Functional super-iteration and hierarchy of functional hyper-iterations

[bo198214]

bo, you needed to see my explanation.

1. Evaluate g(x) at c first.
2. Hyper-n-iterate f to the OUTPUT of Step 1.
3. Evaluate the resulting function at c.

For n=1 (iteration), to evaluate this expression at any given natural x=c:
1. Evaluate g(x) at c first.
2. Iterate f to the OUTPUT of Step 1.
3. Evaluate the resulting function at c.

The set of all ordered pairs resulting from this evaluation is {(x, [f It_1 g(x)] (x))}.

I know, but I dont know what you want to say with that *questioningly look*.
We agree on the meaning, the question is more how to write it down properly.

Edit: Oh ok I see you extended your article. Yes and that computer program can be expressed with the 3 lines (1),(2),(3) that I gave.
Perhaps the difficulty of mutual understanding results from that you have no experience in functional programming.