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7. Bond Conjunction

A dyad such as ^ can be used to provide a family of monadic functions:
```   ]b=: i.7
0 1 2 3 4 5 6

b^2                        Squares
0 1 4 9 16 25 36

b^3                        Cubes
0 1 8 27 64 125 216

b^0.5                      Square roots
0 1 1.41421 1.73205 2 2.23607 2.44949
```
The bond conjunction & can be used to bind an argument to a dyad in order to produce a corresponding defined verb. For example:
```   square=: ^&2               Square (power and 2)
square b
0 1 4 9 16 25 36

(sqrt=: ^&0.5) b           Square root function
0 1 1.41421 1.73205 2 2.23607 2.44949
```
A left argument can be similarly bound:
```   Log=: 10&^.                Base-10 logarithm
Log 2 4 6 8 10 100 1000
0.30103 0.60206 0.778151 0.90309 1 2 3
```
Such defined verbs can of course be used in forks. For example:
```   in29=: 2&< *. <&9          Interval test
in29 0 1 2 5 8 13 21
0 0 0 1 1 0 0

IN29=: in29 # ]            Interval selection
IN29 0 1 2 5 8 13 21
5 8

LOE=: <+.=
5 LOE 3 4 5 6 7
0 0 1 1 1

integertest=: <. = ]       The monad <. is floor
integertest 0 0.5 1 1.5 2 2.5 3
1 0 1 0 1 0 1

int=: integertest
int (i.13)%3
1 0 0 1 0 0 1 0 0 1 0 0 1
```

Exercises

 7.1 The verb # is used dyadically in the program IN29 . Enter expressions such as(j=: 3 0 4 0 1) # i.5 to determine the behaviour of #, and state the result of #j#i.5 . (Also try 1j1#i.5 .) Answer: +/j 7.2 Cover the answers on the right and apply the following programs to lists to determine (and state in English) the purpose of each: ``` test1=: >&10 *. <&100 Test if in 10 to 100 int=: ] = <. Test if integer test2=: int *. test1 Test if integer and in 10 to 100 test3=: int +. test1 Test if integer or in 10 to 100 sel=: test2 # ] Select integers in 10 to 100 ``` 7.3 Cover the program definitions on the left of the preceding exercise, and make new programs for the stated effects. 7.4 Review the use of the fix adverb in Exercises 6.4-5, and experiment with its use on the programs of Exercise 7.2.

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