Procedures as First-Class Citizens

Goals

This laboratory exercise provides practice with procedures:

• procedures passed as procedures to other procedures, and
• procedures that apply procedures to lists and other data

Procedures as Arguments, map, apply, and eval

Consider the following procedure every? that takes two arguments, a predicate pred and a list ls, and determines whether or not the predicate is true of every element of the list.

(define every?
   (lambda (pred ls)
   ;Pre-condition:  pred is a procedure; ls is a list
   ;Post-conditions:  returns error if pre-conditions are not met
   ;                  returns #t if pred is true for every element of list
     ; precondition tests
     (if (not (procedure? pred))
         (error 'every? "The first argument must be a predicate"))
     (if (not (list? ls))
         (error 'every? "The second argument must be a list"))
     (every-kernel pred ls)))

(define every-kernel
   (lambda (pred ls)
   ;Pre-condition:  pred is a procedure; ls is a list
   ;Post-conditions:  returns #t if pred is true for every element of list 
      (or (null? ls)
          (and (pred (car ls))         ; Invoke the predicate here!
               (every-kernel pred (cdr ls))))))

1. Using every? as a model, write and test an analogous procedure any? that determines whether a given predicate is true of at least one element of a given list. (Note: every? returns #t if it is given an empty list; any? should return #f in this case.)

2. Consider the following procedure capitalize that capitalizes all letters in a string:

   (define capitalize
      (lambda (str)
      ;Pre-condition:  str is a character string
      ;Post-condition:  str is returned with all letters capitalized
          (list->string (map char-upcase (string->list str)))
       )
   )
   

   Run capitalize on several strings to test precisely what it does.

3. Explain in a few sentences what capitalize does.

4. The map procedure can actually take more than two arguments, if all of the extras are lists:

   > (map string-append '("left" "start" "beginning")
                        '("-to-" "-to-" "-to-")
                        '("right" "finish" "end"))
   ("left-to-right" "start-to-finish" "beginning-to-end")
   
   

   Define a procedure pairwise-sum that takes as arguments two lists of numbers, equal in length, and returns a new list whose components are the sums of the corresponding components of the arguments. Define this procedure using map.

5. Define a procedure dot-product that takes as arguments two lists of numbers, equal in length, and returns the sum of the products of corresponding elements of the arguments:

   > (dot-product '(3 4 -1) '(1 -2 -3))
   -2
   
   > (dot-product '(0.003 0.035) '(8 2))
   0.094
   
   > (dot-product '(5.3e4) '(2.0e-3))
   106.0
   
   > (dot-product '() '())
   0
   

   Use apply and map to give a concise definition of this procedure.

6. Write a procedure do-it that reads an expression, evaluates it, and prints the result -- paralleling one pass through the read-eval-print cycle.

7. Modify do-it so that it reads, evaluates, and prints multiple expressions, until the user types (exit).

This document is available on the World Wide Web as

http://www.walker.cs.grinnell.edu/courses/153.sp05/labs/lab-procedure-arguments.shtml

created March 24, 1997 by John David Stone last revised January 31, 2005 by Henry M. Walker
For more information, please contact Henry M. Walker at walker@cs.grinnell.edu.