Terminology

Frequently used terms are gathered here for easy reference.

Term	Explanation
Argument	One of the expressions between the parentheses of a relational application or the brackets of a partial relational application.
Arity	Number 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 relation	A base relation is defined completely by the data it contains. This corresponds to a table in SQL.
Binary relation	Relation of arity 2.
Body	The main expression in a definition or a relational abstraction.
Cardinality	Number of tuples in a relation.
Column	The k-th column of relation `R` is the set of data values that are the k-th elements of the tuples in `R`.
Data value	A number, a string, etc. See Values.
Derived relation	A 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.
Element	A data value in a tuple. Elements are ordered by position from 1 to $N$ , where $N$ is the length of the tuple.
Empty relation	Relation with no tuples (cardinality 0).
Formula	An expression that evaluates to a relation of arity 0 (i.e., to `true` or `false`).
Function	Relation with a functional dependency from the initial elements of a tuple to the last element.
$n$ -ary relation	Relation of arity $n$ .
Nullary relation	Relation 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 name	A 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]`.
Parameter	A variable introduced in the head of a definition or in the “bindings” part of a relational abstraction.
Relation	A 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.
Set	An unsorted collection of items, each of which is unique in the collection.
Singleton	Relation of cardinality 1 and arity 1.
Ternary relation	Relation of arity 3.
Tuple	An ordered list of data values. A relation of cardinality 1 (any arity) is often identified with the tuple that it contains, and vice versa.
Type	The 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 relation	Relation of arity 1.

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