Mike Schaeffer's Blog

February 14, 2008

A couple weeks ago, I got into a brief reddit discussion on the relative merits of Lisp's car and cdr functions. Given a Lisp list, applying car to the list returns the first element of the list and applying cdr to the list returns a list of every element excluding the first. For someone new to Lisp (as we all were once), these names can be a bit awkward. However, like many other aspects of the language, there is more to car and cdr than meets the eye.

The first implementation of Lisp was done by Steve Russell on an IBM 704. The 704 was a 36-bit vacuum tube machine that IBM started selling in 1954. By the time it was discontinued in 1960, they had sold a total of 123 of the machines, each capable of a whopping 40,000 calculations per second. Russell's original 1959 implementation of Lisp on this machine took advantage of the fact that the 704's instruction set had special capabilities for accessing two distinct 15 bit fields of a 36 bit value loaded into a machine register: the address and decrement fields. In Russell's own words: "Because of an unfortunate temporary lapse of inspiration, we couldn't think of any other names for the 2 pointers in a list node than 'address' and 'decrement', so we called the functions CAR for 'Contents of Address of Register' and CDR for 'Contents of Decrement of Register'." Interestingly enough, he continues with this: "After several months and giving a few classes in LISP, we realized that 'first' and 'rest' were better names, and we (John McCarthy, I and some of the rest of the AI Project) tried to get people to use them instead. ... Alas, it was too late! We couldn't make it stick at all. So we have CAR and CDR. " So there you have it: car and cdr, two of the most famous and widely used functions of Lisp and its descendents, owe their names to a bizarre quirk of a computer architecture that's been obsolete for close to fifty years. For the record, here's a source listing for the original 704 implementataion of car taken from MIT AI Lab Memo 6:

CLA 0,4
PAX 0,4
PSX 0,4

But the story of car and cdr doesn't stop there. In the 1960's and early 70's, the University of Texas at Austin ran a computer called a CDC 6600. The 6600 was one of Seymour Cray's first big supercomputer designs, and was the fastest computer in the world for a time. It had a 60-bit machine word and an 18-bit address space, so you can probably see where this is going. The designers of UT's Lisp for the CDC 6600 added a third field to cons cells, giving them each three pointers, the car, cdr, and csr. I'm sure the third pointer was useful for implementing things like trees of nodes and lists of key/value pairs, although apparantly not useful enough to stick around. Two pointer cons cells are a better fit for modern hardware, and two two pointer cons cells can represent everything that a single three pointer cons cell can represent.

Back at MIT in the 70's, and before things like defstruct, Maclisp took the idea of multi-pointer cons cells to what must be its logical extreme: hunks. A Maclisp hunk was a structure like a cons cell that could hold an arbitrary number of pointers, up to total of 512. Each of these slots in a hunk was referred to as a numbered cxr, with a numbering scheme that went like this: `( cxr-1 cxr-2 cxr-3 ... cxr-n cxr-0 ). No matter how many slots were in the hunk, car was equivalent to (cxr 1 hunk) and cdr was equivalent to (cxr 0 hunk)`. This is a nice generalization of the basic idea of a cons cell, but modern Lisps offer other ways to structure data that are both possibly more useful and more readable: structures for a fixed collection of named slots, hash tables for a variable collection of named slots, and vectors for a collection of numbered slots.

After these historical blind alleys, it's interesting to think about why car and cdr still persist fifty years after McCarthy and Russell roamed the halls of MIT evangelising first and rest. Common Lisp does at least have first and rest as part of the standard. However, when I was taught Lisp in the mid-90's, I was encouraged to primarily favor the older car and cdr. I remember two primary reasons for this. The first was that existing code favored car and cdr, so it was important to be able to read code written in that style. The second reason was that first and rest impose a particular meaning on the fields of a cons cell that may or may not be appropriate. In the common case of a linear list, first and rest work rather well. If you call first on the list, you get the first element, if you call rest, you get the rest. In the case of a cons cell as a node of an association list, they work less well, unless, that is, you can figure out a reason why first makes sense as 'key', and rest makes sense as 'value'.

Some of this confusion stems from the fact that most Lisps, despite the name List Processing, don't have an official list data type. What they have instead is a two element cons cell and a set of conventions in the library, reader, and writer for using the to make linear lists. In a sense, this is a lot like strings in C. C doesn't have a string type, what it has instead is a pointer to character data (char *) and a set of library conventions for using blocks of memory as strings of characters. This laxness on the part of both languages comes with the advantages and disadvantages you'd expect from letting the deatils of an underlying implementation leak through. In the case of C 'strings', the representation lends itself both to things like Rob Pike's beautiful regex implementation in The Practice of Programming and a seemingly never ending series of buffer overrun attacks. In the case of Lisp cons cells, it provides both an incredibly flexible data structure, and confusion over such basic notions as the 'first', 'second', and 'rest' of a list.

If something as baroque as 'car' actually makes more sense than 'first' because 'first' doesn't match up well to underlying abstraction, it might them make sense to reconsider the underlying implementation. Some modern Lisps like Clojure do just that; A Clojure 'list' isn't a string of cons cells, but rather an instance of a JVM object that implements the interface ISeq:

public interface ISeq extends IPersistentCollection{
   Object first();
   ISeq rest();
   ISeq cons(Object o);

Clojure's user-visible first and rest functions ultimately call into their like-named methods in ISeq:

static public Object first(Object x){
   ISeq seq = seq(x);
   if(seq == null)
      return null;
   return seq.first();

// ...

static public ISeq rest(Object x){
   ISeq seq = seq(x);
   if(seq == null)
      return null;
   return seq.rest();

A noteworthy difference between this and a 'conventional' Lisp is the return type of rest: it's another ISeq, rather than a Object. Because of this, the 'CDR' of a Clojure cons cell has a new constraint: it is constrained to be another sequence, increasing greatly the likelihood that 'rest' really is 'the rest'. While this could be done even if rest returned an Object, constraining rest to be a sequence eliminates a number of edge cases in the language that arise when you allow the rest of a list to be something other than a list itself. This altered representation also fits in nicely with Clojure's host JVM: there's nothing that says ISeq has to be implemented by a two-element pointer. Indeed, Closure "also implements first and rest for vectors, strings, arrays, maps, Java Iterables, lazily calculated and infinite sequences etc." All these implementations of ISeq make it easier for Clojure sequences to interoperate with Java, and it makes it easier to build a sequence library that works on all kinds of sequences. What's lost with this choice is the ability to use a cons cell as an informal two-element structure. Even then, this style of first and rest could co-exist with implementations of car and cdr that work the 'old way'.

So in the end, maybe car and cdr are all right. They aren't the best names in the world, but they fit nicely the semantics of a unrestricted two-pointer cons cell. For those cases where you really are finding the first and rest of a list of cons cells, it is easy to use the first and rest functions in lieu of car and cdr. Then, for dialects like Clojure, your code is automatically portable to other sequence types. If you're using cons cells as a ad hoc structure, then you can either use car and cdr and accept those names as historical baggage of the second oldest major programming language, or investigate some of the other more modern ways of structuring data in Lisp programs.