Description
Exercise 1
In lectures, we explored different ways to model counters. SICP Section 3.1.1 presents different
ways to model transactions on bank accounts. One example is make-withdraw:
(define (make-withdraw balance)
(lambda (amount)
(if (>= balance amount)
(begin (set! balance (- balance amount))
balance)
“Insufficient funds”)))
make-withdraw is used to create independent objects (“withdrawal processors”). Each object
has its own local state variable balance:
> (define W1 (make-withdraw 100))
> (define W2 (make-withdraw 100))
; Withdrawals from W1 don’t affect W2, and vice-versa
> (W1 50)
50
1
> (W2 70)
30
> (W2 40)
“Insufficient funds”
> (W1 40)
10
Experiment with make-withdraw. What happens when these expressions are evaluated?
> (define W1 (make-withdraw 100))
> (W1 50)
> (W1 20)
What happens when these expressions are evaluated?
> ((make-withdraw 100) 50)
> ((make-withdraw 100) 20)
Do they do the same thing as the previous example? Make sure you can explain any differences.
Exercise 2
(SICP Exercise 3.1)
An accumulator is a procedure that is called repeatedly with a single numeric argument and
accumulates its arguments into a sum. Each time it is called, it returns the currently accumulated
sum.
Applying what you learned from Exercise 1, write a procedure make-accumulator that
generates accumulators, each maintaining an independent sum. The input to
make-accumulator should specify the initial value of the sum; for example,
> (define A (make-accumulator 5))
> (A 10)
15
> (A 10)
25
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Exercise 3
SICP Section 3.1.1 presents procedure make-account, which provides a way to model simple
bank accounts that can process deposits and withdrawals. Each time this procedure is called, it
returns a dispatch procedure that represents a bank account object:
(define (make-account balance)
(define (withdraw amount)
(if (>= balance amount)
(begin (set! balance (- balance amount))
balance)
“Insufficient funds”))
(define (deposit amount)
(set! balance (+ balance amount))
balance)
(define (dispatch msg)
(cond ((eq? msg ‘withdraw) withdraw)
((eq? msg ‘deposit) deposit)
(else (error “Unknown request — make-account” msg))))
dispatch)
When the dispatch procedure is called with the “message” ‘deposit as an argument, it
returns the deposit procedure. When it is given the ‘withdraw message, dispatch returns
the withdraw procedure. The deposit or withdraw procedure is then applied to a specified
amount.
This example shows how make-account can be used. Notice that my-account and
your-account are bound to completely separate account objects, each with its own local state
variable balance.
> (define my-account (make-account 100))
> (define your-account (make-account 100))
> ((my-account ‘withdraw) 50)
50
> ((my-account ‘withdraw) 60)
“Insufficient funds”
> ((my-account ‘deposit) 40)
90
> ((my-account ‘withdraw) 60)
30
> ((your-account ‘withdraw) 10)
90
Experiment with make-account. Try the examples shown in the previous paragraph.
What happens when the following expressions are evaluated?
> (define my-account (make-account 100))
> (define my-withdraw-processor (my-account ‘withdraw))
3
> (define my-deposit-processor (my-account ‘deposit))
> (my-withdraw-processor 50)
> (my-withdraw-processor 60)
> (my-deposit-processor 40)
> (my-withdraw-processor 60)
Is there any advantage to requesting account transactions this way, as opposed to the approach
shown earlier in this exercise?
Exercise 4
(SICP Exercise 3.3)
Make a copy of make-account and rename it as make-password-account. Modify this
procedure so that it that creates password-protected accounts. That is,
make-password-account should take a symbol as an additional argument, as in
> (define acc (make-password-account 100 ‘secret-password))
The resulting account object should process a request only if it is accompanied by the password
with which the account was created, and should otherwise return a complaint:
> ((acc ‘secret-password ‘withdraw) 40)
60
> ((acc ‘some-other-password ‘deposit) 50)
“Incorrect password”
Note: ensure that no run-time error occurs when “Incorrect password” is displayed. Hint:
as demonstrated by the examples in the previous paragraph, make-password-account should
return a dispatch procedure, using the same technique as make-account. When the
dispatch procedure is called it returns a procedure. That procedure is always called with a
single argument (an amount of money). In other words, the expression:
> (acc ‘some-other-password ‘deposit)
calls the dispatch procedure bound to acc and returns a procedure, which means that the
expression:
> ((acc ‘some-other-password ‘deposit) 50)
“Incorrect password”
calls the procedure returned by dispatch, passing it 50.
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Exercise 5
In the make-account procedure in SICP Section 3.1.1 (used in Exercise 3), the local state
variable balance is a formal parameter of make-account. We could also create the local state
variable explicitly, using let, as shown here:
(define (make-account-with-let initial-balance)
(let ((balance initial-balance))
(define (withdraw amount)
(if (>= balance amount)
(begin (set! balance (- balance amount))
balance)
“Insufficient funds”))
(define (deposit amount)
(set! balance (+ balance amount))
balance)
(define (dispatch msg)
(cond ((eq? msg ‘withdraw) withdraw)
((eq? msg ‘deposit) deposit)
(else (error “Unknown request — make-account” msg))))
dispatch))
Notice the changes:
● the body of the procedure is a let statement;
● balance is now a local variable, and is defined in the let statement;
● the procedure’s parameter name has been changed to initial-balance, and this
parameter is used to initialize balance.
Experiment with make-account-with-let. Verify that the bank account objects returned by
this procedure respond to the same messages and return the same values as the objects returned
by make-account.
Exercise 6
(SICP Exercise 3.4)
Make a copy of your make-password-account procedure from Exercise 4 and rename it as
make-password-account-monitored.
Applying what you learned from Exercises 4 and 5, modify this procedure. Use a let statement
to add another local state variable so that, if an account is accessed more than seven consecutive
times with an incorrect password, it invokes the procedure call-the-cops. Note: balance
and the password can remain formal parameters – they don’t have to be defined in the let.
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