CDR after the names of the functions used to access them. At the dawn of time, these names were mnemonic, at least to the folks implementing the first Lisp on an IBM 704. But even then they were just lifted from the assembly mnemonics used to implement the operations. However, it's not all bad that these names are somewhat meaningless—when considering individual cons cells, it's best to think of them simply as an arbitrary pair of values without any particular semantics. Thus:
(car (cons 1 2)) ==> 1
(cdr (cons 1 2)) ==> 2
Both CAR and CDR are also SETFable places—given an existing cons cell, it's possible to assign a new value to either of its values.[133]
(defparameter *cons* (cons 1 2))
*cons* ==> (1 . 2)
(setf (car *cons*) 10) ==> 10
*cons* ==> (10 . 2)
(setf (cdr *cons*) 20) ==> 20
*cons* ==> (10 . 20)
Because the values in a cons cell can be references to any kind of object, you can build larger structures out of cons cells by linking them together. Lists are built by linking together cons cells in a chain. The elements of the list are held in the CARs of the cons cells while the links to subsequent cons cells are held in the CDRs. The last cell in the chain has a CDR of NIL, which—as I mentioned in Chapter 4—represents the empty list as well as the boolean value false.
This arrangement is by no means unique to Lisp; it's called a
So when I say a particular value is a list, what I really mean is it's either NIL or a reference to a cons cell. The CAR of the cons cell is the first item of the list, and the CDR is a reference to another list, that is, another cons cell or NIL, containing the remaining elements. The Lisp printer understands this convention and prints such chains of cons cells as parenthesized lists rather than as dotted pairs.
(cons 1 nil) ==> (1)
(cons 1 (cons 2 nil)) ==> (1 2)
(cons 1 (cons 2 (cons 3 nil))) ==> (1 2 3)
When talking about structures built out of cons cells, a few diagrams can be a big help. Box-and-arrow diagrams represent cons cells as a pair of boxes like this:
The box on the left represents the CAR, and the box on the right is the CDR. The values stored in a particular cons cell are either drawn in the appropriate box or represented by an arrow from the box to a representation of the referenced value.[134] For instance, the list (1 2 3), which consists of three cons cells linked together by their CDRs, would be diagrammed like this:
However, most of the time you work with lists you won't have to deal with individual cons cells—the functions that create and manipulate lists take care of that for you. For example, the LIST function builds a cons cells under the covers for you and links them together; the following LIST expressions are equivalent to the previous CONS expressions:
(list 1) ==> (1)
(list 1 2) ==> (1 2)
(list 1 2 3) ==> (1 2 3)
Similarly, when you're thinking in terms of lists, you don't have to use the meaningless names CAR and CDR; FIRST and REST are synonyms for CAR and CDR that you should use when you're dealing with cons cells as lists.
(defparameter *list* (list 1 2 3 4))
(first *list*) ==> 1
(rest *list*) ==> (2 3 4)
(first (rest *list*)) ==> 2
Because cons cells can hold any kind of values, so can lists. And a single list can hold objects of different types.
(list 'foo' (list 1 2) 10) ==> ('foo' (1 2) 10)
The structure of that list would look like this:
Because lists can have other lists as elements, you can also use them to represent trees of arbitrary depth and complexity. As such, they make excellent representations for any heterogeneous, hierarchical data. Lisp-based XML processors, for instance, usually represent XML documents internally as lists. Another obvious example of tree-structured data is Lisp code itself. In Chapters 30 and 31 you'll write an HTML generation library that uses lists of lists to represent the HTML to be generated. I'll talk more next chapter about using cons cells to represent other data structures.
Common Lisp provides quite a large library of functions for manipulating lists. In the sections 'List- Manipulation Functions' and 'Mapping,' you'll look at some of the more important of these functions. However, they will be easier to understand in the context of a few ideas borrowed from functional programming.
The essence of functional programming is that programs are built entirely of functions with no side effects that compute their results based solely on the values of their arguments. The advantage of the functional style is that it makes programs easier to understand. Eliminating side effects eliminates almost all possibilities for action at a distance. And since the result of a function is determined only by the values of its arguments, its behavior is easier to understand and test. For instance, when you see an expression such as (+ 3 4), you know the result is uniquely determined by the definition of the + function and the values 3 and 4. You don't have to worry about what may have happened earlier in the execution of the program since there's nothing that can change the result of evaluating that expression.
Functions that deal with numbers are naturally functional since numbers are immutable. A list, on the other hand, can be mutated, as you've just seen, by SETFing the CARs and CDRs of the cons cells that make up its backbone. However, lists can be treated as a functional data type if you consider their value to be determined by the elements they contain. Thus, any list of the form (1 2 3 4) is functionally equivalent to any other list containing those four values, regardless of what cons cells are actually used to represent the list. And any function that takes a list as an argument and returns a value based solely on the contents of the list can likewise be considered functional. For instance, the REVERSE sequence function, given the list (1 2 3 4), always returns a list (4 3 2 1). Different calls to REVERSE with functionally equivalent lists as the argument will return functionally equivalent result lists. Another aspect of functional programming, which I'll discuss in the section 'Mapping,' is the use of higher-order functions: functions that treat other functions as data, taking them as arguments or returning them as results.
