Define a pervasive function in APL

Question

How can one define a pervasive function in APL?

What I do is

function←{
    (⊃⍣(⍬≡⍴⍵)){the function that apply to scalar}¨⍵
}

I think there should be a better way to do this that I'm not seeing it.

Answer 1

Most primitive functions in APL are already pervasive. So, unless you do fancy stuff, your custom functions will already be pervasive. For instance

f←{÷1+*-⍵}    ⍝ sigmoid, f(x)=1/(1+exp(-x))

will work on arrays as well as scalars.

If you do do fancy stuff and you have a non-pervasive function f, you can turn it into a pervasive one by

g←{0=⍴⍴⍵:f⍵ ⋄ ∇¨⍵}   ⍝ the pervasive version of f

which can be read as: if the argument is a scalar, apply f on it, otherwise recursively go into each item of the argument.

Answer 2

The dfns workspace contains the perv operator which causes its operand function to be applied pervasively, with either one or two arguments:

perv←{⍺←⊢               ⍝ Scalar pervasion
    1=≡⍺ ⍵ ⍵:⍺ ⍺⍺ ⍵     ⍝ (⍺ and) ⍵ depth 0: operand fn application
             ⍺ ∇¨⍵      ⍝ (⍺ or) ⍵ deeper: recursive traversal.
}

Try it online!