Automatically Defined Functions

• ADF tree in its own right
• distribution of possible functions the ADF implements converges to a limiting distribution as the ADF gets bigger.
• For each function, ADF value determined by its input(s)
• inputs is given by a subtree in calling ADF or main program
• if $\vert\mbox{subtree}\vert > \mbox{threshold}$ distribution of ADF argument values also converges
• $\Rightarrow$ distribution of ADF answers converges
• $\Rightarrow$ distribution of whole program answers converges