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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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