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Summary: In the laboratory, you will consider mechanisms for verifying the preconditions of procedures. You will also consider some issues int he documentation of such procedures.
Contents:
a. Document and write the all-real? procedure described in the accompanying reading.
b. What preconditions should all-real? have?
c. Is it necessary to test those preconditions? Why or why not?
When you're done, add all-real? to your library.
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 condition.
I'd recommend that you use cond rather than if 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 number:
(define odd-factorial
(lambda (number)
(if (= number 1)
1
(* number (odd-factorial (- number 2))))))
a. What precondition or preconditions
does 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. Document (using the six-P style), define, and test a procedure
named index-of that takes a symbol sym and a
list ls of symbols as its arguments and returns the index
of sym in ls. You should use 0-based indices,
so that the initial value in a list is at index 0. (Note that we
defined a similar procedure in a recent homework assignment. I would
prefer that you not refer to the answer key in your work here.)
> (index-of 'gamma (list 'alpha 'beta 'gamma 'delta))
2
> (index-of 'easy (list 'easy 'medium 'difficult 'impossible))
0
> (index-of 'the (list 'and 'the 'cat 'sat 'on 'the 'mat))
1
b. Arrange for index-of to signal an error (by invoking the
error procedure) if sym does not occur at all as
an element of ls.
c. If sym does not occur as an element of ls, is it better to have for index-of to invoke error or return a special value (such as -1 or #f)? Explain your answer.
When you're done, add index-of to your library.
Document (using the six P style), define, and test a procedure
named substitute that takes three arguments -- a
symbol new, another symbol old, 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 new and old are symbols and that
ls is a list of symbols before starting into the recursion.
> (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)
> (substitute 'in 'out null)
()
> (substitute "in" 'out null)
substitute: expected a symbol as first parameter
> (substitute 'in 'out (list 'alpha "beta" 23))
substitute: expected a list of symbols as third parameter
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