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21. Gerund and Agenda
In English, a gerund is a noun that carries the force of a verb, as does the noun cooking in the phrase the art of cooking; and agenda is a list of items for action. The tie conjunction``` applies to two verbs to form a gerund, from which elements can be chosen for execution. Thus, if the agenda conjunction`@.` is applied to a gerund, its verb right argument provides the results that choose the elements. For example:

       g=: +`^
       a=:<
       2 a 3
    1

       2 g@.a 3
    8

       3 g@.a 2
    5

       +:`-:`*:`%: @. (4&|@<.)"0 i. 10
    0 0.5 4 1.73205 8 2.5 36 2.64575 16 4.5

The verb produced by`g@.a` is often called a case or case statement, since it selects one of the “cases” of the gerund for execution.
The insert adverb`/` applies to a gerund in a manner analogous to its application to a verb. For example:

       c=:3 [ x=: 4 [ power=: _1
       g/ c,x,power
    3.25

       3+x^_1
    3.25

The elements of the gerund are repeated as required. For example:

       +`*/1,x,3,x,3,x,1
    125

The last sentence above corresponds to Horner’s efficient evaluation of the polynomial with coefficients`1 3 3 1` and argument`x` .

Exercises

21.1 | Define a function`f` such that`(x=: 4) f c=: 1 3 3 1` yields the result used as the argument to`+`*/` in Horner's method. Answer:`f=: }.@,@,.`

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