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A GROUP BY statement in SQL specifies that a SQL SELECT statement partitions result rows into groups, based on their values in one or several columns. Typically, grouping is used to apply some sort of aggregate function for each group. [1] [2] The result of a query using a GROUP BY statement contains one row for
Sum; Others include: Nanmean (mean ignoring NaN values, also known as "nil" or "null") Stddev; Formally, an aggregate function takes as input a set, a multiset (bag), or a list from some input domain I and outputs an element of an output domain O. [1] The input and output domains may be the same, such as for SUM, or may be different, such as ...
For example, the overall sum of a roll-up is just the sum of the sub-sums in each cell. Functions that can be decomposed in this way are called decomposable aggregation functions , and include COUNT, MAX, MIN, and SUM , which can be computed for each cell and then directly aggregated; these are known as self-decomposable aggregation functions.
Most data integration tools skew towards ETL, while ELT is popular in database and data warehouse appliances. Similarly, it is possible to perform TEL (Transform, Extract, Load) where data is first transformed on a blockchain (as a way of recording changes to data, e.g., token burning) before extracting and loading into another data store. [14]
A compiled version of an Access database (file extensions .MDE /ACCDE or .ADE; ACCDE only works with Access 2007 or later) can be created to prevent users from accessing the design surfaces to modify module code, forms, and reports. An MDE or ADE file is a Microsoft Access database file with all modules compiled and all editable source code ...
The sum type corresponds to intuitionistic logical disjunction under the Curry–Howard correspondence. An enumerated type can be seen as a degenerate case: a tagged union of unit types . It corresponds to a set of nullary constructors and may be implemented as a simple tag variable, since it holds no additional data besides the value of the tag.
One of the most common examples of an algebraic data type is the singly linked list. A list type is a sum type with two variants, Nil for an empty list and Cons x xs for the combination of a new element x with a list xs to create a new list. Here is an example of how a singly linked list would be declared in Haskell:
It may be used to prove Nicomachus's theorem that the sum of the first cubes equals the square of the sum of the first positive integers. [2] Summation by parts is frequently used to prove Abel's theorem and Dirichlet's test.