However when you don’t take a birds eye view Of everything a dichotomy exists between say OOP and say functional programming. We don’t talk about these two styles of programming as if they are the same thing just because an isomorphism exist at a different level. We view these two concepts from a different context and in that specific context OOP is different then FP hence the different naming. At the Turing machine level both styles coalesce into assembly language and at this level they are the same.
So at all levels above the Turing machine. If OOP is defined as nodes with states and methods communicating with one another.... Then microservices, rest and corba form an isomorphism. Because that’s what microservices are... nodes of servers with state and methods...
Surely this is different from a stateless pipeline of functions where data is put into the front of the pipe And a new value pops out of the other end of the pipe.
No mathematical proof can describe this dichotomy because essentially Turing completeness says everything is the same thing so I’m operating at a different level if you know what I mean. Maybe a smarter person has a way to illustrate this dichotomy formally but all I’m going for is you understanding what I’m talking about.