array ← ##.pack array                       ⍝ Saves WS by sharing subarrays.

Pack attempts to increase the amount of workspace available by sharing identical
subarrays in its argument.  For a sizeable argument, this takes a very long time
as  each  subarray  is  compared  with every other one (n*2 comparisons).  It is
worth  doing  only when workspace availability is at a premium, perhaps prior to
shipping  an  application  containing complex nested variables. Notice that sub-
arrays  can  be shared _among_ distinct variables - see example below. Note that
in  this  context,  system  function ⎕SIZE can be misleading as it ignores array
sharing.

NB: [pack] shares items at _and_ _between_ all depths in its argument array. For
sharing of subarrays at any particular level,  the following simple  function is
considerably  faster.  Note that it may be applied under each (¨) to share items
at (but not between) greater depths.

    pack1 ← {(∪,⍵){⍺[⍺⍳⍵]}⍵}    ⍝ share top level items.

    ditty ← ('Dime' 'cuándo' 'serás' 'mia') ('Dime' 'cuándo' 'cuándo' 'cuándo')

All recent versions of Dyalog share literal constants, such as  'cuándo'  above.
To emulate a more real situation, where array items  are  typically  created  by
function application, let's make sure we start with an array of unshared items:

    unsh ← ⌽∘⌽                  ⍝ reversal creates a new vector.

    ditty ← unsh¨ ditty         ⍝ force unsharing.

Now pack:

    ditty ← pack1¨ ditty        ⍝ share inside, but not among, sub vectors.

    ditty ← pack   ditty        ⍝ share _all_ subarrays.

NB: Related function →nspack← shares all subarrays within a given namespace.

Technical note:

Pack uses (6≠10|⎕DR ⍵:) to determine whether a subarray is homogeneous or heter-
ogeneous.  In  the  latter  case, the array's items may be shared as well as the
array itself. Compare the following two depth-1 arrays:

      1 0 6 6       ⍝ hom: try to share whole array.

      '1' 0 6 6     ⍝ het: try to share array _and_ its subarrays.

Examples:

      wa←⎕wa ⋄ cvecs←(⍳1e3)⌽¨⊂⎕a ⋄ wa-⎕wa   ⍝ WS used by distinct char vectors,
48032
      wa←⎕wa ⋄ cvecs←pack cvecs  ⋄ wa-⎕wa   ⍝ sharing recovers most of it.
¯42856

      A ← ⌽∘⌽¨ 'Scissors' 'Paper' 'Stone'
      B ← ⌽∘⌽¨ 'Paper' 'Stone' 'Scissors'
      C ← ⌽∘⌽¨ 'Stone' 'Scissors' 'Paper'
      wa←⎕wa
      ⎕wa-wa
0
      A B C←pack A B C      ⍝ Sharing subarrays _among_ variables,
      ⎕wa-wa                ⍝ ... releases some workspace.
144
      nested←⍳¨∘⍳¨∘⍳¨∘⍳¨∘⍳3 3                   ⍝ complex nested array:

      wa←⎕wa ⋄ nested←pack nested ⋄ ⎕wa-wa      ⍝ significant saving.
17936

See also: nspack Data_compression

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