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8. Classification

Classification is a familiar notion. For example, the classification of letters of the alphabet as vowel, consonant, sibilant, or plosive; of colors as primary and secondary; and of numbers as odd, even, prime, and complex.

It is also very important; it provides the basis for many significant notions, such as graphs, barcharts, and sets.

A classification may be complete, (each object falling into at least one class), and it may be disjoint (each object falling into at most one class). A graph is a disjoint classification corresponding to the non-disjoint classification used to produce a barchart.
   x=: 1 2 3 4 5 6 7
   ]y=: (x-3) * (x-5)                      NB. Parabola (roots at 3 and 5)
8 3 0 _1 0 3 8

   range=: >./ - i.@spread 
   spread=: 1: + >./ - <./ 
   spread y
10

   range y
8 7 6 5 4 3 2 1 0 _1
                    
   ((range <:/ ]);{&' *'@(range<:/])) y    NB. Barcharts of y
+-------------+-------+
|1 0 0 0 0 0 1|*     *|
|1 0 0 0 0 0 1|*     *|
|1 0 0 0 0 0 1|*     *|
|1 0 0 0 0 0 1|*     *|
|1 0 0 0 0 0 1|*     *|
|1 1 0 0 0 1 1|**   **|
|1 1 0 0 0 1 1|**   **|
|1 1 0 0 0 1 1|**   **|
|1 1 1 0 1 1 1|*** ***|
|1 1 1 1 1 1 1|*******|
+-------------+-------+

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