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#41
 
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Re: Towards a definition of atomic -
02-01-2008
, 11:57 AM
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"Roy Hann" <specia... (AT) processed (DOT) almost.meat> wrote in message news:rf6dneUOQ-Rltz7anZ2dnUVZ8sylnZ2d (AT) pipex (DOT) net... "David Cressey" <cresse... (AT) verizon (DOT) net> wrote in message news:wOFoj.5441$4f.724 (AT) trndny06 (DOT) .. I think we could make the meaning of "atomic" more tangible if we can define what decompositions of an attribute are valid. Perhaps the place to start is to define what kinds of compositions a relational system is capable of. Once you have that in place, it should be straightforward to define relational decompositions as the inverse of relational compositions. Why not just understand that relational systems don't care about about composition/decomposition and want nothing to do with the idea? It is no more relevant than is the concept of colour to Euclidean geometry. I disagree. A relation is composed of attributes. (If you prefer, a table is composed of columns). Relational systems are clearly concerned with composition in some contexts. One of the relational operators discussed is the "compose" operator, by which a result relation can be composed from given relations. (If you prefer, a result table can be composed from given tables (or views)). |
speaking
of decomposition of individual values within a relation and David
speaking
of decomposing relations via projection, etc.
Marshall
#42
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#43
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#44
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#45
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#46
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#47
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#48
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#49
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The important thing in this discussion is: The relational model treats domain values as neither composable nor decomposable. They are simply values upon which one may evaluate defined operations. |
is equality, which is clearly necessary for natural join, etc. A theta
join, for example, is a join of two operand relations and a further
join with the < relation.
Marshall
#50
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AFAIK the conventional wisdom is that no absolute definition of atomic exists for domain types. |
wise to go looking for a definition if it is not clear to you want you
want to do with that definition. If you don't know where you are
going, any road will take you there.
Quote:
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*Throwing caution to the wind, in this post I wish to conjecture a definition of atomic that, perhaps with some more effort at its formalisation, can provide some absolute meaning for a given attribute within a given RDB schema. |
my own warning. :-)
The usual intuition is that something is not atomic if it is
decomposable into smaller parts. In this case that would mean parts
with less information. For the case of decomposition into two
components this leads to something like:
DEFINITION: A domain D is said to be decomposable if there are domains
D1 and D2 and functions f1 : D -> D1 and f2 : D -> D2 such that (1) f1
and f2 are not injective and (2) <f1,f2> is injective where <f1,f2> :
D -> (D1 x D2) is defined such that <f1,f2>(x) = (f1(x), f2(x)).
Note that (1) says that each individual decomposition function loses
information and (2) says that together they don't. However, we can
then make the following observation:
THEOREM: A domain is decomposable iff it contains more than 2 values.
As you more or less already observed, if you have a relational schema
that uses an infinite domain (i.e. with infinitely many values) then
you cannot map it losslessly it to a relational schema that uses only
non-decomposable domains. But, if you allow the exception of abstract
identifiers, then you can.
Quote:
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Continuing with example 2, note that no further decomposition allowing information equivalence is possible. *For example, a person's name is represented as a string domain type, and this is atomic because any attempt at decomposing the string into its individual characters forces the introduction of additional identifiers. |
of the components will always be an infinite domain again. You could
for example split it into the first character and the rest.
-- Jan Hidders
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