Hints for Assignment 1

Common errors

Procedure calls

Remember the rules for evaluating a procedure call:

A procedure call is formatted as a list:
- The first element must be a procedure
- The rest of the elements are evaluated to detemine the argument values

You can't use C/C++ style for calling functions. The following is illegal:

  ackermann(i j)

It should be:

  (ackermann i j)

Nesting `if` statements

Several students have written functions like the following example:

  (define (example x)
    (if (> x 3)
	89)
    (if (< x -78)
	(* x 4)
	(/ x 7))

Although this is legal Scheme, it will not do what you think it will do. This is an example of thinking procedurally, rather than fuctionally.

A procedure will return only one value, so you really only get one expression to evaluate. How do you do two things with just one expression? In this case, you have to think in terms of nested if statements. The way the above code should be written is:

  (define (example x)
    (if (> x 3)
	89
	(if (< x -78)
	    (* x 4)
	    (/ x 7))))

Hints

Problem 7

Use a "helper" function. For example:

  (define (list-sums l)
    (list-sums-helper <arg1> <arg2>))

  (define (list-sums-helper <arg1-name> <arg2-name>)
    <procedure body>)

The basic idea is that the "main" function sets up a call to a "helper" function that actually does the work.

Here is a concrete example. Consider the factorial function we did on the first day:

  (define (fac n)
    (if (= n 0)
	1
	(* n (fac (- n 1)))))

Here is a version that uses a helper function:

  (define (fac n)
    (fac-helper n 1))

  (define (fac-helper n result)
    (if (= n 0)
	result
	(fac-helper (- n 1) (* result n))))

Essentially what happens is that the result is built up in one of the arguments to the recursive call, and at the end, the result can be returned directly without unwinding the chain of recursive calls.