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5. Lists

A list represents a sequence of zero or more elements (which may be any Lisp objects). The important difference between lists and vectors is that two or more lists can share part of their structure; in addition, you can insert or delete elements in a list without copying the whole list.

5.1 Lists and Cons Cells  How lists are made out of cons cells.
5.2 Lists as Linked Pairs of Boxes  Graphical notation to explain lists.
5.3 Predicates on Lists  Is this object a list? Comparing two lists.
5.4 Accessing Elements of Lists  Extracting the pieces of a list.
5.5 Building Cons Cells and Lists  Creating list structure.
5.6 Modifying Existing List Structure  Storing new pieces into an existing list.
5.7 Using Lists as Sets  A list can represent a finite mathematical set.
5.8 Association Lists  A list can represent a finite relation or mapping.

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5.1 Lists and Cons Cells

Lists in Lisp are not a primitive data type; they are built up from cons cells. A cons cell is a data object that represents an ordered pair. That is, it has two slots, and each slot holds, or refers to, some Lisp object. One slot is known as the CAR, and the other is known as the CDR. (These names are traditional; see 2.3.6 Cons Cell and List Types.) CDR is pronounced "could-er."

We say that "the CAR of this cons cell is" whatever object its CAR slot currently holds, and likewise for the CDR.

A list is a series of cons cells "chained together," so that each cell refers to the next one. There is one cons cell for each element of the list. By convention, the CARs of the cons cells hold the elements of the list, and the CDRs are used to chain the list: the CDR slot of each cons cell refers to the following cons cell. The CDR of the last cons cell is nil. This asymmetry between the CAR and the CDR is entirely a matter of convention; at the level of cons cells, the CAR and CDR slots have the same characteristics.

Because most cons cells are used as part of lists, the phrase list structure has come to mean any structure made out of cons cells.

The symbol nil is considered a list as well as a symbol; it is the list with no elements. For convenience, the symbol nil is considered to have nil as its CDR (and also as its CAR).

The CDR of any nonempty list l is a list containing all the elements of l except the first.

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5.2 Lists as Linked Pairs of Boxes

A cons cell can be illustrated as a pair of boxes. The first box represents the CAR and the second box represents the CDR. Here is an illustration of the two-element list, (tulip lily), made from two cons cells:

 
 ---------------         ---------------
| car   | cdr   |       | car   | cdr   |
| tulip |   o---------->| lily  |  nil  |
|       |       |       |       |       |
 ---------------         ---------------

Each pair of boxes represents a cons cell. Each box "refers to", "points to" or "holds" a Lisp object. (These terms are synonymous.) The first box, which describes the CAR of the first cons cell, contains the symbol tulip. The arrow from the CDR box of the first cons cell to the second cons cell indicates that the CDR of the first cons cell is the second cons cell.

The same list can be illustrated in a different sort of box notation like this:

 
    --- ---      --- ---
   |   |   |--> |   |   |--> nil
    --- ---      --- ---
     |            |
     |            |
      --> tulip    --> lily

Here is a more complex illustration, showing the three-element list, ((pine needles) oak maple), the first element of which is a two-element list:

 
    --- ---      --- ---      --- ---
   |   |   |--> |   |   |--> |   |   |--> nil
    --- ---      --- ---      --- ---
     |            |            |
     |            |            |
     |             --> oak      --> maple
     |
     |     --- ---      --- ---
      --> |   |   |--> |   |   |--> nil
           --- ---      --- ---
            |            |
            |            |
             --> pine     --> needles

The same list represented in the first box notation looks like this:

 
 --------------       --------------       --------------
| car   | cdr  |     | car   | cdr  |     | car   | cdr  |
|   o   |   o------->| oak   |   o------->| maple |  nil |
|   |   |      |     |       |      |     |       |      |
 -- | ---------       --------------       --------------
    |
    |
    |        --------------       ----------------
    |       | car   | cdr  |     | car     | cdr  |
     ------>| pine  |   o------->| needles |  nil |
            |       |      |     |         |      |
             --------------       ----------------

See section 2.3.6 Cons Cell and List Types, for the read and print syntax of cons cells and lists, and for more "box and arrow" illustrations of lists.

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5.3 Predicates on Lists

The following predicates test whether a Lisp object is an atom, is a cons cell or is a list, or whether it is the distinguished object nil. (Many of these predicates can be defined in terms of the others, but they are used so often that it is worth having all of them.)

