Community hub
Recent from talks
Contribute something to knowledge base
Content stats: 0 posts, 0 articles, 0 media, 0 notes
Members stats: 0 subscribers, 0 contributors, 0 moderators, 0 supporters
Subscribers
Supporters
Contributors
Moderators
Hub AI
Tuple relational calculus AI simulator
(@Tuple relational calculus_simulator)
Hub AI
Tuple relational calculus AI simulator
(@Tuple relational calculus_simulator)
Tuple relational calculus
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.[citation needed] Subsequently, query languages for the relational model were called relationally complete if they could express at least all of these queries.
Since the calculus is a query language for relational databases we first have to define a relational database. 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 relation is a set of (compatible) tuples. Although these relational concepts are mathematically defined, those definitions map loosely to traditional database concepts. A table is an accepted visual representation of a relation; a tuple is similar to the concept of a row.
We first assume the existence of a set C of column names, examples of which are "name", "author", "address", etcetera. We define headers as finite subsets of C. A relational database schema is defined as a tuple S = (D, R, h) where D is the domain of atomic values (see relational model for more on the notions of domain and atomic value), R is a finite set of relation names, and
a function that associates a header with each relation name in R. (Note that this is a simplification from the full relational model where there is more than one domain and a header is not just a set of column names but also maps these column names to a domain.) Given a domain D we define a tuple over D as a partial function that maps some column names to an atomic value in D. An example would be (name : "Harry", age : 25).
The set of all tuples over D is denoted as TD. The subset of C for which a tuple t is defined is called the domain of t (not to be confused with the domain in the schema) and denoted as dom(t).
Finally we define a relational database given a schema S = (D, R, h) as a function
that maps the relation names in R to finite subsets of TD, such that for every relation name r in R and tuple t in db(r) it holds that
The latter requirement simply says that all the tuples in a relation should contain the same column names, namely those defined for it in the schema.
Tuple relational calculus
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.[citation needed] Subsequently, query languages for the relational model were called relationally complete if they could express at least all of these queries.
Since the calculus is a query language for relational databases we first have to define a relational database. 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 relation is a set of (compatible) tuples. Although these relational concepts are mathematically defined, those definitions map loosely to traditional database concepts. A table is an accepted visual representation of a relation; a tuple is similar to the concept of a row.
We first assume the existence of a set C of column names, examples of which are "name", "author", "address", etcetera. We define headers as finite subsets of C. A relational database schema is defined as a tuple S = (D, R, h) where D is the domain of atomic values (see relational model for more on the notions of domain and atomic value), R is a finite set of relation names, and
a function that associates a header with each relation name in R. (Note that this is a simplification from the full relational model where there is more than one domain and a header is not just a set of column names but also maps these column names to a domain.) Given a domain D we define a tuple over D as a partial function that maps some column names to an atomic value in D. An example would be (name : "Harry", age : 25).
The set of all tuples over D is denoted as TD. The subset of C for which a tuple t is defined is called the domain of t (not to be confused with the domain in the schema) and denoted as dom(t).
Finally we define a relational database given a schema S = (D, R, h) as a function
that maps the relation names in R to finite subsets of TD, such that for every relation name r in R and tuple t in db(r) it holds that
The latter requirement simply says that all the tuples in a relation should contain the same column names, namely those defined for it in the schema.