Description
Exercise 1
To run the calculator interpreter, click Run, then type (calc) in the Interactions area. This will
call the procedure that executes the interpreter’s read-eval-print loop (REPL). The REPL will
display a prompt (calc:) and wait for you to type an expression in the input box.
The calculator supports four operations: +, -, * and /. Arithmetic expressions are typed using the
same syntax as Racket; for example, to calculate 1 + 2 + 3, enter this expression:
(+ 1 2 3)
The interpreter evaluates the expression, displays the result (6), then prompts you to enter
another expression. To exit the interpreter, type a bad expression; e.g., exit.
Experiment with the calculator. Which operators require no arguments? What do they do? Try
these expressions: (+), (-), (*), (/).
What operations are performed when the operators have exactly one argument? Try these
expressions: (+ 3), (- 3), (* 3), (/ 3).
What operations are performed when the operators have multiple arguments? Try some
expressions with two arguments. Try some expressions with three or four arguments.
Read procedures calc-eval and calc-apply. Make sure you understand how calc-eval
evaluates expressions that have nested expressions; for example (+ 2 (* 3 4) 5 6). Make
sure you understand how calc-apply handles expressions with 0 arguments, 1 argument and
multiple arguments.
1
Exercise 2
Modify calc-apply to provide an abs operator. This operator expects exactly one argument,
and the expression (abs x) calculates the absolute value of x. Racket provides a procedure that
calculates absolute values (check Section 4.2.2, Generic Numerics, in the Racket Reference.) The
calculator interpreter should call this procedure.
When abs expressions with an incorrect number of arguments are entered, the calculator should
call error to display this message: “Calc: abs requires exactly 1 arg”.
Test your modifications. Verify that the calculator correctly evaluates abs expressions in which
the argument is a simple number; for example (abs 4), as well as expressions in which the
argument is a nested arithmetic expression; for example, (abs (* 3 (- 5 8))).
Exercise 3
Modify calc-apply to provide an ** operator. This operator expects exactly two arguments,
and the expression (** a b) calculates a raised to the power of b. Racket provides a procedure
that calculates powers (check Section 4.2.2, Generic Numerics, in the Racket Reference.) The
calculator interpreter should call this procedure.
When ** expressions with an incorrect number of arguments are entered, the calculator should
call error to display this message: “Calc: ** requires exactly 2 args”.
Test your modifications. Verify that the calculator correctly evaluates ** expressions in which
the arguments are simple numbers as well as expressions in which one or both arguments are
nested arithmetic expressions.
Interlude – Racket’s foldr procedure
When you did Exercise 1, you saw that calc-apply calls foldr to perform addition and
multiplication with 0 or more arguments, and subtraction and division with two or more
arguments. Before starting the next exercise, we need to have a closer look at foldr.
foldr accepts a procedure proc, an initial value init, and a list:
(foldr proc init lst)
It applies proc to each element in the list, and combines the return values in a way that is
determined by proc. Procedure proc must take 2 arguments. The first time proc is called, its
first argument is the last item in the list, and the second argument is init. In subsequent
invocations of proc, the second argument is the return value from the previous invocation of
proc. The list is traversed from right to left, and the result of the entire foldr call is the result
of the last invocation of proc.
Try these expressions in the Interactions area.
> (foldr + 0 ‘(2 3 4))
> (foldr + 1 ‘(2 3 4))
> (foldr * 0 ‘(2 3 4))
> (foldr * 1 ‘(2 3 4))
2
What does each expression calculate? For each expression, what are the arguments each time
foldr calls + or *?
Exercise 4
Racket provides a max procedure that accepts one or more integers or real numbers and returns
the largest of the numbers. For example,
(max 1.0 3.0 2.0) returns 3.0
and
(max 1 3 2) returns 3.
Modify calc-apply to provide a max operator. This operator should accept one or more
numbers and should call Racket’s max procedure to calculate the largest one.
When max expressions with an incorrect number of arguments are entered, the calculator should
call error to display this message: “Calc: max requires 1 or more args”.
Hint: Suppose you enter this calculator language expression: (max 1 3 2). When
calc-apply is called, parameter fn is bound to ‘max and parameter args is bound to
the list ‘(1 3 2). Racket’s max procedure expects one or more numeric arguments, not
a list, so the calculator interpreter can’t call Racket’s max this way:
…(max args)…
How could you use foldr to apply Racket’s max to all the numbers in the list?
Test your modifications. Verify that the calculator correctly evaluates max expressions in which
the arguments are simple numbers as well as expressions in which the arguments are nested
arithmetic expressions; for example, (max (+ 2 1) (* 3 2) (- 4 2))
Also, verify that the calculator can evaluate expressions such as this one:
(+ 3 (abs -4) (** 2 3) (max 4 6 5) (abs (* -2 3)))
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