SICP exercise 2.07

From Drewiki

Problem

Alyssa's interval arithmetic program (see section 2.1.4 of the text) is incomplete because she has not specified the implementation of the interval abstraction. Here is a definition of the interval constructor:

Define selectors upper-bound and lower-bound</tt> to complete the implementation.

Solution

Here is a definition of the interval constructor:

The implementations of upper-bound and lower-bound are trivial: we know that one will involve cons and the other car. The only issue to decide is which is which.

The definition of add-interval given in the text dictates the order:

add-interval expects the order of arguments to the constructor to be first the lower bound, then the upper bound. Here, then, are the definitions of the selectors:

Test:

Output:

1.3

Output:

0.7