NOT.2:5.2 - Two ports of the same type with different roles

A diagram notation describes a ratio operation. It has two numeric inputs, numerator and denominator, and a numeric output. The supplied rule divides the numerator by a nonzero denominator. Source A supplies 6 and source B supplies 3.

The first drawing joins both sources to an unlabeled box. Knowing that both connections carry numbers leaves their operand positions undecided. Choose named input ports and preserve their identities when the box is moved or redrawn:

A: 6 -> ratio.numerator
B: 3 -> ratio.denominator
ratio.result -> answer

The result is 2. Reversing the two input connections is another well-formed construction with result 0.5. Port names make that change visible even though the input types remain the same.

Now enclose the ratio in a reusable component. Its exposed inputs refer to those two ports, and its output refers to ratio.result. Renaming the internal ratio box or changing its position can preserve those boundary connections. Swapping the connections changes the expressed operation. A rule that permits the former does not thereby permit the latter.

The same design question arises whenever compatible participants occupy different roles in a relation or operation. More elaborate diagram calculi can give the permitted connections and drawing equivalences mathematical definitions.