Re “atomic”
In Codd’s original 1969 and 1970 papers he defined relations as having a value for every attribute in a row. The value could be anything, including a relation. This used no notion of “atomic”. He explained that “atomic” meant not relation-valued (ie not table-valued):
So far, we have discussed examples of relations which are defined on
simple domains–domains whose elements are atomic (nondecomposable)
values. Nonatomic values can be discussed within the relational
framework. Thus, some domains may have relations as elements.
He used “simple”, “atomic” and “nondecomposable” as informal expository notions. He understood that a relation has rows of which each column has an associated name and value; attributes are by definition “single-valued”; the value is of any type. The only structural property that matters relationally is being a relation. It is also just a value, but you can query it relationally. Then he used “nonsimple” etc meaning relation-valued.
By the time of Codd’s 1990 book The Relational Model for Database Management: Version 2:
From a database perspective, data can be classified into two types:
atomic and compound. Atomic data cannot be decomposed into smaller
pieces by the DBMS (excluding certain special functions). Compound
data, consisting of structured combinations of atomic data, can be
decomposed by the DBMS.In the relational model there is only one type of compound data: the
relation. The values in the domains on which each relation is defined
are required to be atomic with respect to the DBMS. A relational
database is a collection of relations of assorted degrees. All of the
query and manipulative operators are upon relations, and all of them
generate relations as results. Why focus on just one type of compound
data? The main reason is that any additional types of compound data
add complexity without adding power.
“In the relational model there is only one type of compound data: the relation.”
Sadly, “atomic = non-relation” is not what you’re going to hear. (Unfortunately Codd was not the clearest writer and his expository remarks get confused with his bottom line.) Virtually all presentations of the relational model get no further than what was for Codd merely a stepping stone. They promote an unhelpful confused fuzzy notion canonicalized/canonized as “atomic” determining “normalized”. Sometimes they wrongly use it to define realtion. Whereas Codd used everyday “nonatomic” to introduce defining relational “nonatomic” as relation-valued and defined “normalized” as free of relation-valued domains.
(Neither is “not a repeating group” helpful as “atomic”, defining it as not something that is not even a relational notion. And sure enough in 1970 Codd says “terms attribute and repeating group in present database terminology are roughly analogous to simple domain and nonsimple domain, respectively”.)
Eg: This misinterpretation was promoted for a long time from early on by Chris Date, honourable early relational explicator and proselytizer, primarily in his seminal still-current book An Introduction to Database Systems. Which now (2004 8th edition) thankfully presents the helpful relationally-oriented extended notion of distinguishing relation, row and “scalar” (non-relation non-row) domains:
This definition merely states that all [relation variables] are in 1NF
Eg: Maiers’ classic The Theory of Relational Databases (1983):
The definition of atomic is hazy; a value that is atomic in one application could be non-atomic in another. For a general guideline, a value is non-atomic if the application deals with only a part of the value.
Eg: The current Wikipedia article on First NF (Normal Form) section Atomicity actually quotes from the introductory parts above. And then ignores the precise meaning. (Then it says something unintelligible about when the nonatomic turtles should stop.):
Codd states that the “values in the domains on which each
relation is defined are required to be atomic with respect to the
DBMS.” Codd defines an atomic value as one that “cannot be decomposed
into smaller pieces by the DBMS (excluding certain special functions)”
meaning a field should not be divided into parts with more than one
kind of data in it such that what one part means to the DBMS depends
on another part of the same field.
Re “normalized” and “1NF”
When Codd used “normalize” in 1970, he meant eliminate relation-valued (“non-simple”) domains from a relational database:
For this reason (and others to be cited below) the possibility of
eliminating nonsimple domains appears worth investigating. There is,
in fact, a very simple elimination procedure, which we shall call
normalization.
Later the notion of “higher NFs” (involving FDs (functional dependencies) & then JDs (join dependencies)) arose and “normalize” took on a different meaning. Since Codd’s original normalization paper, normalization theory has always given results relevant to all relations, not just those in Codd’s 1NF. So one can “normalize” in the original sense of going from just relations to a “normalized” “1NF” without relation-valued columns. And one can “normalize” in the normalization-theory sense of going from a just-relations “1NF” to higher NFs while ignoring whether domains are relations. And “normalization” is commonly also used for the “hazy” notion of eliminating values with “parts”. And “normalization” is also wrongly used for designing a relational version of a non-relational database (whether just relations and/or some other sense of “1NF”).
Relational spirit is to eschew multiple columns with the same meaning or domains with interesting parts in favour of another base table. But we must always come to an informal ergonomic decision about when to stop representing parts and just treat a column as “atomic” (non-relation-valued) vs “nonatomic” (relation-valued).