Association Lists

Summary: We consider a number of Scheme procedures that can be used to look up information.

Contents:

• Introduction
• Representing Database Tables
• assoc, Scheme's Built-in Lookup Procedure
• Extracting Information
• Looking Up a Telephone Number, Revised
• Using More Complex Records
• Implementing assoc
• Using Other Keys
• Related Procedures

Procedures covered in this reading:

• (assoc key alist)
• (assq key alist)
• (assv key alist)

Introduction

Consider the organization of a simple telephone directory for on-campus telephones: a sequence of entries, each consisting of a name and a four-digit telephone number. In Scheme, it is natural to use strings for names; it turns out that telephone numbers should also be represented as strings, since string operations make a useful kind of sense when applied to telephone numbers and integer operations do not. (For instance, (string-append "269-" extension) does something useful if the value of extension is a string, but not if it is an integer.)

Representing Database Tables

To represent each individual entry in a telephone directory, we can use a list, such as ("Henry Walker" "4208"), ("John Stone" "3181"), or ("Sam Rebelsky" "4410"), with the name as the car of the entry and a list of the telephone number as the cadr. An entire directory, then, would be a list of such entries:

;;; Value:
;;;   science-chairs-directory
;;; Type:
;;;   List of lists.
;;;   Each sublist is of length two and contains a name and a phone number.
;;;   Both of those values are strings.
;;; Contents:
;;;   A list of the department and division chairs in the Science division 
;;;   in academic year 2002-2003.
(define science-chairs-directory
  (list (list "Mark Schneider" "3018")
        (list "Jackie Brown" "3096")
        (list "Martin Minelli" "3007")
        (list "Gene Herman" "4202")
        (list "Charles Cunningham" "3182")
        (list "Ann Ellis" "4865")))

In Scheme, a list of pairs or lists is called an association list or alist.

As the telephone-directory example illustrates, a particularly common application of association lists involves looking for a desired name or first component of a pair and retrieving the second component of a pair. Thus, the first component of each pair (the car of a pair) often is called a key, and the cdr of the pair is its associated data or value. For example, in the above illustration, "Martin Minelli", "Gene Herman", and "Ann Ellis" are some of the keys, and the lists that contain only telephone numbers are the associated data. Thus an association list is a simple way to implement a small table in a database.

assoc, Scheme's Built-in Lookup Procedure

Since such applications are very common, Scheme provides procedures to retrieve from an association list the pair containing a specified key. The most frequently used procedure of this kind is assoc. Given a key and association list, assoc returns the first pair with the given key. If the key does not occur in the association list, then assoc returns #f. For example,

> (assoc "Gene Herman" science-chairs-directory)
("Gene Herman" "4202")
> (assoc "Sam Rebelsky" science-chairs-directory)
#f

Extracting Information

To find the telephone number corresponding to a given name, we could apply the cadr (car of cdr) procedure to the result of assoc. Here's an example.

;;; Procedure:
;;;   look-up-telephone-number
;;; Parameters:
;;;   name, a string
;;;   directory, a list of telephone book entries
;;; Purpose:
;;;   Looks up someone's telephone number in the directory.
;;; Produces:
;;;   number, a string
;;; Preconditions:
;;;   Each telephone book entry must be a list. [Unverified]
;;;   Element 0 of each telephone book entry must be a string which
;;;     represents a name. [Unverified]
;;;   Element 1 of each telephone book entry must be a string which
;;;     represents that person's phone number. [Unverified]
;;; Postconditions:
;;;   If an entry for name appears somewhere in the directory, returns
;;;     the corresponding phone number.
;;;   If multiple entries with the same name appear, returns one of them.
;;;   If no entries appear, returns the string "unlisted"
;;;   Does not affect the directory.
(define look-up-telephone-number
  (lambda (name directory)
    (if (assoc name directory)
        (cadr (assoc name directory))
        "unlisted")))

For example,

> (look-up-telephone-number "Gene Herman" science-chairs-directory)
"4202"
> (look-up-telephone-number "Sam Smith" science-chairs-directory) 
"unlisted"

Note that the result depends on the directory. For example,

> (look-up-telephone-number "Gene Herman" null)
"unlisted"

Some of you may recall asking why if might take a value other than #t or #f as a parameter. This procedure is one example of why.

