NOT.1:5.1 - Same components, different composition

A team is designing a diagram notation for constructing pipelines of functions. Its first sketch shows the input, output and an unordered collection of function names. The current operation is to determine the result and then exchange two functions without losing their connections.

Use the supplied functions f(z) = z + 1 and g(z) = 2z, with input 3. Applying f then g gives g(f(3)) = 8. Applying g then f gives f(g(3)) = 7. Both cases have the same named components. The unordered sketch therefore loses a difference that the operation needs.

The designer tries directed connections, with the rule that a connection passes the output of one function to the input of the next:

3 -> f -> g -> result     gives 8
3 -> g -> f -> result     gives 7

Now the reader can recover the composition order and derive each result from the supplied functions. Exchanging the two functions changes their connections; merely dragging a box on the page must either preserve those connections or expose that it changed them. The design has acquired both an expression requirement and a question about the editing operation.

If the diagram is only an inventory of available functions, the original unordered sketch can remain adequate. If later work needs branching or shared intermediate results, try those operations before deciding how their connections and identities will be expressed. Success with this linear case leaves those questions open.