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In [[SHARP APL]], [[Rationalized APL]], and [[J]], function rank refers to a built-in property of a function indicating which argument [[ | In [[SHARP APL]], [[Rationalized APL]], and [[J]], '''function rank''' refers to a built-in property of a function indicating which argument [[rank]]s it accepts. A function will be applied as though it were given that rank with the [[Rank operator]]. The function rank may also have other observable effects: in [[J]], the ranks of <syntaxhighlight lang=apl inline>f</syntaxhighlight> may be viewed using <syntaxhighlight lang=apl inline>f b. 0</syntaxhighlight> and another function <syntaxhighlight lang=apl inline>g</syntaxhighlight> may be given those ranks using <syntaxhighlight lang=apl inline>g"f</syntaxhighlight> (<syntaxhighlight lang=apl inline>"</syntaxhighlight> is the Rank operator). Every language with function rank defines [[Close composition|"close" composition operators]] which inherit the rank of their right operand—the [[derived function]] produced by such a composition has ranks derived from that function's ranks. | ||
== History == | == History == | ||
Function rank was first introduced without being given a name in [[SHARP APL]], as a feature of the compositions [[Over|with]] and [[Atop|over]]. New compositions such as < | Function rank was first introduced without being given a name in [[SHARP APL]], as a feature of the compositions [[Over|with]] and [[Atop|over]]. New compositions such as <syntaxhighlight lang=apl inline>f⍤g</syntaxhighlight> were described as "close in the sense that the expression… is applied individually to each subarray argument of <syntaxhighlight lang=apl inline>g</syntaxhighlight>".<ref>K.E. Iverson. [https://www.jsoftware.com/papers/satn41.htm "Composition and Enclosure"]. SATN 41, 1981-06-20.</ref> The concept of function rank was formalized, and applied to most primitives, when the [[Rank operator]] was introduced to SHARP version 19.0 in 1987.<ref>Bernecky, Robert. [https://dl.acm.org/citation.cfm?id=55632 "An Introduction to Function Rank"]. APL88 Conference Proceedings. ''ACM SIGAPL Quote Quad'', 18(2), December 1987.</ref> In [[J]] every function, primitive or user-defined, has a function rank. | ||
== Definition and properties == | == Definition and properties == | ||
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A function with rank applies only to cells of the appropriate rank. In order to operate on those cells it will map over arguments of larger rank as though the [[Rank operator]] were applied to it. | A function with rank applies only to cells of the appropriate rank. In order to operate on those cells it will map over arguments of larger rank as though the [[Rank operator]] were applied to it. | ||
As the Rank operator accepts up to three specified ranks in its right argument, a function with a defined function rank has three ranks, one for the argument in the [[ | As the Rank operator accepts up to three specified ranks in its right argument, a function with a defined function rank has three ranks, one for the argument in the [[monadic]] case plus two for the arguments in the [[dyadic]] case. These ranks may be [[Infinity|infinite]], or larger than the [[maximum rank]] if there is one, in which case they have no effect on the function's application. | ||
A function's rank is obtained from its definition: | A function's rank is obtained from its definition: | ||
* Ranks of [[ | * Ranks of [[primitive function]]s are defined by the interpreter. | ||
* The ranks of a [[derived function]] are determined by its operands. For most operators they are infinite; for [[close | * The ranks of a [[derived function]] are determined by its operands. For most operators they are infinite; for [[close composition]]s they are obtained from the right argument, and for functions derived from the [[Rank operator]] they are obtained from the right operand. | ||
* The ranks of a [[user-defined function]] are infinite. | * The ranks of a [[user-defined function]] are infinite. | ||
It is not possible to modify the ranks of a function. Instead, apply the [[Rank operator]] to create a new function which has the given rank, but functions like the left operand on arrays of that rank. Notably, given a function is defined with a particular rank, it is impossible to make it work on arrays of a higher rank. Applying Rank with larger numbers will produce a function whose rank is higher, but the function's results will be no different: the inner function will still map over cells because it retains its rank. | It is not possible to modify the ranks of a function. Instead, apply the [[Rank operator]] to create a new function which has the given rank, but functions like the left operand on arrays of that rank. Notably, given a function is defined with a particular rank, it is impossible to make it work on arrays of a higher rank. Applying Rank with larger numbers will produce a function whose rank is higher, but the function's results will be no different: the inner function will still map over cells because it retains its rank. | ||
== External links == | |||
[[J]] resources: | |||
* [https://www.jsoftware.com/help/jforc/loopless_code_i_verbs_have_r.htm Loopless Code I: Verbs Have Rank] from ''J for C Programmers'' | |||
* [https://www.jsoftware.com/help/learning/07.htm#03 Intrinsic Ranks] from ''Learning J'' | |||
* [https://www.jsoftware.com/help/primer/verb_rank.htm Verb Rank] from the J Primer | |||
* [https://code.jsoftware.com/wiki/Vocabulary/EZRank#The_rank_of_a_verb The rank of a verb] from "Rank in a hurry" | |||
== References == | == References == | ||
<references /> | <references /> | ||
{{APL features}}[[Category:Leading axis theory]][[Category:Function characteristics]] | |||