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Lists


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In Lisp, a list looks like this: '(rose violet daisy buttercup). This list is preceded by a single apostrophe. It could just as well be written as follows, which looks more like the kind of list you are likely to be familiar with:


A D V E R T I S E M E N T

Lists are containers that supports sequential traversal. List is also a recursive data structure: its definition is recursive. As such, most of its traversal algorithms are recursive functions. In order to better understand a recursive abstract data type and prepare oneself to develop recursive operations on the data type, one should present the data type in terms of its constructors, selectors and recognizers.

Constructors are forms that create new instances of a data type (possibly out of some simpler components). A list is obtained by evaluating one of the following constructors:

  1. nil: Evaluating nil creates an empty list;
  2. (cons x L): Given a LISP object x and a list L, evaluating (cons x L) creates a list containing x followed by the elements in L.

Notice that the above definition is inherently recursive. For example, to construct a list containing 1 followed by 2, we could type in the expression:

USER(21): (cons 1 (cons 2 nil))
(1 2)
LISP replies by printing (1 2), which is a more readable representation of a list containing 1 followed by 2. To understand why the above works, notice that nil is a list (an empty one), and thus (cons 2 nil) is also a list (a list containing 1 followed by nothing). Applying the second constructor again, we see that (cons 1 (cons 2 nil)) is also a list (a list containing 1 followed by 2 followed by nothing).

Typing cons expressions could be tedious. If we already know all the elements in a list, we could enter our list as list literals. For example, to enter a list containing all prime numbers less than 20, we could type in the following expression:

USER(22): (quote (2 3 5 7 11 13 17 19))
(2 3 5 7 11 13 17 19)
Notice that we have quoted the list using the quote special form. This is necessary because, without the quote, LISP would interpret the expression (2 3 5 7 11 13 17 19) as a function call to a function with name "2" and arguments 3, 5, ..., 19 The quote is just a syntactic device that instructs LISP not to evaluate the a form in applicative order, but rather treat it as a literal. Since quoting is used frequently in LISP programs, there is a shorthand for quote:
USER(23): '(2 3 5 7 11 13 17 19)
(2 3 5 7 11 13 17 19)
The quote symbol ' is nothing but a syntactic shorthand for (quote ...).

The second ingredient of an abstract data type are its selectors. Given a composite object constructed out of several components, a selector form returns one of its components. Specifically, suppose a list L1 is constructed by evaluating (cons x L2), where x is a LISP object and L2 is a list. Then, the selector forms (first L1) and (rest L1) evaluate to x and L2 respectively, as the following examples illustrate:

Lists

USER(24): (first '(2 4 8))
2
USER(25): (rest '(2 4 8))
(4 8)
USER(26): (first (rest '(2 4 8)))
4
USER(27): (rest (rest '(2 4 8)))
(8)
USER(28): (rest (rest (rest '(8))))
NIL

Finally, we look at recognizers, expressions that test how an object is constructed. Corresponding to each constructor of a data type is a recognizer. In the case of list, they are null for nil and consp for cons. Given a list L, (null L) returns t iff L is nil, and (consp L) returns t iff L is constructed from cons.

USER(29): (null nil)
T
USER(30): (null '(1 2 3))
NIL
USER(31): (consp nil)
NIL
USER(32): (consp '(1 2 3))
T

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Keywords: Lisp string,lisp command,lisp comment,lisp manual,lisp programme,lisp function list,lisp object

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