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In database theory, a relation, as originally defined by E. F. Codd, [1] is a set of tuples (d 1,d 2,...,d n), where each element d j is a member of D j, a data domain. Codd's original definition notwithstanding, and contrary to the usual definition in mathematics, there is no ordering to the elements of the tuples of a relation.
(t.name = "Codd") — tuple t has a name attribute and its value is "Codd" Book(t) — tuple t is present in relation Book. The formal semantics of such atoms is defined given a database db over S and a tuple variable binding val : V → T D that maps tuple variables to tuples over the domain in S: v.a = w.b is true if and only if val(v)(a ...
The relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that is part of the relational model for databases and provide a declarative way to specify database queries.
A table in a SQL database schema corresponds to a predicate variable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates. However, SQL databases deviate from the relational model in many details, and Codd fiercely argued against deviations that compromise the original principles. [3]
Tuples in a relation are by definition unique, with duplicates removed after each operation, so the set of all attributes is always uniquely valued for every tuple. A candidate key (or minimal superkey) is a superkey that can't be reduced to a simpler superkey by removing an attribute.
As well, objects are managed on-heap and are under full control of a single process, while database tuples are shared and must incorporate locking, merging, and retry. Object–relational mapping provides automated support for mapping tuples to objects and back, while accounting for all of these differences. [1]
Tuple-versioning (also called point-in-time) is a mechanism used in a relational database management system to store past states of a relation. Normally, only the current state is captured. Using tuple-versioning techniques, typically two values for time are stored along with each tuple: a start time and an end time. These two values indicate ...
In Python, a distinction between expressions and statements is rigidly enforced, in contrast to languages such as Common Lisp, Scheme, or Ruby. This leads to duplicating some functionality. For example: List comprehensions vs. for-loops; Conditional expressions vs. if blocks