CAR and CDR

For other meanings, see CAR (disambiguation), CDR (disambiguation), and CADR (disambiguation).

In computer programming, car ⁱ/ˈkɑːr/ and cdr (ⁱ/ˈkʌdər/ or ⁱ/ˈkʊdər/) are primitive operations on cons cells (or "non-atomic S-expressions") introduced in the Lisp programming language. A cons cell is composed of two pointers; the car operation extracts the first pointer, and the cdr operation extracts the second.

Thus, the expression (car (cons x y)) evaluates to x, and (cdr (cons x y)) evaluates to y.

When cons cells are used to implement singly linked lists (rather than trees and other more complicated structures), the car operation returns the first element of the list, while cdr returns the rest of the list. For this reason, the operations are sometimes given the names first and rest or head and tail.

Etymology

Lisp was originally implemented on the IBM 704 computer, in the late 1950s. The 704 hardware had special support for splitting a 36-bit machine word into four parts, an "address part" and "decrement part" of 15 bits each and a "prefix part" and "tag part" of three bits each.

Precursors to Lisp included functions:

• car (short for "Contents of the Address part of Register number"),
• cdr ("Contents of the Decrement part of Register number"),
• cpr ("Contents of the Prefix part of Register number"), and
• ctr ("Contents of the Tag part of Register number"),

each of which took a machine address as an argument, loaded the corresponding word from memory, and extracted the appropriate bits.

The 704 assembler macro for cdr was:

 LXD JLOC,4
 CLA 0,4
 PDX 0,4
 PXD 0,4

A machine word could be reassembled by cons, which took four arguments (a,d,p,t).

The prefix and tag parts were dropped in the early stages of Lisp's design, leaving CAR, CDR, and a two-argument CONS.

Continued acceptance

The alternative names first and rest, which date back at least to 1959, are sometimes preferred to car and cdr. However, car and cdr have the advantage that short compositions of the functions can be given short and more or less pronounceable names of the same form. In Lisp, (cadr '(1 2 3)) is the equivalent of (car (cdr '(1 2 3))); its value is 2. This is because 2 is the first item of the rest of (1 2 3). Similarly, (caar '((1 2) (3 4))) is the same as (car (car '((1 2) (3 4)))); its value is 1. Most Lisps set a limit on the number of composed forms they support; Common Lisp and Scheme both provide forms with up to four repetitions of the a and d. However, further compositions can easily be defined (if not used) by the user.

Other computer languages

Many languages (particularly functional languages and languages influenced by the functional paradigm) use a singly linked list as a basic data structure, and provide primitives or functions similar to car and cdr. These are named variously first and rest, head and tail, etc. In Lisp, however, the cons cell is not used only to build linked lists but also to build pair and nested pair structures, i.e. the cdr of a cons cell need not be a list. In this case, most other languages provide different primitives as they typically distinguish pair structures from list structures either typefully or semantically. Particularly in typed languages, lists, pairs, and trees will all have different accessor functions with different type signatures: in Haskell, for example, car and cdr become fst and snd when dealing with a pair type. Exact analogues of car and cdr are thus rare in other languages.

References

Notes

• Russel, S. (undated, c. late 1950s) Writing and Debugging Programs. MIT Artificial Intelligence Laboratory Memo 6.