Function: consp object
This function returns t if object is a cons cell, nil otherwise. nil is not a cons cell, although it is a list.

Function: atom object
This function returns t if object is an atom, nil otherwise. All objects except cons cells are atoms. The symbol nil is an atom and is also a list; it is the only Lisp object that is both.

 
(atom object) == (not (consp object))

Function: listp object
This function returns t if object is a cons cell or nil. Otherwise, it returns nil.

 
(listp '(1))
     => t
(listp '())
     => t

Function: nlistp object
This function is the opposite of listp: it returns t if object is not a list. Otherwise, it returns nil.

 
(listp object) == (not (nlistp object))

Function: null object
This function returns t if object is nil, and returns nil otherwise. This function is identical to not, but as a matter of clarity we use null when object is considered a list and not when it is considered a truth value (see not in 10.3 Constructs for Combining Conditions).

 
(null '(1))
     => nil
(null '())
     => t

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5.4 Accessing Elements of Lists

Function: car cons-cell
This function returns the value referred to by the first slot of the cons cell cons-cell. Expressed another way, this function returns the CAR of cons-cell.

As a special case, if cons-cell is nil, then car is defined to return nil; therefore, any list is a valid argument for car. An error is signaled if the argument is not a cons cell or nil.

 
(car '(a b c))
     => a
(car '())
     => nil

Function: cdr cons-cell
This function returns the value referred to by the second slot of the cons cell cons-cell. Expressed another way, this function returns the CDR of cons-cell.

As a special case, if cons-cell is nil, then cdr is defined to return nil; therefore, any list is a valid argument for cdr. An error is signaled if the argument is not a cons cell or nil.

 
(cdr '(a b c))
     => (b c)
(cdr '())
     => nil

Function: car-safe object
This function lets you take the CAR of a cons cell while avoiding errors for other data types. It returns the CAR of object if object is a cons cell, nil otherwise. This is in contrast to car, which signals an error if object is not a list.

 
(car-safe object)
==
(let ((x object))
  (if (consp x)
      (car x)
    nil))

Function: cdr-safe object
This function lets you take the CDR of a cons cell while avoiding errors for other data types. It returns the CDR of object if object is a cons cell, nil otherwise. This is in contrast to cdr, which signals an error if object is not a list.

 
(cdr-safe object)
==
(let ((x object))
  (if (consp x)
      (cdr x)
    nil))

Macro: pop listname
This macro is a way of examining the CAR of a list, and taking it off the list, all at once. It is new in Emacs 21.

It operates on the list which is stored in the symbol listname. It removes this element from the list by setting listname to the CDR of its old value--but it also returns the CAR of that list, which is the element being removed.

 
x
     => (a b c)
(pop x)
     => a
x
     => (b c)

Function: nth n list
This function returns the nth element of list. Elements are numbered starting with zero, so the CAR of list is element number zero. If the length of list is n or less, the value is nil.

If n is negative, nth returns the first element of list.

 
(nth 2 '(1 2 3 4))
     => 3
(nth 10 '(1 2 3 4))
     => nil
(nth -3 '(1 2 3 4))
     => 1

(nth n x) == (car (nthcdr n x))

The function elt is similar, but applies to any kind of sequence. For historical reasons, it takes its arguments in the opposite order. See section 6.1 Sequences.

Function: nthcdr n list
This function returns the nth CDR of list. In other words, it skips past the first n links of list and returns what follows.

If n is zero or negative, nthcdr returns all of list. If the length of list is n or less, nthcdr returns nil.

 
(nthcdr 1 '(1 2 3 4))
     => (2 3 4)
(nthcdr 10 '(1 2 3 4))
     => nil
(nthcdr -3 '(1 2 3 4))
     => (1 2 3 4)

Function: last list &optional n
This function returns the last link of list. The car of this link is the list's last element. If list is null, nil is returned. If n is non-nil the n-th-to-last link is returned instead, or the whole list if n is bigger than list's length.

Function: safe-length list
This function returns the length of list, with no risk of either an error or an infinite loop.

If list is not really a list, safe-length returns 0. If list is circular, it returns a finite value which is at least the number of distinct elements.

The most common way to compute the length of a list, when you are not worried that it may be circular, is with length. See section 6.1 Sequences.

Function: caar cons-cell
This is the same as (car (car cons-cell)).

