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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. 6 Addition table ft=: /~ Function table adverb + ft i Addition table ! ft i Binomial coefficients inv=: ^:_1 Inverse adverb sub3=: 3&+ inv Subtract-three function sub3 i

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