Scalar extension: Difference between revisions
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Separate "Rank extension" section
Miraheze>Marshall (Created page with "Scalar extension is a way to apply a function with a scalar argument when an array of a particular non-empty shape would be expected. The scalar is ''extended'' to thi...") |
Miraheze>Marshall (Separate "Rank extension" section) |
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The word "extension" applies to scalar extension in two ways: first, a function is extended by making a case which would have been a [[RANK ERROR]] into a valid application. Second, the application works by conceptually extending the scalar to function as though it were an array of higher rank. | The word "extension" applies to scalar extension in two ways: first, a function is extended by making a case which would have been a [[RANK ERROR]] into a valid application. Second, the application works by conceptually extending the scalar to function as though it were an array of higher rank. | ||
Two arrays are said to [[Conformability|conform]] if they have the same shape or at least one can be extended (it is a scalar, or, in langauges with singleton extension, has exactly one element). A pair of conforming arrays defines a single shape which describes how their elements are paired: if neither is a scalar, it is their shared shape; if one is a scalar, it is the other's shape; if both are scalars, it is <code>⍬</code>. | |||
=== Rank extension === | |||
The term "scalar extension" is sometimes used to refer to the practice of allowing a scalar when a higher rank is expected. The scalar is treated as an array of the expected minimum rank whose shape is a vector of 1s (that is, a [[singleton]]). For example, <code>⍳8</code> and <code>8⍴'a'</code> both produce an 8-element array even though the shape of an array is always a vector and so cannot be equal to <code>8</code>. This type of extension, which differs from ordinary scalar extension in that there is no expected shape and only an expected rank, has also been present since [[APL\360]]. | |||
=== Singleton extension === | === Singleton extension === | ||