Computer Science Fundamentals (CS153 2004S)
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Summary: In this laboratory, you will begin to explore some of the key builtin higherorder procedures. You will also write your first higherorder procedures.
Contents:
Related Pages:
best.scm
, our example from class.Start DrScheme
map
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, (dotproduct 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:
> (dotproduct (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 > (dotproduct null null) 0 ; ... because in this case there are no products to add
Sarah and Steven Schemer suggest that
they say,
apply
is irrelevant. After all,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, (maketallier 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 countodds (maketallier odd?))
> (countodds (list 1 2 3 4 5))
3
You can assume that tally
already exists for the purpose
of this problem.
Write a procedure, (makeremover predicate)
,
that creates a procedure that takes a list as a parameter and
removes all elements for which predicate holds.
For example,
> (define removewhitespace (makeremover charwhitespace?))
> (removewhitespace (list #\a #\space #\b #\c))
(#\a #\b #\c)
> ((makeremover odd?) (list 1 2 3 4 5))
(2 4)
maketallier
, revisited
Rewrite maketallier
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]
http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2000F/Labs/higherorder.html
Wednesday, 14 February 2001 [Samuel A. Rebelsky]
Sunday, 8 April 2001 [Samuel A. Rebelsky]
http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2001S/Labs/higherorder.html
.
Tuesday, 15 October 2002 [Samuel A. Rebelsky]
Wednesday, 16 October 2002 [Samuel A. Rebelsky]
map
.
http://www.cs.grinnell.edu/~rebelsky/Courses/CS151/2002F/Labs/higherorder.html
.
Sunday, 16 February 2003 [Samuel A. Rebelsky]
if you have extra timesection.
makeremover
exercise.
http://www.cs.grinnell.edu/~rebelsky/Courses/CS153/2003S/Labs/higherorder.html
.
Monday, 16 February 2004 [Samuel A. Rebelsky]
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[SamR]
Disclaimer:
I usually create these pages on the fly
, which means that I rarely
proofread them and they may contain bad grammar and incorrect details.
It also means that I tend to update them regularly (see the history for
more details). Feel free to contact me with any suggestions for changes.
This document was generated by
Siteweaver on Fri May 7 09:44:15 2004.
The source to the document was last modified on Tue Feb 17 13:26:40 2004.
This document may be found at http://www.cs.grinnell.edu/~rebelsky/Courses/CS153/2004S/Labs/higherorder1.html
.
; ; Check with Bobby
Samuel A. Rebelsky, rebelsky@grinnell.edu