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# 2F. Hooks

A pair of functions in isolation form a hook whose monadic case is defined as in:

> `(= <.) y` is equivalent to `y = <. y`

hence the function`h=: =<.` compares its argument with its integer part, and therefore provides a test for integers. Hooks occur frequently in most sections.

`m0=: It=: =<.` | Integer test
`m1=: Rt=: =+` | Real test
`d2=: $,:` | `x` copies of `y`
`d3=: $,` | Reshape as in APL
`m4=: cf=: (+%)/` | Continued fraction
`m5=: cfc=: (+%)/\` | Continued fraction convergents
`m6=: ifb=: # i.@#` | Integers from boolean list
`m7=: [m` | `([m)y` invokes`m y` ,`` then returns`y`

For example:

       cf 3 7 15 1		NB. Approximation to pi
    3.14159

       cfc 3 7 15 1		NB. Convergents to pi
    3 3.14286 3.14151 3.14159

       cfc 1 1 1 1 1 1 1	NB. Convergents to golden mean
    1 2 1.5 1.66667 1.6 1.625 1.61538

       cfc 10$1x		NB. As above in extended precision
    1 2 3r2 5r3 8r5 13r8 21r13 34r21 55r34 89r55

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