Scalar extension: Difference between revisions
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Miraheze>Adám Brudzewsky |
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== History and terminology == | == History and terminology == | ||
The concept of scalar extension has been around since [[APL\360]]. An example which extends the scalar < | The concept of scalar extension has been around since [[APL\360]]. An example which extends the scalar <source lang=apl inline>2</code> is: | ||
<source lang=apl> | <source lang=apl> | ||
2 × 1 2 3 4 | 2 × 1 2 3 4 | ||
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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 < | 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 <source lang=apl inline>⍬</code>. | ||
=== Rank extension === | === 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, < | 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, <source lang=apl inline>⍳8</code> and <source lang=apl inline>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 <source lang=apl inline>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 === | ||