Function: cadr cons-cell
This is the same as (car (cdr cons-cell)) or (nth 1 cons-cell).

Function: cdar cons-cell
This is the same as (cdr (car cons-cell)).

Function: cddr cons-cell
This is the same as (cdr (cdr cons-cell)) or (nthcdr 2 cons-cell).

Function: butlast x &optional n
This function returns the list x with the last element, or the last n elements, removed. If n is greater than zero it makes a copy of the list so as not to damage the original list. In general, (append (butlast x n) (last x n)) will return a list equal to x.

Function: nbutlast x &optional n
This is a version of butlast that works by destructively modifying the cdr of the appropriate element, rather than making a copy of the list.

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5.5 Building Cons Cells and Lists

Many functions build lists, as lists reside at the very heart of Lisp. cons is the fundamental list-building function; however, it is interesting to note that list is used more times in the source code for Emacs than cons.

Function: cons object1 object2
This function is the fundamental function used to build new list structure. It creates a new cons cell, making object1 the CAR, and object2 the CDR. It then returns the new cons cell. The arguments object1 and object2 may be any Lisp objects, but most often object2 is a list.

 
(cons 1 '(2))
     => (1 2)
(cons 1 '())
     => (1)
(cons 1 2)
     => (1 . 2)

cons is often used to add a single element to the front of a list. This is called consing the element onto the list. (1) For example:

 
(setq list (cons newelt list))

Note that there is no conflict between the variable named list used in this example and the function named list described below; any symbol can serve both purposes.

Macro: push newelt listname
This macro provides an alternative way to write (setq listname (cons newelt listname)). It is new in Emacs 21.

 
(setq l '(a b)) 
     => (a b)
(push 'c l)
     => (c a b)
l
     => (c a b)

Function: list &rest objects
This function creates a list with objects as its elements. The resulting list is always nil-terminated. If no objects are given, the empty list is returned.

 
(list 1 2 3 4 5)
     => (1 2 3 4 5)
(list 1 2 '(3 4 5) 'foo)
     => (1 2 (3 4 5) foo)
(list)
     => nil

Function: make-list length object
This function creates a list of length elements, in which each element is object. Compare make-list with make-string (see section 4.3 Creating Strings).

 
(make-list 3 'pigs)
     => (pigs pigs pigs)
(make-list 0 'pigs)
     => nil
(setq l (make-list 3 '(a b))
     => ((a b) (a b) (a b))
(eq (car l) (cadr l))
     => t

Function: append &rest sequences
This function returns a list containing all the elements of sequences. The sequences may be lists, vectors, bool-vectors, or strings, but the last one should usually be a list. All arguments except the last one are copied, so none of the arguments is altered. (See nconc in 5.6.3 Functions that Rearrange Lists, for a way to join lists with no copying.)

More generally, the final argument to append may be any Lisp object. The final argument is not copied or converted; it becomes the CDR of the last cons cell in the new list. If the final argument is itself a list, then its elements become in effect elements of the result list. If the final element is not a list, the result is a "dotted list" since its final CDR is not nil as required in a true list.

The append function also allows integers as arguments. It converts them to strings of digits, making up the decimal print representation of the integer, and then uses the strings instead of the original integers. Don't use this feature; we plan to eliminate it. If you already use this feature, change your programs now! The proper way to convert an integer to a decimal number in this way is with format (see section 4.7 Formatting Strings) or number-to-string (see section 4.6 Conversion of Characters and Strings).

Here is an example of using append:

 
(setq trees '(pine oak))
     => (pine oak)
(setq more-trees (append '(maple birch) trees))
     => (maple birch pine oak)

trees
     => (pine oak)
more-trees
     => (maple birch pine oak)
(eq trees (cdr (cdr more-trees)))
     => t

You can see how append works by looking at a box diagram. The variable trees is set to the list (pine oak) and then the variable more-trees is set to the list (maple birch pine oak). However, the variable trees continues to refer to the original list:

 
more-trees                trees
|                           |
|     --- ---      --- ---   -> --- ---      --- ---
 --> |   |   |--> |   |   |--> |   |   |--> |   |   |--> nil
      --- ---      --- ---      --- ---      --- ---
       |            |            |            |
       |            |            |            |
        --> maple    -->birch     --> pine     --> oak

An empty sequence contributes nothing to the value returned by append. As a consequence of this, a final nil argument forces a copy of the previous argument:

 
trees
     => (pine oak)
(setq wood (append trees nil))
     => (pine oak)
wood
     => (pine oak)
(eq wood trees)
     => nil

This once was the usual way to copy a list, before the function copy-sequence was invented. See section 6. Sequences, Arrays, and Vectors.

