Suppose we have a stream of nested intervals represented as , whose end points are represented as signed binary streams (section 3.5), and with the following property:

We also have a function *f* which takes three signed binary stream
*x*, *y*, and *z* as inputs, and outputs a signed binary stream
representing by examining *x* and *z*, determining common
digits from them if it can using the method described above, and then
using *y* directly to determine the rest of the output.

We can now compute the signed binary stream represented by the stream of
nested intervals *y* as the result of , where the
function function is defined as: