Implement Map function in APL Language

Question

I have created the map function using Scheme, but I want to implement it in APL.

(define (map func lstt)
 (cond
 ((null? lst) '())
 (else (cons (func (car lst))
 (map func (cdr lst))))
 )
)

The map function takes two arguments: a function: func (like double: *2) and list of integers: lst

Calling map with double (*2) and list (1 2 3) will result in list (2 4 6)

Any help to implement it in APL

Answer 1

Map is doubly built into APL:

1. Every arithmetic function have an implicit map:

   double←×∘2
   double 1 2 3
   4 5 6
   

2. A general purpose map is also built in, namely ¨:

   reverse←⌽
   reverse 'abc' 'def' 'ghi'
   ┌───┬───┬───┐
   │ghi│def│abc│
   └───┴───┴───┘
   reverse¨'abc' 'def' 'ghi'
   ┌───┬───┬───┐
   │cba│fed│ihg│
   └───┴───┴───┘
   

That said, you can define map recursively as in your example code. For simplicity, let's restrict the domain to lists:

map←{0=≢⍵:⍵ ⋄ (⊂⍺⍺⊃⍵),∇1↓⍵}
reverse map 'abc' 'def' 'ghi'
┌───┬───┬───┐
│cba│fed│ihg│
└───┴───┴───┘

This is how it works:

map←{…⍺⍺…} defines map to be a monadic operator

0=≢⍵: if the argument has no elements (zero equals the tally of the argument)

⍵ return the argument

⋄ else

(⊂⍺⍺⊃⍵) open up the first element, apply the function and close it again

,∇1↓⍵ concatenated with recursion the rest of the argument (one element dropped from the argument)