You are working on the contact list for some new cell phone. The phone’s owner updates and consults this list on various occasions. For le Problemnow, you are assigned the task of designing a function that consumes this list of contacts and determines whether it contains the name “Flatt.”

Once we have a solution to this sample problem, we will generalize it to a function that finds any name on a list.
The data definition for List-of-names from the preceding is appropriate for representing the list of names that the function is to search. Next we turn to the header material:
; List-of-names -> Boolean
; determines whether "Flatt" is on a-list-of-names
(define (contains-flatt? a-list-of-names)
#false)
While a-list-of-names is a good name for the list of names that the function consumes, it is a mouthful and we therefore shorten it to alon.
Following the general design recipe, we next make up some examples that illustrate the purpose of the function. First, we determine the output for the simplest input: '(). Since this list does not contain any strings, it certainly does not contain "Flatt":
(check-expect (contains-flatt? '()) #false)

Then we consider lists with a single item. Here are two examples:
(check-expect (contains-flatt? (cons "Find" '()))
#false)
(check-expect (contains-flatt? (cons "Flatt" '()))
#true)
In the first case, the answer is #false because the single item on the list is not "Flatt"; in the second case, the single item is "Flatt", so the answer is #true. Finally, here is a more general example:
(check-expect
(contains-flatt?
(cons "A" (cons "Flatt" (cons "C" '()))))
#true)
Again, the answer case must be #true because the list contains "Flatt". Stop! Make a general example for which the answer must be #false.
Take a breath. Run the program. The header is a “dummy” definition for the function; you have some examples; they have been turned into tests; and best of all, some of them actually succeed. They succeed for the wrong reason but succeed they do. If things make sense now, read on.

The fourth step is to design a function template that matches the data definition. Since the data definition for lists of strings has two clauses, the function’s body must be a cond expression with two clauses. The two conditions determine which of the two kinds of lists the function received:
(define (contains-flatt? alon)
(cond
[(empty? alon) ...]
[(cons? alon) ...]))
Instead of (cons? alon), we could use else in the second clause.
We can add one more hint to the template by studying each clause of the cond expression in turn. Specifically, recall that the design recipe suggests annotating each clause with selector expressions if the corresponding class of inputs consists of compounds. In our case, we know that '() does not have compounds, so there are no components. Otherwise the list is constructed from a string and another list of strings, and we remind ourselves of this fact by adding (first alon) and (rest alon) to the template:
(define (contains-flatt? alon)
(cond
[(empty? alon) ...]
[(cons? alon)
(... (first alon) ... (rest alon) ...)]))
Now it is time to switch to the programming task proper, the fifth step of our design recipe. It starts from a template and deals with each cond clause separately. If (empty? alon) is true, the input is the empty list, in which case the function must produce the result #false. In the second case, (cons? alon) is true. The annotations in the template remind us that there is a first string and then the rest of the list. So let’s consider an example that falls into this category:
(cons "A"
(cons ...
... '()))
The function, like a person, must compare the first item with "Flatt". In this example, the first one is "A" and not "Flatt", so the comparison yields #false. If we had considered some other example instead, say,
(cons "Flatt"
(cons ...
... '()))
the function would determine that the first item on the input is "Flatt", and would therefore respond with #true. This implies that the second line in the cond expression should contain an expression that compares the first name on the list with "Flatt":
(define (contains-flatt? alon)
(cond
[(empty? alon) #false]
[(cons? alon)
(... (string=? (first alon) "Flatt")
... (rest alon) ...)]))
Furthermore, if the comparison yields #true, the function must produce #true. If the comparison yields #false, we are left with another list of strings: (rest alon). Clearly, the function can’t know the final answer in this case, because the answer depends on what “...” represents. Put differently, if the first item is not "Flatt", we need some way to check whether the rest of the list contains "Flatt".
Fortunately, we have contains-flatt? and it fits the bill. According to its purpose statement, it determines whether a list contains "Flatt". The statement implies that (contains-flatt? l) tells us whether the list of strings l contains "Flatt". And, in the same vein, (contains-flatt? (rest alon)) determines whether "Flatt" is a member of (rest alon), which is precisely what we need to know.

In short, the last line should be (contains-flatt? (rest alon)):
; List-of-names -> Boolean
(define (contains-flatt? alon)
(cond
[(empty? alon) #false]
[(cons? alon)
(... (string=? (first alon) "Flatt") ...
... (contains-flatt? (rest alon)) ...)]))

Public Answer