) and B(x,z) where attributes y
> and z are orderings. In the
> example we have
>
> A(x,y)
> -------
> 1 0
> 2 1
> 1 2
>
> B(x,z)
> -------
> 2 0
> 1 1
> 2 2
>
> Join the relations
>
> A(x,y)&&B(y,z)
> -------------
> 2 1 0
> 1 0 1
> 1 2 1
> 2 1 2
>
> Make the list of values x ordered by z*100+y (where the magic constant
> 100
> is the greatest y in B). Project away the ordering columns y and z.
>
> This definition should be equipped with a proposition that proves
> independence from the choice of auxiliary ordering columns.
>
Thanks for explaining it, must admit this definition had never occurred to me, perhaps partly because how to insert isn't clear when 'position' attributes are used. Also, I presume that the z*100+y ordering could have been y*100+z too.
p Received on Thu Mar 23 2006 - 04:44:33 CET