REL
REFERENCE
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.
SingletonRelation of cardinality 1 and arity 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.