In the previous reading, you encountered some basic issues for higher order procedures. Today, we continue some more sophisticated uses of such procedures.
An operator section is a procedure that is derived from another
procedure by ``filling in'' some but not all of its arguments. For
double procedure defined by
(define double (lambda (n) (* 2 n)))
qualifies as an operator section, since it fills in the first argument to
* procedure with the particular value 2. Operator
sections are often used as arguments to higher-order procedures.
For instance, once we've written the
tallier procedure that
generates a procedure that can tally values in a list that meet a precidate,
we could construct a procedure that counts the number of
occurrences of the symbol
'n/a (``not available'') in a given
(tallier (lambda (whatever) (eq? 'n/a whatever))).
Here the value of the
lambda-expression is an operator section
eq?, with the first argument filled in with the particular
We can even define higher-order procedures to construct operator sections
for us. Such procedures are not primitives, but they are easily defined --
Let's use the name
left-section for a higher-order procedure
that takes a procedure of two arguments and a value to drop in as its first
argument, and returns the relevant operator section:
;;; Procedure: ;;; left-section ;;; Parameters: ;;; proc, A procedure with two parameters ;;; param1, The first parameter to that procedure ;;; Purpose: ;;; Fills in one parameter to the procedure. ;;; Produces: ;;; A new procedure with one parameter, param2, that applies proc ;;; to param1 and param2. ;;; Preconditions: ;;; proc is a procedure with two parameters. ;;; param1 is of appropriate type for the first parameter of proc. ;;; Postconditions: ;;; The result procedure expects a parameter of the same type as ;;; the second parameter of proc. (define left-section (lambda (proc param1) (lambda (expected) (proc param1 expected))))
So we could define
(left-section * 2)
(lambda (whatever) (eq? 'n/a whatever)) as
(left-section eq? 'n/a).
To filter a list is to examine each of its elements in turn, retaining some for a new list while eliminating others. For instance, given a list of integers, the following procedure filters it to remove the negative ones:
;;; Procedure: ;;; remove-negatives ;;; Parameters: ;;; A list of numbers ;;; Purpose: ;;; Removes negative numbers from the list. ;;; Produces: ;;; A list containing no negative numbers. ;;; Preconditions: ;;; The input list contains only numbers [Unverified] ;;; Postconditions: ;;; The output list contains all non-negative numbers in the original ;;; list (and in the same order). ;;; The output list contains no other numbers. (define remove-negatives (lambda (ls) (cond ((null? ls) null) ((negative? (car ls)) (remove-negatives (cdr ls))) (else (cons (car ls) (remove-negatives (cdr ls)))))))
We could write similar procedures to remove the whitespace characters from
a list of characters, or to exclude any occurrences of the symbol
'n/a from a list:
(define remove-whitespace (lambda (ls) (cond ((null? ls) null) ((char-whitespace? (car ls)) (remove-whitespace (cdr ls))) (else (cons (car ls) (remove-whitespace (cdr ls))))))) (define remove-n/a-symbols (lambda (ls) (cond ((null? ls) null) ((eq? 'n/a (car ls)) (remove-n/a-symbols (cdr ls))) (else (cons (car ls) (remove-n/a-symbols (cdr ls)))))))
Similar filtering procedures occur so frequently that it's useful to have a higher-order procedure to construct them.
(define remove (lambda (predicate) (letrec ((remover (lambda (ls) (cond ((null? ls) null) ((predicate (car ls)) (remover (cdr ls))) (else (cons (car ls) (remover (cdr ls)))))))) remover)))
In other words, ``let remover be a recusive procedurer that steps through the list, keeping the values that don't match the predicate; return that procedure''.
We can now define the variations in terms of our new procedure
(define remove-negatives (remove negative?)) (define remove-whitespace (remove char-whitespace?)) (define remove-n/a-symbols (remove (left-section eq? 'n/a)))
October 30, 1997 [John Stone or Henry Walker]
March 17, 2000 [John Stone]
Thursday, 2 November 2000 (Sam Rebelsky)
Wednesday, 14 March 2001
Disclaimer: I usually create these pages on the fly. This means that they are rarely proofread and may contain bad grammar and incorrect details. It also means that I may update them regularly (see the history for more details). Feel free to contact me with any suggestions for changes.
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