Difference between CDR, CAR and REST, FIRST and possible implementation?

Question

I'm learning a little bit about functional programming in LISP and here's what I've bumped into: LISP uses CAR, CDR functions as well as FIRST and REST functions. Both related to lists.

From what I've learned so far, there's a difference between these two, but I don't quite see what the difference is.

Could anyone sum this up for me? And how do I eventually implement FIRST/REST using CDR, CAR?

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Edit: Since accepted answer mentions documentation, but does not link, here is the link for the documentation for CAR/CDR, here then for FIRST/REST.

In addition - important note - that linked documentation is "just implementation notes" for CLISP, which is a commonly used environment. Generally it is almost impossible to find "official documentations" for languages such is this one.

Answer 1

In terms of what they do, car and cdr are equivalent to first and rest. This is quite clear in the documentation. The HyperSpec says on the entry for first, second, &c:

The functions first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, and tenth access the first, second, third, fourth, fifth, sixth, seventh, eighth, ninth, and tenth elements of list, respectively. Specifically,

(first list)    ==   (car list)
(second list)   ==   (car (cdr list))
(third list)    ==   (car (cddr list))

…

Notes:

first is functionally equivalent to car, second is functionally equivalent to cadr, third is functionally equivalent to caddr, and fourth is functionally equivalent to cadddr.

Now, there is a difference, not in functionality, but in style, when you're using these functions. This is actually called out in the HyperSpec as well, e.g., in the entry on rest:

Notes:

rest is often preferred stylistically over cdr when the argument is to being subjectively viewed as a list rather than as a cons.

For instance, consider two ways of mapping over structures built from cons cells. In the first, we're mapping over a tree of cons cells, calling some function with each leaf (i.e., non-cons) of the tree. We check whether something is a cons with consp, and if it is, we recurse onto its car and cdr. We combine the results into a new cons cell by calling cons.

(defun map-over-cons (function tree)
  (if (not (consp tree))
      (funcall function tree)
      (cons (map-over-cons function (car tree))
            (map-over-cons function (cdr tree)))))

Alternatively, when we map over a list, we typically check for the terminal condition with endp (or null, but endp emphasizes that we're looking for the end of a list, not just looking for nil), and we call the function on the first of the list and recurse into the rest of the list. While it's pretty common to see the result constructed using cons, there's actually list* that will perform the same task when called with two arguments (in general, it can do a bit more) that emphasizes that a list is being constructed:

(defun map-over-list (function list)
  (if (endp list)
      '()
      (list* (funcall function (first list))
             (map-over-list function (rest list)))))

Either of these functions could be written using car, cdr, and cons, or with first, rest, and list*, or any combination of them, but sticking to one or the other helps people that may read the code later (including the original author), and signals the intent of the author.

And how do I eventually implement FIRST/REST using CDR, CAR?

How about:

(defun first (x) (car x))
(defun rest (x) (cdr x))

or possibly even better, if you have symbol-function:

(setf (symbol-function 'first) (symbol-function 'car))
(setf (symbol-function 'rest) (symbol-function 'cdr))