Here we show the use of vectors and strings as arguments to append:

 
(append [a b] "cd" nil)
     => (a b 99 100)

With the help of apply (see section 12.5 Calling Functions), we can append all the lists in a list of lists:

 
(apply 'append '((a b c) nil (x y z) nil))
     => (a b c x y z)

If no sequences are given, nil is returned:

 
(append)
     => nil

Here are some examples where the final argument is not a list:

 
(append '(x y) 'z)
     => (x y . z)
(append '(x y) [z])
     => (x y . [z])

The second example shows that when the final argument is a sequence but not a list, the sequence's elements do not become elements of the resulting list. Instead, the sequence becomes the final CDR, like any other non-list final argument.

Function: reverse list
This function creates a new list whose elements are the elements of list, but in reverse order. The original argument list is not altered.

 
(setq x '(1 2 3 4))
     => (1 2 3 4)
(reverse x)
     => (4 3 2 1)
x
     => (1 2 3 4)

Function: remq object list
This function returns a copy of list, with all elements removed which are eq to object. The letter `q' in remq says that it uses eq to compare object against the elements of list.

 
(setq sample-list '(a b c a b c))
     => (a b c a b c)
(remq 'a sample-list)
     => (b c b c)
sample-list
     => (a b c a b c)
The function delq offers a way to perform this operation destructively. See 5.7 Using Lists as Sets.

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5.6 Modifying Existing List Structure

You can modify the CAR and CDR contents of a cons cell with the primitives setcar and setcdr. We call these "destructive" operations because they change existing list structure.

Common Lisp note: Common Lisp uses functions rplaca and rplacd to alter list structure; they change structure the same way as setcar and setcdr, but the Common Lisp functions return the cons cell while setcar and setcdr return the new CAR or CDR.

5.6.1 Altering List Elements with setcar  Replacing an element in a list.
5.6.2 Altering the CDR of a List  Replacing part of the list backbone. This can be used to remove or add elements.
5.6.3 Functions that Rearrange Lists  Reordering the elements in a list; combining lists.

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5.6.1 Altering List Elements with setcar

Changing the CAR of a cons cell is done with setcar. When used on a list, setcar replaces one element of a list with a different element.

Function: setcar cons object
This function stores object as the new CAR of cons, replacing its previous CAR. In other words, it changes the CAR slot of cons to refer to object. It returns the value object. For example:

 
(setq x '(1 2))
     => (1 2)
(setcar x 4)
     => 4
x
     => (4 2)

When a cons cell is part of the shared structure of several lists, storing a new CAR into the cons changes one element of each of these lists. Here is an example:

 
;; Create two lists that are partly shared.
(setq x1 '(a b c))
     => (a b c)
(setq x2 (cons 'z (cdr x1)))
     => (z b c)

;; Replace the CAR of a shared link.
(setcar (cdr x1) 'foo)
     => foo
x1                           ; Both lists are changed.
     => (a foo c)
x2
     => (z foo c)

;; Replace the CAR of a link that is not shared.
(setcar x1 'baz)
     => baz
x1                           ; Only one list is changed.
     => (baz foo c)
x2
     => (z foo c)

Here is a graphical depiction of the shared structure of the two lists in the variables x1 and x2, showing why replacing b changes them both:

 
        --- ---        --- ---      --- ---
x1---> |   |   |----> |   |   |--> |   |   |--> nil
        --- ---        --- ---      --- ---
         |        -->   |            |
         |       |      |            |
          --> a  |       --> b        --> c
                 |
       --- ---   |
x2--> |   |   |--
       --- ---
        |
        |
         --> z

Here is an alternative form of box diagram, showing the same relationship:

 
x1:
 --------------       --------------       --------------
| car   | cdr  |     | car   | cdr  |     | car   | cdr  |
|   a   |   o------->|   b   |   o------->|   c   |  nil |
|       |      |  -->|       |      |     |       |      |
 --------------  |    --------------       --------------
                 |
x2:              |
 --------------  |
| car   | cdr  | |
|   z   |   o----
|       |      |
 --------------

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5.6.2 Altering the CDR of a List

The lowest-level primitive for modifying a CDR is setcdr:

Function: setcdr cons object
This function stores object as the new CDR of cons, replacing its previous CDR. In other words, it changes the CDR slot of cons to refer to object. It returns the value object.

