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A '''prefix''' of a [[vector]] is another vector which is no longer than that vector, and shares all of its leading [[element]]s. In [[leading axis theory]], an array may be considered a prefix of another array of the same rank if the same relation holds with [[major cell]]s in place of elements. The function [[Take]] produces prefixes of its right argument as long as the left argument is no greater than that argument's length ([[Tally]]). A vector is a prefix of another if and only if its [[Reverse]] is a [[suffix]] of that vector's reverse. | A '''prefix''' of a [[vector]] is another vector which is no longer than that vector, and shares all of its leading [[element]]s. In [[leading axis theory]], an array may be considered a prefix of another array of the same rank if the same relation holds with [[major cell]]s in place of elements. Consequently, a prefix is a kind of [[subarray]]. The function [[Take]] produces prefixes of its right argument as long as the left argument is non-negative and no greater than that argument's length ([[Tally]]). A vector is a prefix of another if and only if its [[Reverse]] is a [[suffix]] of that vector's reverse. | ||
A vector is a prefix of another vector if its length is [[Less than or Equal to]] that vector's length, and every [[element]] in the prefix vector [[match]]es the corresponding element of the other vector (the one at the same [[index]]). This may be tested using [[Take]] and [[Match]]: | A vector is a prefix of another vector if its length is [[Less than or Equal to]] that vector's length, and every [[element]] in the prefix vector [[match]]es the corresponding element of the other vector (the one at the same [[index]]). This may be tested using [[Take]] and [[Match]]: | ||
< | <syntaxhighlight lang=apl> | ||
isPrefix ← {(≢⍺)≤(≢⍵) ∧ ⍺≡(≢⍺)↑⍵} | isPrefix ← {((≢⍺)≤(≢⍵)) ∧ ⍺≡(≢⍺)↑⍵} | ||
'pre' isPrefix 'prefix' | 'pre' isPrefix 'prefix' | ||
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'pre ' isPrefix 'pre' | 'pre ' isPrefix 'pre' | ||
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</ | </syntaxhighlight> | ||
In [[leading axis theory]], the [[frame]] for k-cells of an array is a prefix of that array's [[shape]], while the [[cell shape]] is a [[suffix]]. | In [[leading axis theory]], the [[frame]] for k-cells of an array is a prefix of that array's [[shape]], while the [[cell shape]] is a [[suffix]]. | ||
[[Iverson notation]] included the notion of a prefix vector <math>\alpha^j(n)</math> consisting of <math>j</math> ones followed by <math>n-j</math> zeros; such a vector could be used to produce a length-<math>j</math> prefix of a length-<math>n</math> vector using [[Compress]]. | [[Iverson notation]] included the notion of a prefix vector <math>\alpha^j(n)</math> consisting of <math>j</math> ones followed by <math>n-j</math> zeros; such a vector could be used to produce a length-<math>j</math> prefix of a length-<math>n</math> vector using [[Compress]]. A prefix function <syntaxhighlight lang=apl inline>n ⍺ j</syntaxhighlight> was included in early versions of [[APL\360]]. | ||
In [[Dyalog APL's | In [[Dyalog APL]]'s [[Total array ordering]], a prefix of another array always orders earlier than that array; this is a consequence of the principally "nothing is less than something" used as the foundation for Dyalog's TAO. | ||
[[Category:Array relationships]] | |||