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15. Defined Adverbs

Names may be assigned to adverbs, as they are to nouns and verbs: 
   a=:1 2 3 4 5
   prefix=: \
   < prefix 'abcdefg'
+-+--+---+----+-----+------+-------+
|a|ab|abc|abcd|abcde|abcdef|abcdefg|
+-+--+---+----+-----+------+-------+

   +/ prefix a
1 3 6 10 15
Moreover, new adverbs result from a string of adverbs (such as /\) and from a conjunction together with one of its arguments. Such adverbs can be defined by assigning names. Thus:
   IP=: /\                     NB. Insert Prefix
   + IP a
1 3 6 10 15

   with3=: &3
   % with3 a
0.333333 0.666667 1 1.33333 1.66667

   ^ with3 a
1 8 27 64 125

   I=: ^: _1                   NB. Inverse adverb
   *: I a
1 1.41421 1.73205 2 2.23607

   + IP I 1 3 6 10 15
1 2 3 4 5

   ten=: 10&
   ^. ten 5 10 20 100
0.69897 1 1.30103 2

   #. ten 3 6 5
365

   from=: -~ 
   into=: %~
   10 into 17 18 19
1.7 1.8 1.9

   10 from 17 18 19
7 8 9

   i=: "_1                NB. Apply to items
   {. i i. 3 4
0 4 8

Exercises

15.1   Experiment with, and explain the behaviour of, the adverbs pow=: ^& and log=: &^.

15.2   State the significance of the following expressions, and test your conclusions by entering them:
+/~ i=: i. 6Addition table
ft=: /~Function table adverb
+ ft iAddition table
! ft iBinomial coefficients
inv=: ^:_1Inverse adverb
sub3=: 3&+ inv  Subtract-three function
sub3 i



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