Here is an example of replacing the CDR of a list with a different list. All but the first element of the list are removed in favor of a different sequence of elements. The first element is unchanged, because it resides in the CAR of the list, and is not reached via the CDR.

 
(setq x '(1 2 3))
     => (1 2 3)
(setcdr x '(4))
     => (4)
x
     => (1 4)

You can delete elements from the middle of a list by altering the CDRs of the cons cells in the list. For example, here we delete the second element, b, from the list (a b c), by changing the CDR of the first cons cell:

 
(setq x1 '(a b c))
     => (a b c)
(setcdr x1 (cdr (cdr x1)))
     => (c)
x1
     => (a c)

Here is the result in box notation:

 
                   --------------------
                  |                    |
 --------------   |   --------------   |    --------------
| car   | cdr  |  |  | car   | cdr  |   -->| car   | cdr  |
|   a   |   o-----   |   b   |   o-------->|   c   |  nil |
|       |      |     |       |      |      |       |      |
 --------------       --------------        --------------

The second cons cell, which previously held the element b, still exists and its CAR is still b, but it no longer forms part of this list.

It is equally easy to insert a new element by changing CDRs:

 
(setq x1 '(a b c))
     => (a b c)
(setcdr x1 (cons 'd (cdr x1)))
     => (d b c)
x1
     => (a d b c)

Here is this result in box notation:

 
 --------------        -------------       -------------
| car  | cdr   |      | car  | cdr  |     | car  | cdr  |
|   a  |   o   |   -->|   b  |   o------->|   c  |  nil |
|      |   |   |  |   |      |      |     |      |      |
 --------- | --   |    -------------       -------------
           |      |
     -----         --------
    |                      |
    |    ---------------   |
    |   | car   | cdr   |  |
     -->|   d   |   o------
        |       |       |
         ---------------

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5.6.3 Functions that Rearrange Lists

Here are some functions that rearrange lists "destructively" by modifying the CDRs of their component cons cells. We call these functions "destructive" because they chew up the original lists passed to them as arguments, relinking their cons cells to form a new list that is the returned value.

See delq, in 5.7 Using Lists as Sets, for another function that modifies cons cells.

Function: nconc &rest lists
This function returns a list containing all the elements of lists. Unlike append (see section 5.5 Building Cons Cells and Lists), the lists are not copied. Instead, the last CDR of each of the lists is changed to refer to the following list. The last of the lists is not altered. For example:

 
(setq x '(1 2 3))
     => (1 2 3)
(nconc x '(4 5))
     => (1 2 3 4 5)
x
     => (1 2 3 4 5)

Since the last argument of nconc is not itself modified, it is reasonable to use a constant list, such as '(4 5), as in the above example. For the same reason, the last argument need not be a list:

 
(setq x '(1 2 3))
     => (1 2 3)
(nconc x 'z)
     => (1 2 3 . z)
x
     => (1 2 3 . z)

However, the other arguments (all but the last) must be lists.

A common pitfall is to use a quoted constant list as a non-last argument to nconc. If you do this, your program will change each time you run it! Here is what happens:

 
(defun add-foo (x)            ; We want this function to add
  (nconc '(foo) x))           ;   foo to the front of its arg.

(symbol-function 'add-foo)
     => (lambda (x) (nconc (quote (foo)) x))

(setq xx (add-foo '(1 2)))    ; It seems to work.
     => (foo 1 2)
(setq xy (add-foo '(3 4)))    ; What happened?
     => (foo 1 2 3 4)
(eq xx xy)
     => t

(symbol-function 'add-foo)
     => (lambda (x) (nconc (quote (foo 1 2 3 4) x)))

Function: nreverse list
This function reverses the order of the elements of list. Unlike reverse, nreverse alters its argument by reversing the CDRs in the cons cells forming the list. The cons cell that used to be the last one in list becomes the first cons cell of the value.

