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: