Intro07

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

   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