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:''This page describes the array datatype as defined by array languages. For the role of arrays in [[APL syntax]], see [[Array]].'' | |||
The distinguishing feature of APL and the array language family is its focus on '''arrays'''. In most array languages the array is the only first class datatype. While this sounds like a very strict model of language design, in fact it imposes no restrictions at all: any kind of data can be treated as a [[scalar]], or array with rank 0! | The distinguishing feature of APL and the array language family is its focus on '''arrays'''. In most array languages the array is the only first class datatype. While this sounds like a very strict model of language design, in fact it imposes no restrictions at all: any kind of data can be treated as a [[scalar]], or array with rank 0! | ||
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Flat array theory is often called "grounded" in contrast to "floating" nested array theory. | Flat array theory is often called "grounded" in contrast to "floating" nested array theory. | ||
== Based array theory == | |||
Based array theory discards the principle that all data should be stored in arrays, instead defining basic types such as characters and numbers independently of arrays and arrays as a collection type—possibly one of many—that can contain any data. This model does not have any widely accepted name, with the term "based system" introduced in an [[APL Quote Quad]] paper in 1981.<ref>Randall Mercer. [https://dl.acm.org/doi/abs/10.1145/586656.586663 "A based system for general arrays"]. [[APL Quote Quad]] Volume 12, Issue 2. 1981-12.</ref> However, as it is the natural model when arrays are added to an existing programming system, it is common in array libraries such as [[NumPy]], [[wikipedia:ILNumerics|ILNumerics]], and [[wikipedia:Haskell (programming language)|Haskell]]'s [https://hackage.haskell.org/package/repa Repa], as well as the language [[Julia]]. It is used by the APL-family language [[BQN]]. | |||
=== Mutable based arrays === | |||
In many languages with this array style, such as NumPy and Julia, the arrays are [[wikipedia:Immutable object|mutable]], meaning that copies of an array can be made, so that one copy reflects changes made to any copy. In contrast, APL operations that appear to modify an array, like [[indexed assignment]], will only change the particular copy of the array used, and can be said to create a new array rather than change an existing one: there is no special connection between the old and modified array. Mutable arrays make it possible for an array to contain itself, by replacing one element of an existing array with the whole array. This means that more values are possible than in an immutable based array language, and that some properties of immutable arrays, such as a finite [[depth]], do not hold. | |||
== Other features of the array model == | == Other features of the array model == | ||
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=== Numeric type coercion === | === Numeric type coercion === | ||
Most APLs, flat or nested, implicitly store simple numeric arrays as one of many [[numeric type]]s. When a numeric array is formed from numbers with different types, all numbers are converted to a common type in order to be represented as a flat array. If the hierarchy of numeric types is not strict, that is, there are some pairs of numeric types for which neither type is a subset of the other, then this coercion may affect the behavior of the numbers in the array. For example, [[J]] on a 64-bit machine uses both 64-bit integers and [[wikipedia:IEEE_754|double-precision floats]]. [[Catenate|Catenating]] the two results in an array of doubles, which will lose precision for integers whose absolute value is larger than 2<sup>53</sup>. In [[Dyalog APL]] a similar issue occurs with [[decimal | Most APLs, flat or nested, implicitly store simple numeric arrays as one of many [[numeric type]]s. When a numeric array is formed from numbers with different types, all numbers are converted to a common type in order to be represented as a flat array. If the hierarchy of numeric types is not strict, that is, there are some pairs of numeric types for which neither type is a subset of the other, then this coercion may affect the behavior of the numbers in the array. For example, [[J]] on a 64-bit machine uses both 64-bit integers and [[wikipedia:IEEE_754|double-precision floats]]. [[Catenate|Catenating]] the two results in an array of doubles, which will lose precision for integers whose absolute value is larger than 2<sup>53</sup>. In [[Dyalog APL]] a similar issue occurs with [[decimal float]]s and [[complex number]]s: combining the two results in an array of complex numbers, but this loses precision since Dyalog's complex numbers are stored as pairs of double-precision floats and its 128-bit decimal floats have higher precision than doubles. | ||
== Array characteristics == | == Array characteristics == | ||
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== External links == | == External links == | ||
* [ | * [https://help.dyalog.com/latest/index.htm#Language/Introduction/Variables/Arrays.htm Dyalog array model] | ||
* [https://chat.stackexchange.com/rooms/52405/conversation/lesson-1-introduction-to-arrays-in-apl APL Cultivation] | * [https://chat.stackexchange.com/rooms/52405/conversation/lesson-1-introduction-to-arrays-in-apl APL Cultivation] | ||
* [https://www.sacrideo.us/tag/apl-a-day/ APL a Day] series | * [https://www.sacrideo.us/tag/apl-a-day/ APL a Day] series | ||
{{APL | * [https://www.jsoftware.com/papers/array.htm What is an Array?] by [[Roger Hui]] (in [[J]]) | ||
== References == | |||
<references /> | |||
{{APL features}}[[Category:Arrays| ]] | |||