Saturday, February 16, 2019

Class, Type, Set, Relvar, and Relation

Note: This is a rewrite of a part of an older post (now redirecting here), to bring into line with McGoveran's formalization, re-interpretation, and extension of Codd's RDM[1] (the rewrite of the other part was posted last week).
“[According to Date] relvar = class. [But i]n simple terms, class applies to a collection of values allowed by a predicate, regardless of whether such a collection could actually exist. Every set has a corresponding class, although a class may have no corresponding set ... in mathematical logic, a relation is a class (and trivially also a set), which contributes to confusion.”

“In modern programming parlance, class is generally distinguished from type only in that the latter refers to primitive (system-defined) data definitions, while class refers to higher-level (user-defined) data definitions. This distinction is almost arbitrary, and in some contexts, type and class are actually synonymous.”
Class, type, and set are often used interchangeably in the industry. Relations are neither class nor type, and Date's relvars must be placed properly in their formal context. While details regarding these concepts vary with the flavor of set theory, they are sufficiently well defined to be distinguishable in each of the three formal foundations of the RDM, simple set theory (SST), mathematical relation theory, and first order predicate logic (FOPL).

Sunday, February 10, 2019

Understanding Domains and Attributes

Note: This is a rewrite of one section of an older post (page thereof now links here), to bring it into line with McGoveran's formalization, re-interpretation, and extension of Codd's RDM[1]. The rewrite of the other part will be posted next.
“I don't understand the concepts of domain and attribute in relational database modeling. Can someone give me an effective example?”

“Domain is an overloaded word in the DB lexicon. It probably should also be avoided. When one refers to an attribute domain in practice it is only referring to columns that have a check constraint on them that limit the values. Reference tables with foreign key constraints in general also fulfill the spirit of what domain attributes do outside of an RDBMS.”

“A domain in most SQL usage is essentially an alias name for an existing type + restrictions on an existing type that can be used in a column. As for an attribute, it's essentially a COLUMN in SQL, a field in other types of databases, etc.”
To the extent that practitioners are familiar with domains, they equate them with programming data types (PDT), or, at best, with SQL data types.

Test your foundation knowledge -- are domains the same as PDTs or SQL data types?