Looking Up a Telephone Number, Revised

One problem with the look-up-telephone-number procedure given above is that it calls assoc twice, once to determine whether the phone number is in the list and once to determine the phone number. Rather than calling assoc twice, we might call it once and send the result to a helper procedure.

(define look-up-telephone-number
  (let ((lutn-helper (lambda (assoc-result)
          (if assoc-result (cadr assoc-result) "unlisted"))))
    (lambda (name directory)
      (lutn-helper (assoc name directory)))))

Using More Complex Records

In the previous example, we have only one value (the phone number) associated with a key. However, in practice, we often want to associate many values with the same key. For example, we might want to note which department each chair is associated with. Here's a new version of our previous list that also includes that information.

;;; Value:
;;;   science-chairs-directory
;;; Type:
;;;   List of lists.
;;;   Each sublist is of length three and contains a name, a phone number,
;;;     and a division.
;;;   All three of those values are strings.
;;; Contents:
;;;   A list of department and other chairs in the Science division in 
;;;   academic year 2002-2003.
(define science-chairs-directory
  (list (list "Mark Schneider"     "3018"  "Science")
        (list "Jackie Brown"       "3096"  "Biology")
        (list "Martin Minelli"     "3007"  "Chemistry")
        (list "Gene Herman"        "4202"  "Math/CS")
        (list "Charles Cunningham" "3182"  "Physics")
        (list "Ann Ellis"          "4865"  "Psychology")))

You should note a few things about this list. First, we've left the phone number as element 1 so that look-up-telephone-number still works. Second, we've taken advantage of Scheme's decision to ignore spaces between values by using spaces to put stuff in more tabular form.

Implementing assoc

As is the case with many of the built-in Scheme procedures, assoc is relatively easy to implement ourselves. In essence, assoc recursively steps through the list until it finds a match or runs out of elements.

(define assoc
  (lambda (key alist)
    (cond
       ; If there are no entries left in the association list,
       ; there are no entries with the given key.
       ((null? alist) #f)
       ; If the key we're looking for is the key of the first
       ; entry, then use that entry.       
       ((equal? key (car (car alist))) (car alist))
       ; Otherwise, look in the rest of the association list.
       (else (assoc key (cdr alist))))))

The DrScheme implementation of assoc also includes some error checking that you'll learn how to do later this semester.

Using Other Keys

The assoc procedure works fine if the key is the first element of a data item. But what if it's the second (or third, or fourth, or ...). For example, what if we know someone's phone number and want to find his or her name? Then we can't rely on assoc, because it only looks at the first element of each list. Instead, we need to write our own procedure. For example, to find someone with a particular phone number, we might write:

;;; Procedure:
;;;   look-up-by-number
;;; Parameters:
;;;   number, a string
;;;   directory, a list of telephone book entries
;;; Purpose:
;;;   Looks up the entry for a particular phone number.
;;; Produces:
;;;   entry, a telephone book entry.
;;; Preconditions:
;;;   Each telephone book entry must be a list. [Unverified]
;;;   Element 1 of each telephone book entry must be a string which
;;;     represents that person's phone number. [Unverified]
;;; Postconditions:
;;;   If an entry with phone number number appears in the directory, 
;;;     (1) number equals (list-ref entry 1); 
;;;     (2) entry is an element of directory
;;;   If no entries with that phone number appear, entry is false (#f).
;;;   Does not affect the directory.
(define look-up-by-number
  (lambda (number directory)
    (cond
       ; If there are no entries in the directory, our desired
       ; entry is not there.
       ((null? directory) #f)
       ; If the number we're looking for is in the initial entry,
       ; use that entry
       ((equal? number (list-ref (car directory) 1))
        (car directory))
       ; Otherwise, look in the rest of the directory.
       (else (look-up-by-number number (cdr directory))))))        

Related Procedures

The assoc procedure is actually one of three related built-in procedures in Scheme; the other two are assq and assv. Each of these procedures scan association lists for keys. They differ only in the test used for determining when a key is found:

• assoc uses the predicate equal? to compare the key sought with the key components of the entries in the association list.
• assq uses the predicate eq? for those comparisons.
• assv uses the predicate eqv? for those comparisons.

You may wish to refresh your memory on the purpose of these predicates (hint hint).