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)