Lists

When you type

(cons 1 empty)

in the interaction window, DrScheme replies with

(cons 1 empty)

DrScheme's reply is the same as your input expression because there is no shorter name for the list containing the number 1.

On the other hand, enter

(cons (+ 1 2) empty)

and DrScheme replies with

(cons 3 empty)

In this case, (+ 1 2) can be reduced to the simpler 3. But, as before, there is no simpler name for a list containing 3 other than (cons 3 empty).

The first and rest Operators

The first and rest operators only operate on lists created with cons, i.e., non-empty lists. So

(first empty)

gives the error message:

first: expects type <non-empty list> as 1st arg: given empty

Exercise Notes

Exercise 5.1.5 The function in Scheme is sqrt.