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[1] [2] One of the significant differences between the two is that a call to a partially applied function returns the result right away, not another function down the currying chain; this distinction can be illustrated clearly for functions whose arity is greater than two. [25] Given a function of type : (), currying produces (): (()).
If the self-same product is a member of two different hierarchies ([Product].[ByManufacturer] and [Product].[ByCategory]), there will be two different members visible that may need to be coordinated in sets and tuples (see below). Tuple. Tuple is an ordered collection of one or more members from different dimensions.
A dependent type is a type whose definition depends on a value. Two common examples of dependent types are dependent functions and dependent pairs. The return type of a dependent function may depend on the value (not just type) of one of its arguments. A dependent pair may have a second value of which the type depends on the first value.
A 1‑tuple is called a single (or singleton), a 2‑tuple is called an ordered pair or couple, and a 3‑tuple is called a triple (or triplet). The number n can be any nonnegative integer . For example, a complex number can be represented as a 2‑tuple of reals, a quaternion can be represented as a 4‑tuple, an octonion can be represented as ...
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 db : R → 2 T D
Thus, in some accounts, a tuple is described as a function, mapping names to values. A set of attributes in which no two distinct elements have the same name is called a heading. It follows from the above definitions that to every tuple there corresponds a unique heading, being the set of names from the tuple, paired with the domains from which ...
Relational algebra: Each row or record in the above table meets the standard definition of a tuple under relational algebra (the above example depicts a series of 3-tuples). Additionally, the first row specifies the field names that are associated with the values of each row.
Use of a user-defined function sq(x) in Microsoft Excel. The named variables x & y are identified in the Name Manager. The function sq is introduced using the Visual Basic editor supplied with Excel. Subroutine in Excel calculates the square of named column variable x read from the spreadsheet, and writes it into the named column variable y.