Terminology

# Terminology

Frequently used terms are gathered here for easy reference.

TermExplanation
ArgumentOne of the expressions between the parentheses of a relational application or the brackets of a partial relational application.
ArityNumber of elements in the tuples of a relation. If a relation contains tuples of various lengths, the relation has multiple arities. If N is the arity of the relation to which an expression E evaluates, then E is also said to have arity N.
Base relationA base relation is defined completely by the data it contains. This corresponds to a table in SQL.
Binary relationRelation of arity 2.
BodyThe main expression in a definition or a relational abstraction.
CardinalityNumber of tuples in a relation.
ColumnThe k-th column of relation R is the set of data values that are the k-th elements of the tuples in R.
Data valueA number, a string, etc. See Values.
Derived relationA derived relation is a relation whose content is defined by logical statements. These statements can refer to other relations (base or derived) or refer directly to data values. A derived relation corresponds to a view in SQL.
ElementA data value in a tuple. Elements are ordered by position from 1 to $N$, where $N$ is the length of the tuple.
Empty relationRelation with no tuples (cardinality 0).
FormulaAn expression that evaluates to a relation of arity 0 (i.e., to true or false).
FunctionRelation with a functional dependency from the initial elements of a tuple to the last element.
$n$-ary relationRelation of arity $n$.
Nullary relationRelation of arity 0. There exist only two nullary relations: the empty set {} (cardinality 0) and the empty tuple {()} (cardinality 1). See Boolean Constant Relations.
Qualified nameA name that consists of an identifier immediately followed by one or more Symbols, such as foo:bar:baz. Equivalent to a partial relational application, such as foo[:bar, :baz].
ParameterA variable introduced in the head of a definition or in the “bindings” part of a relational abstraction.
RelationA conventional relation is a set of tuples of the same type, a subset of a Cartesian product of data types. A Rel relation may consist of a number of different conventional relations, each of which has tuples of a different type.
SetAn unsorted collection of items, each of which is unique in the collection.
SingletonA relation of cardinality 1.
Ternary relationRelation of arity 3.
TupleAn ordered list of data values. A relation of cardinality 1 (any arity) is often identified with the tuple that it contains, and vice versa.
TypeThe type of an element in a tuple is always one of Rel’s data types, a value type or an entity type. The type of a tuple is the sequence of the types of its elements. The type of a relation — also known as the type signature — is the type of its tuples.
Unary relationRelation of arity 1.