a. Discuss the self check with your partner.
b. Do the normal lab setup. That is
loudhum package is up to date.(require loudhum) to the top of the definitions pane.c. Add the procedures and associated documentation from the corresponding reading to the definitions pane. Be sure to include a short note as to the source of that code.
d. Create a list named mixed-values that contains a dozen or so different
kinds of values. You will likely use an instruction like the following.
(define mixed-values
(list 1 'two "three" 4.5 6/7 (list) (list 8) 9+10i ...))
sum procedurea. Read through sum so that you have a sense of how it accomplishes
its purpose.
b. Verify that sum produces the same results as in the corresponding reading.
c. What value do you expect sum to produce for the empty list?
d. Check your answer experimentally.
e. What value do you expect sum to produce for a singleton list? (A “singleton list” is a list with only one value.)
f. Check your answer experimentally.
g. Try sum for a few other lists, too.
h. What do you expect the following to compute?
> (sum 1 2 3)
i. Check your answer experimentally.
a. Reread the definition of select-numbers to try to understand what it does.
Then copy the code into your definitions pane.
b. Determine which values in mixed-values are numbers with
(map number? mixed-values).
c. Create a list of numbers with (select-numbers mixed-values).
d. Verify that all the resulting values are numbers, using a technique similar to the one that you used in step b.
Suppose the length procedure, which computes the length of a list,
were not defined. We could define it by recursing through the list,
counting 1 for each value in the list. In some sense, this is much like
the definition of sum, except that we use the value 1 rather than the
value of each element.
a. Using this idea, write a recursive procedure, (list-length
lst) that finds the length of a list. You may not use
length in defining list-length.
b. Check your answer on a few examples: the empty list, the list of values you created, and a few more lists of your choice.
Write a recursive procedure, (product nums), that computes
the product of a list of numbers. You should feel free to use sum
as a template for product. However, you should think carefully about
the base case.
The length procedure counts the number of values in a list. What if
we don’t want to count every value in a list? For example, suppose we
only want to count the numbers in a mixed list. In this case,
we still recur over the list, but we sometimes count 1 (when the
element is a number) and sometimes count 0 (when it is not).
a. Using this idea, write a procedure, (tally-numbers lst),
that, given a list, counts how many are numbers. Note: You should not
call list-length, length, filter, tally, or select-numbers in
your solution. Instead, use the ideas behind some or all of these
functions in crafting your own recursive solution.
b. Check how your procedure functions on a variety of inputs. For example, you might start with the following
> (tally-numbers null)
> (tally-numbers (list 1 2 3))
> (tally-numbers (list "a" "b" "c"))
> (tally-numbers (list 1 "a" 2 "b" 3 "c"))
> (tally-numbers mixed-values)
Using recursion (hence, without reduce or sort or any similar
procedure), write a procedure, (largest lst), that finds the largest
value in a non-empty list of real numbers. You need not check the
precondition that the list is non-empty nor the precondition that it
contains only reals.
largestRewrite largest using the Husk and Kernel strategy introduced in
the reading on preconditions.
The following exercises will challenge you to extend the problem-solving strategies you’ve learned so far.
(a) Without using index-of, write a procedure, (find-first-skip
lst) that takes a list of symbols as a parameter and returns
the index of the first instance of the symbol skip in lst, if skip
appears in lst. Your procedure may return an error if the symbol skip
does not appear in the list.
> (find-first-skip (list 'hop 'skip 'and 'jump))
1
> (find-first-skip (list 'skip 'hop 'jump 'skip 'and 'skip 'again))
0
> (find-first-skip (list 'hop 'to 'work 'jump 'to 'school 'but 'never 'skip 'class))
8
(b) Extend your find-first-skip procedure so that, when the symbol
skip is not in the list, the procedure produces #f rather than
an error.
> (find-first-skip (list 'hop 'to 'work 'jump 'to 'school 'but 'never 'skip 'class))
8
> (find-first-skip (list 'hop 'and 'jump))
#f
Write a procedure, (my-index-of val lst) that takes a
value and a list of values as its parameters and returns the index of
the first instance of val in lst, if the value appears in the
list. If the value does not appear, index-of should return #f.
> (my-index-of 'skip (list 'hop 'skip 'and 'jump))
1
> (index-of 5 (list 5 4 3 2 1 2 3 4 5))
0
> (my-index-of "eraser" (list "pencils" "paper" "index cards" "markers" "ball-point pens"))
#f
Write and document a function (riffle first second) that produces a new list containing alternating elements from the lists first ... second. If one list runs out before the other, then the remaining elements should appear at the end of the new list.
> (riffle (list 'a 'b 'c) (list 'x 'y 'z))
(a x b y c z)
> (riffle (list 'a 'b 'c) (iota 10))
(a 0 b 1 c 2 3 4 5 6 7 8 9)
The sum procedure adds up all of the elements in a list. Suppose we
want to compute the difference of the values in the list. For example,
given the list '(a b c d e), we want a - b - c - d - e.
> (difference (list 5))
5
> (difference (list 5 2))
3
> (difference (list 5 2 1))
2
> (difference (list 5 2 1 7))
-5
> (difference (list 5 2 1 7 8))
-13
> (difference (list 5 2 1 7 8 10))
-23
a. Come up with a strategy for implementing difference recursively.
b. Implement that strategy.