a. Write the
all-real? procedure described in the
b. What preconditions should
c. Is it necessary to test those preconditions? Why or why not?
Revise the definition of
greatest-of-list given in the
corresponding reading so that
it prints a different (and appropriate) error message for each error
I'd recommend that you use
cond rather than
in writing this revised version.
Revise the definition of the
count-from procedure presented in
the reading on
recursion with natural numbers so that it enforces the precondition
that its first argument be less than or equal to its second argument.
Here is a procedure that computes the product of all of the odd natural
numbers up to and including
(define odd-factorial (lambda (number) (if (= number 1) 1 (* number (odd-factorial (- number 2))))))
a. What precondition or preconditions
odd-factorial impose on its argument?
b. What will happen if these preconditions are not met?
c. Revise the definition of
odd-factorial as a
husk-and-kernel program in which the husk enforces the precondition.
d. How can we be certain, in this case, that none of the recursive calls we make to the kernel procedure violates the precondition?
a. Define and test a procedure named
index that takes a symbol
sym and a list
ls of symbols as its arguments and
returns the index of
ls. You should use 0-based indices (so
that the initial value in a list is at index 0).
> (index 'gamma (list 'alpha 'beta 'gamma 'delta)) 2 > (index 'easy (list 'easy 'medium 'difficult 'impossible)) 0 > (index 'the (list 'and 'the 'cat 'sat 'on 'the 'mat)) 1
b. Arrange for
index to signal an error (by invoking the
error procedure) if
sym does not occur at all as
an element of
Define and test a procedure named
substitute that takes three
arguments -- a symbol
new, another symbol
and a list
ls of symbols -- and returns a list just like
ls except that every occurrence of
old has been
replaced with an occurrence of
new. Use the husk-and-kernel
structure to make sure that
symbols and that
ls is a list of symbols before starting into
> (substitute 'alpha 'omega (list 'phi 'chi 'psi 'omega 'omega) (phi chi psi alpha alpha) > (substitute 'starboard 'port (list 'port 'starboard 'port 'port)) (starboard starboard starboard starboard) > (substitution 'in 'out null) ()
Friday, 15 September 2000 [Samuel A. Rebelsky]
Monday, 18 September 2000 [Samuel A. Rebelsky]
Thursday, 22 February 2001 [Samuel A. Rebelsky]
Sunday, 4 March 2001 [Samuel A. Rebelsky]
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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