Summary: In this laboratory, you will begin to explore
some of the key built-in higher-order procedures. You will also write
your first higher-order procedures.
Contents:
Related Pages:
Start DrScheme
Recall that (map proc lst) builds a list by applying
proc to each element of lst in succession.
a. Use map to compute the successors to the squares of
the integers between 1 and 10. Your result should be
the list (2 5 10 17 26 37 50 65 82 101).
b. Use map to take the last element of each list in a
list of lists. The result should be a list of the last elements.
For example, given ((1 2 3) (4 5 6) (7 8 9 10) (11 12))
as input, you should produce the list (3 6 10 12).
c. Use apply and map to sum the last elements
of each list in a list of lists of numbers. The result should be a
number.
Note that you may have written a similar expression for another lab.
Your goal here is to see whether you can solve the problem more concisely.
Although we often use the map procedure with only two
parameters (a procedure and a list), it can take more than two
parameters, as long as the first parameter is a procedure and the
remaining parameters are lists.
a. What do you think the value of the following expression will be?
(map (lambda (x y) (+ x y)) (list 1 2 3) (list 4 5 6))
b. Verify your answer through experimentation.
c. What do you think the value of the following expression will be?
(map list (list 1 2 3) (list 4 5 6) (list 7 8 9))
d. Verify your answer through experimentation.
e. What do you think Scheme will do when evaluating the following expression?
(map list (list 1 2 3) (list 4 5))
f. Verify your answer through experimentation.
g. What do you think Scheme will do when evaluating the following expression?
(map (lambda (x y) (+ x y)) (list 1 2) (list 3 4) (list 5 6))
h. Verify your answer through experimentation.
Use apply and map to concisely define a
procedure, (dot-product list1 list2), 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 (list 1 2 4 8) (list 11 5 7 3))
73
; ... because (1 x 11) + (2 x 5) + (4 x 7) + (8 x 3) = 11 + 10 + 28 + 24 = 73
> (dot-product null null)
0
; ... because in this case there are no products to add
Sarah and Steven Schemer suggest that
apply is irrelevant. After all,
they say,
when you write
(apply proc (arg1 ... argn))
you're just doing the same thing as
(proc arg1 arg2 ... argn).
Given your experience in the previous exercise, are they correct?
Why or why not?
a. Document and write a procedure, (tally predicate
list),
that counts the number of values in list for which
predicate holds.
b. Demonstrate the procedure by tallying the number of odd values
in the list of the first twenty integers.
c. Demonstrate the procedure by tallying the number of multiples of
three in the list of the first twenty integers.
Document and write a procedure, (make-tallier predicate),
that builds a procedure that takes a list as a parameter and tallies
the values in the list for which the predicate holds. For example
> (define count-odds (make-tallier odd?))
> (count-odds (list 1 2 3 4 5))
3
You can assume that tally already exists for the purpose
of this problem.
Write a procedure, (make-remover predicate),
that creates a procedure that takes a list as a parameter and
removes all elements for which predicate holds.
For example,
> (define remove-whitespace (make-remover char-whitespace?))
> (remove-whitespace (list #\a #\space #\b #\c))
(#\a #\b #\c)
> ((make-remover odd?) (list 1 2 3 4 5))
(2 4)
Rewrite make-tallier so that it doesn't call tally
and so that it doesn't call itself. (You'll have to create a local
recursive procedure and then return it.)
Write a procedure, (map! proc vec), that
replaces each element of vec with the result of applying proc
to the original element.
Thursday, 2 November 2000 [Samuel A. Rebelsky]
Wednesday, 14 February 2001 [Samuel A. Rebelsky]
- Moved many problems into a new lab so that there are now two
higher-order procedures labs.
- Added new problems (1, 4, and 5).
- Removed unused notes section.
Sunday, 8 April 2001 [Samuel A. Rebelsky]
Tuesday, 15 October 2002 [Samuel A. Rebelsky]
- Reformatted slightly.
- Added some introductory notes.
Wednesday, 16 October 2002 [Samuel A. Rebelsky]
Sunday, 16 February 2003 [Samuel A. Rebelsky]
Monday, 16 February 2004 [Samuel A. Rebelsky]
- Added some preliminary stuff (summary, links to related pages).
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Check with Bobby