For example:

 
(setq x '(a b c))
     => (a b c)
x
     => (a b c)
(nreverse x)
     => (c b a)
;; The cons cell that was first is now last.
x
     => (a)

To avoid confusion, we usually store the result of nreverse back in the same variable which held the original list:

 
(setq x (nreverse x))

Here is the nreverse of our favorite example, (a b c), presented graphically:

 
Original list head:                       Reversed list:
 -------------        -------------        ------------
| car  | cdr  |      | car  | cdr  |      | car | cdr  |
|   a  |  nil |<--   |   b  |   o  |<--   |   c |   o  |
|      |      |   |  |      |   |  |   |  |     |   |  |
 -------------    |   --------- | -    |   -------- | -
                  |             |      |            |
                   -------------        ------------

Function: sort list predicate
This function sorts list stably, though destructively, and returns the sorted list. It compares elements using predicate. A stable sort is one in which elements with equal sort keys maintain their relative order before and after the sort. Stability is important when successive sorts are used to order elements according to different criteria.

The argument predicate must be a function that accepts two arguments. It is called with two elements of list. To get an increasing order sort, the predicate should return t if the first element is "less than" the second, or nil if not.

The comparison function predicate must give reliable results for any given pair of arguments, at least within a single call to sort. It must be antisymmetric; that is, if a is less than b, b must not be less than a. It must be transitive---that is, if a is less than b, and b is less than c, then a must be less than c. If you use a comparison function which does not meet these requirements, the result of sort is unpredictable.

The destructive aspect of sort is that it rearranges the cons cells forming list by changing CDRs. A nondestructive sort function would create new cons cells to store the elements in their sorted order. If you wish to make a sorted copy without destroying the original, copy it first with copy-sequence and then sort.

Sorting does not change the CARs of the cons cells in list; the cons cell that originally contained the element a in list still has a in its CAR after sorting, but it now appears in a different position in the list due to the change of CDRs. For example:

 
(setq nums '(1 3 2 6 5 4 0))
     => (1 3 2 6 5 4 0)
(sort nums '<)
     => (0 1 2 3 4 5 6)
nums
     => (1 2 3 4 5 6)

Warning: Note that the list in nums no longer contains 0; this is the same cons cell that it was before, but it is no longer the first one in the list. Don't assume a variable that formerly held the argument now holds the entire sorted list! Instead, save the result of sort and use that. Most often we store the result back into the variable that held the original list:

 
(setq nums (sort nums '<))

See section 32.15 Sorting Text, for more functions that perform sorting. See documentation in 24.2 Access to Documentation Strings, for a useful example of sort.

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5.7 Using Lists as Sets

A list can represent an unordered mathematical set--simply consider a value an element of a set if it appears in the list, and ignore the order of the list. To form the union of two sets, use append (as long as you don't mind having duplicate elements). Other useful functions for sets include memq and delq, and their equal versions, member and delete.

Common Lisp note: Common Lisp has functions union (which avoids duplicate elements) and intersection for set operations, but GNU Emacs Lisp does not have them. You can write them in Lisp if you wish.

Function: memq object list
This function tests to see whether object is a member of list. If it is, memq returns a list starting with the first occurrence of object. Otherwise, it returns nil. The letter `q' in memq says that it uses eq to compare object against the elements of the list. For example:

 
(memq 'b '(a b c b a))
     => (b c b a)
(memq '(2) '((1) (2)))    ; (2) and (2) are not eq.
     => nil

Function: member-ignore-case object list
This function is like member, except that it ignores differences in letter-case and text representation: upper-case and lower-case letters are treated as equal, and unibyte strings are converted to multibyte prior to comparison.

Function: delq object list
This function destructively removes all elements eq to object from list. The letter `q' in delq says that it uses eq to compare object against the elements of the list, like memq and remq.

When delq deletes elements from the front of the list, it does so simply by advancing down the list and returning a sublist that starts after those elements:

 
(delq 'a '(a b c)) == (cdr '(a b c))

When an element to be deleted appears in the middle of the list, removing it involves changing the CDRs (see section 5.6.2 Altering the CDR of a List).

 
(setq sample-list '(a b c (4)))
     => (a b c (4))
(delq 'a sample-list)
     => (b c (4))
sample-list
     => (a b c (4))
(delq 'c sample-list)
     => (a b (4))
sample-list
     => (a b (4))

Note that (delq 'c sample-list) modifies sample-list to splice out the third element, but (delq 'a sample-list) does not splice anything--it just returns a shorter list. Don't assume that a variable which formerly held the argument list now has fewer elements, or that it still holds the original list! Instead, save the result of delq and use that. Most often we store the result back into the variable that held the original list:

 
(setq flowers (delq 'rose flowers))

In the following example, the (4) that delq attempts to match and the (4) in the sample-list are not eq:

 
(delq '(4) sample-list)
     => (a c (4))

The following two functions are like memq and delq but use equal rather than eq to compare elements. See section 2.7 Equality Predicates.

