Addressing Scheme

[zenna]

How should we give addresses/identities to choices in forward and inverse execution of a function.

The origins of this problem are in reconciling a parameter generating function with a parametric inverse. That is, suppose we have a function like

function f(x, y)
  a = x + y
  b = a / y
end

We want to be able to:

1. Construct the pdf of f that will produce parameter values for the two operationrs
2. Construct the pi of f and use those parameters with it. Hence, we need some kind of way to say that some value corresponds to the parameter used in +.

In straight line programs this is not an issue. It only becomes problematic when we have recursion and nested functions. The reason it becomes problematic is that the structural position of a statement does not uniquely identify the thing we're trying to identify.

A few questions:

• What exactly are we trying to identify or address
• Do we need to do this at all?

What are we trying to identify

Problem with Control

The problem is that for any particular st

Consider:

function f2(n)
  a = 1
  i = 1
  while i < n
    a += g(a)
    i += 1
  end
  a
end

If we enter this function from the inverse direction and enter the while loop essentially from the inverse direction, we don't know what iteration we are on. But if our addressing scheme is assigning values to statements we need in some sense to know what iteration we're on, which is too much to ask.

Alternative

g(x) = x^2
function f1(a, n, i)
  if i >= n
    a
  else
    a_ = g(a) + a
     f1(a_, n, i + 1)
   end
end