From 229e2cd2f5c78b13c483a8559dead2c8f31d8e42 Mon Sep 17 00:00:00 2001 From: Marshall Lochbaum Date: Sat, 18 Jul 2020 18:26:52 -0400 Subject: Terminology changes: subject, 1/2-modifier, Box/Unbox to Enclose/Merge, blocks --- docs/doc/join.html | 6 +++--- 1 file changed, 3 insertions(+), 3 deletions(-) (limited to 'docs/doc/join.html') diff --git a/docs/doc/join.html b/docs/doc/join.html index 744fa923..b65dc46e 100644 --- a/docs/doc/join.html +++ b/docs/doc/join.html @@ -1,6 +1,6 @@

Join

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Join (∾) is an extension of the monadic function Raze from A+ and J to arbitrary argument ranks. It has the same relationship to Join to, the dyadic function sharing the same glyph, as Unbox (>) does to Couple (≍): a≍b is >a‿b and a∾b is ∾a‿b. While Unbox and Couple combine arrays (the elements of Unbox's argument, or the arguments themselves for Coups) along a new leading axis, Join and Join to combine them along the existing leading axis. Both Unbox and Join can also be called on a higher-rank array, causing Unbox to add multiple leading axes while Join combines elements along multiple existing axes.

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Join (∾) is an extension of the monadic function Raze from A+ and J to arbitrary argument ranks. It has the same relationship to Join to, the dyadic function sharing the same glyph, as Merge (>) does to Couple (≍): a≍b is >a‿b and a∾b is ∾a‿b. While Merge and Couple combine arrays (the elements of Merge's argument, or the arguments themselves for Couple) along a new leading axis, Join and Join to combine them along the existing leading axis. Both Merge and Join can also be called on a higher-rank array, causing Merge to add multiple leading axes while Join combines elements along multiple existing axes.

Join can be used to combine several strings into a single string, like array.join() in Javascript (but it doesn't force the result to be a string).

    ∾"time"‿"to"‿"join"‿"some"‿"words"
 [ timetojoinsomewords ]
@@ -33,6 +33,6 @@
   3 3 3 3 4 4 5 5 5 5 5
                         ┘
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Join has fairly strict requirements on the shapes of its argument elements—although less strict than those of Unbox, which requires they all have identical shape. Suppose the argument to Join has rank m. Each of its elements must have the same rank, n, which is at least m. The trailing shapes m↓⟜≢¨𝕩 must all be identical (the trailing shape m↓≢∾𝕩 of the result will match these shapes as well). The other entries in the leading shapes need not be the same, but the shape of an element along a particular axis must depend only on the location of the element along that axis in the full array. For a vector argument this imposes no restriction, since the one leading shape element is allowed to depend on position along the only axis. But for higher ranks the structure quickly becomes more rigid.

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To state this requirement more formally in BQN, we say that there is some vector s of length vectors, so that (≢¨s)≡≢𝕩. We require element i⊑𝕩 to have shape i⊑¨s. Then the first m axes of the result are +´¨s.

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Join has fairly strict requirements on the shapes of its argument elements—although less strict than those of Merge, which requires they all have identical shape. Suppose the argument to Join has rank m. Each of its elements must have the same rank, n, which is at least m. The trailing shapes m↓⟜≢¨𝕩 must all be identical (the trailing shape m↓≢∾𝕩 of the result will match these shapes as well). The other entries in the leading shapes need not be the same, but the shape of an element along a particular axis must depend only on the location of the element along that axis in the full array. For a list argument this imposes no restriction, since the one leading shape element is allowed to depend on position along the only axis. But for higher ranks the structure quickly becomes more rigid.

+

To state this requirement more formally in BQN, we say that there is some list s of lists of lengths, so that (≢¨s)≡≢𝕩. We require element i⊑𝕩 to have shape i⊑¨s. Then the first m axes of the result are +´¨s.

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