Function: member object list
The function member tests to see whether object is a member of list, comparing members with object using equal. If object is a member, member returns a list starting with its first occurrence in list. Otherwise, it returns nil.

Compare this with memq:

 
(member '(2) '((1) (2)))  ; (2) and (2) are equal.
     => ((2))
(memq '(2) '((1) (2)))    ; (2) and (2) are not eq.
     => nil
;; Two strings with the same contents are equal.
(member "foo" '("foo" "bar"))
     => ("foo" "bar")

Function: delete object sequence
If sequence is a list, this function destructively removes all elements equal to object from sequence. For lists, delete is to delq as member is to memq: it uses equal to compare elements with object, like member; when it finds an element that matches, it removes the element just as delq would.

If sequence is a vector or string, delete returns a copy of sequence with all elements equal to object removed.

For example:

 
(delete '(2) '((2) (1) (2)))
     => ((1))
(delete '(2) [(2) (1) (2)])
     => [(1)]

Function: remove object sequence
This function is the non-destructive counterpart of delete. If returns a copy of sequence, a list, vector, or string, with elements equal to object removed. For example:

 
(remove '(2) '((2) (1) (2)))
     => ((1))
(remove '(2) [(2) (1) (2)])
     => [(1)]

Common Lisp note: The functions member, delete and remove in GNU Emacs Lisp are derived from Maclisp, not Common Lisp. The Common Lisp versions do not use equal to compare elements.

See also the function add-to-list, in 11.8 How to Alter a Variable Value, for another way to add an element to a list stored in a variable.

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5.8 Association Lists

An association list, or alist for short, records a mapping from keys to values. It is a list of cons cells called associations: the CAR of each cons cell is the key, and the CDR is the associated value.(2)

Here is an example of an alist. The key pine is associated with the value cones; the key oak is associated with acorns; and the key maple is associated with seeds.

 
((pine . cones)
 (oak . acorns)
 (maple . seeds))

The associated values in an alist may be any Lisp objects; so may the keys. For example, in the following alist, the symbol a is associated with the number 1, and the string "b" is associated with the list (2 3), which is the CDR of the alist element:

 
((a . 1) ("b" 2 3))

Sometimes it is better to design an alist to store the associated value in the CAR of the CDR of the element. Here is an example of such an alist:

 
((rose red) (lily white) (buttercup yellow))

Here we regard red as the value associated with rose. One advantage of this kind of alist is that you can store other related information--even a list of other items--in the CDR of the CDR. One disadvantage is that you cannot use rassq (see below) to find the element containing a given value. When neither of these considerations is important, the choice is a matter of taste, as long as you are consistent about it for any given alist.

Note that the same alist shown above could be regarded as having the associated value in the CDR of the element; the value associated with rose would be the list (red).

Association lists are often used to record information that you might otherwise keep on a stack, since new associations may be added easily to the front of the list. When searching an association list for an association with a given key, the first one found is returned, if there is more than one.

In Emacs Lisp, it is not an error if an element of an association list is not a cons cell. The alist search functions simply ignore such elements. Many other versions of Lisp signal errors in such cases.

Note that property lists are similar to association lists in several respects. A property list behaves like an association list in which each key can occur only once. See section 8.4 Property Lists, for a comparison of property lists and association lists.

Function: assoc key alist
This function returns the first association for key in alist. It compares key against the alist elements using equal (see section 2.7 Equality Predicates). It returns nil if no association in alist has a CAR equal to key. For example:

 
(setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
     => ((pine . cones) (oak . acorns) (maple . seeds))
(assoc 'oak trees)
     => (oak . acorns)
(cdr (assoc 'oak trees))
     => acorns
(assoc 'birch trees)
     => nil

Here is another example, in which the keys and values are not symbols:

 
(setq needles-per-cluster
      '((2 "Austrian Pine" "Red Pine")
        (3 "Pitch Pine")
        (5 "White Pine")))

(cdr (assoc 3 needles-per-cluster))
     => ("Pitch Pine")
(cdr (assoc 2 needles-per-cluster))
     => ("Austrian Pine" "Red Pine")

The functions assoc-ignore-representation and assoc-ignore-case are much like assoc except using compare-strings to do the comparison. See section 4.5 Comparison of Characters and Strings.

