Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model.
It formed the inspiration for the database-query languages QUEL and SQL, of which the latter, although far less faithful to the original relational model and calculus, is now the de facto standard database-query language; a dialect of SQL is used by nearly every relational-database-management system.
Michel Lacroix and Alain Pirotte proposed domain calculus, which is closer to first-order logic and together with Codd showed that both of these calculi (as well as relational algebra) are equivalent in expressive power.
The basic relational building block is the domain (somewhat similar, but not equal to, a data type).
A tuple is a finite sequence of attributes, which are ordered pairs of domains and values.
A table is an accepted visual representation of a relation; a tuple is similar to the concept of a row.
This can be proven by showing that for a schema S = (D, R, h), a given set K of constants in the query expression, a tuple variable v and a header H we can construct a safe formula for every pair v.a with a in H that states that its value is in the active domain.