Intro 15. Defined Adverbs

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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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