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Ingy döt Net 2023-07-01 11:58:00 -04:00
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NB. j assumes an unknown name f is a verb of infinite rank
NB. f has infinite ranks
f b. 0
_ _ _
NB. The verb g makes a table.
g=: f/~
NB. * has rank 0
f=: *
NB. indeed, make a multiplication table
f/~ i.5
0 0 0 0 0
0 1 2 3 4
0 2 4 6 8
0 3 6 9 12
0 4 8 12 16
NB. g was defined as if f had infinite rank.
g i.5
0 1 4 9 16
NB. f is known to have rank 0.
g=: f/~
NB. Now we reproduce the table
g i.5
0 0 0 0 0
0 1 2 3 4
0 2 4 6 8
0 3 6 9 12
0 4 8 12 16
NB. change f to another rank 0 verb
f=: +
NB. and construct an addition table
g i.5
0 1 2 3 4
1 2 3 4 5
2 3 4 5 6
3 4 5 6 7
4 5 6 7 8
NB. f is multiplication at infinite rank
f=: *"_
NB. g, however, has rank 0
g i.5
0 0 0 0 0
0 1 2 3 4
0 2 4 6 8
0 3 6 9 12
0 4 8 12 16