Lisp: Benefits of lists as code over arrays as code?

Question

Question for lisp programmers:

Lisp code is lisp data, usually lists. Is there an advantage to code being lists over code being arrays?

Would macros be easier to write/faster to run?

You can assume that, in such a language (you could call it "arrap"), elements can be deleted from or inserted into arrays and that the arrays would grow and shrink as needed.

Answer 1

Lists are much more versatile than arrays. With lists, you can recurse (e.g., for mapping or folding) by cdring down a list. This doesn't work for arrays; you'd have to pass in the array index too.

For example, this is a simple implementation of map and fold that take one list only:

(define (map1 f l)
  (if (null? l) l
      (cons (f (car l)) (map1 f (cdr l)))))

(define (left-fold1 f init l)
  (if (null? l) init
      (left-fold1 f (f (car l) init) (cdr l))))

How would you do that for arrays, without having to pass in another argument (for the index)? (Remember, Lisp and Scheme have no pointers, at least none that user code can touch.)

---

Also, lists can share storage, but arrays cannot. Take this Scheme code for example:

(define (x-world x)
  (cons x '(world)))

(define hello-world (x-world 'hello))
(define goodbye-world (x-world 'goodbye))

Here, hello-world has the value (hello world) and goodbye-world has the value (goodbye world).

There is one important fact, though: in many Scheme implementations, the (world) part of both lists is actually shared. This sharing would be impossible for arrays.

---

Addendum: To answer compman's point that recursion is somehow "non-production-grade", in Scheme, all standard looping/iteration is done using tail recursion. Here's a tail-recursive version of map1, for example:

(define (map1 f l)
  (let loop ((r '())
             (l (reverse l)))
    (if (null? l) r
        (loop (cons (f (car l)) r) (cdr l)))))

or, even more simply using left-fold1:

(define (map1 f l)
  (left-fold1 (lambda (e r) (cons (f e) r))
              '() (reverse l)))

reverse is a Scheme built-in, but its implementation is equally trivial (and also uses iteration only):

(define (reverse l)
  (left-fold1 cons '() l))

Answer 2

Insertion itself is O(1) at the beginning of the list.

(cons x '(world))

Inserts "x" at the beginning of the list containing world. If you have an array and you want to insert an element at the beginning, you have to shift everything over by one. Not so with lists!

Answer 3

Some lisps used to use a technique known as CDR coding fro list representation. This, essentially, replaces the CDR-half of the cell with the contents of the pointed-to cell, allowing you to represent a list with what's effectively an array of CAR pointers, while preserving list semantics (you can have part of a list CDR coded, share CDR-coded tails and other things that normal lists can handle)

However, efficient implementation of CDR coding requires hardware support, so it (as far as I understand) pretty much went out with dedicated Lisp machines.

As far as lisp-the-language-family is concerned, no, I don't think macros would be easier to write. At best, I think it would be no harder to write macros.