Index origin: Difference between revisions

{{Primitive|⎕IO|Index origin}} is the number used for the first [[index]] along each [[axis]] of an array. Many APLs allow the user to configure index origin using the [[system variable]] <source lang=apl inline>⎕IO</code>. Even array languages which do not have such a configuration parameter must make a choice of index origin; for example, [[J]] uses a non-configurable index origin of 0. The [https://en.wikipedia.org/wiki/English_language English language] uses an index origin of one: thus the element with index <source lang=apl inline>⎕IO</code> in APL is referred to in English as the "first" element.

The index origin affects both the handling of index arguments to functions (and other functionality like [[axis specification]]) and their results. For example, [[Iota]] (or "Index Generator") creates results which begin with <source lang=apl inline>⎕IO</code>.

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Any number could consistently be used for the index origin, but almost all APLs restrict the choice to 0 or 1. [[ngn/apl]] supports <source lang=apl inline>⎕IO</code> but only allows it to have the value 0. Attempting to assign an unsupported value to <source lang=apl inline>⎕IO</code> typically results in a [[DOMAIN ERROR]].

The following functions depend on <source lang=apl inline>⎕IO</code> in at least some APLs. They are listed with the [[glyphs]] used for them in [[Dyalog APL]]. For functions, only the result depends on <source lang=apl inline>⎕IO</code> except where noted with <source lang=apl inline>⍺</code> in which case the left argument does instead. For operators the dependence is noted.

! [[Monadic functions]]        !! [[Dyadic functions]]                          !! [[Operators]]

| [[Iota]] (<source lang=apl inline>⍳</code>)     || [[Index-Of]] (<source lang=apl inline>⍳</code>)                || [[Key]] (<source lang=apl inline>⌸</code>) argument to <source lang=apl inline>⍺⍺</code>

| [[Roll]] (<source lang=apl inline>?</code>)    || [[Deal]] (<source lang=apl inline>?</code>)                    || [[At]] (<source lang=apl inline>@</code>) result of <source lang=apl inline>⍵⍵</code>

| [[Grade]] (<source lang=apl inline>⍒⍋</code>)  || (<source lang=apl inline>⍒⍋</code>)                            ||

| [[Indices]] (<source lang=apl inline>⍸</code>)  || [[Interval Index]] (<source lang=apl inline>⍸</code>)          ||

|                              || [[Transpose]] (<source lang=apl inline>⍉</code>) <source lang=apl inline>⍺</code> ||

|                              || [[Pick]] (<source lang=apl inline>⊃</code>) <source lang=apl inline>⍺</code>      ||

|                              || [[Squad]] (<source lang=apl inline>⌷</code>) <source lang=apl inline>⍺</code>    ||

Additionally, [[indexing]] with brackets and [[axis specification]] depend on index origin.

* [https://en.wikipedia.org/wiki/Array_data_type#Index_origin Wikipedia]

 

 

{{APL built-ins}}