Function: rassoc value alist
This function returns the first association with value value in alist. It returns nil if no association in alist has a CDR equal to value.

rassoc is like assoc except that it compares the CDR of each alist association instead of the CAR. You can think of this as "reverse assoc", finding the key for a given value.

Function: assq key alist
This function is like assoc in that it returns the first association for key in alist, but it makes the comparison using eq instead of equal. assq returns nil if no association in alist has a CAR eq to key. This function is used more often than assoc, since eq is faster than equal and most alists use symbols as keys. See section 2.7 Equality Predicates.

 
(setq trees '((pine . cones) (oak . acorns) (maple . seeds)))
     => ((pine . cones) (oak . acorns) (maple . seeds))
(assq 'pine trees)
     => (pine . cones)

On the other hand, assq is not usually useful in alists where the keys may not be symbols:

 
(setq leaves
      '(("simple leaves" . oak)
        ("compound leaves" . horsechestnut)))

(assq "simple leaves" leaves)
     => nil
(assoc "simple leaves" leaves)
     => ("simple leaves" . oak)

Function: rassq value alist
This function returns the first association with value value in alist. It returns nil if no association in alist has a CDR eq to value.

rassq is like assq except that it compares the CDR of each alist association instead of the CAR. You can think of this as "reverse assq", finding the key for a given value.

For example:

 
(setq trees '((pine . cones) (oak . acorns) (maple . seeds)))

(rassq 'acorns trees)
     => (oak . acorns)
(rassq 'spores trees)
     => nil

Note that rassq cannot search for a value stored in the CAR of the CDR of an element:

 
(setq colors '((rose red) (lily white) (buttercup yellow)))

(rassq 'white colors)
     => nil

In this case, the CDR of the association (lily white) is not the symbol white, but rather the list (white). This becomes clearer if the association is written in dotted pair notation:

 
(lily white) == (lily . (white))

Function: assoc-default key alist &optional test default
This function searches alist for a match for key. For each element of alist, it compares the element (if it is an atom) or the element's CAR (if it is a cons) against key, by calling test with two arguments: the element or its CAR, and key. The arguments are passed in that order so that you can get useful results using string-match with an alist that contains regular expressions (see section 34.3 Regular Expression Searching). If test is omitted or nil, equal is used for comparison.

If an alist element matches key by this criterion, then assoc-default returns a value based on this element. If the element is a cons, then the value is the element's CDR. Otherwise, the return value is default.

If no alist element matches key, assoc-default returns nil.

Function: copy-alist alist
This function returns a two-level deep copy of alist: it creates a new copy of each association, so that you can alter the associations of the new alist without changing the old one.

 
(setq needles-per-cluster
      '((2 . ("Austrian Pine" "Red Pine"))
        (3 . ("Pitch Pine"))
        (5 . ("White Pine"))))
=>
((2 "Austrian Pine" "Red Pine")
 (3 "Pitch Pine")
 (5 "White Pine"))

(setq copy (copy-alist needles-per-cluster))
=>
((2 "Austrian Pine" "Red Pine")
 (3 "Pitch Pine")
 (5 "White Pine"))

(eq needles-per-cluster copy)
     => nil
(equal needles-per-cluster copy)
     => t
(eq (car needles-per-cluster) (car copy))
     => nil
(cdr (car (cdr needles-per-cluster)))
     => ("Pitch Pine")
(eq (cdr (car (cdr needles-per-cluster)))
    (cdr (car (cdr copy))))
     => t

This example shows how copy-alist makes it possible to change the associations of one copy without affecting the other:

 
(setcdr (assq 3 copy) '("Martian Vacuum Pine"))
(cdr (assq 3 needles-per-cluster))
     => ("Pitch Pine")

Function: assq-delete-all key alist
This function deletes from alist all the elements whose CAR is eq to key. It returns alist, modified in this way. Note that it modifies the original list structure of alist.

 
(assq-delete-all 'foo
                 '((foo 1) (bar 2) (foo 3) (lose 4)))
     => ((bar 2) (lose 4))

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