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<p>So as to more efficiently represent this commonly occurring array, a new datatype &mdash; '''Arithmetic Progression Arrays''' ('''APAs''') &mdash; are created by the [[Index Generator]] function and may be reshaped arbitrarily (as long as no replication occurs) and still retain the datatype.</p>

<p>For example, <apll>2 3 4⍴⍳24</apll> has a very compact storage consisting of the array shape (<apll>2 3 4</apll>), the starting offset (<apll>⎕IO</apll>) and multiplier (<apll>1</apll>), plus the normal array overhead (which includes the number of elements (<apll>24</apll>)), for a total of <apll>96</apll> bytes.  This datatype is also used to store reshaped Boolean or integer scalars, as in <apll>1e6⍴12</apll> or <apll>1e6/12</apll> both of which use <apll>80</apll> bytes (<apll>16</apll> bytes less than the preceding example because it has two fewer shape elements at eight bytes per).</p>