Commutativity of addition is a correlation P1=P2, where P1(x,y)=x+y, and P2(x,y)=y+x. So, f()+g() = [using this correlation] = g()+f().
But you’re right. In order to use this, I have to be able to calculate evaluations and comparisons on arbitrary pieces of code, not just the ones existing in U()...
Commutativity of addition is a correlation P1=P2, where P1(x,y)=x+y, and P2(x,y)=y+x.
So, f()+g() = [using this correlation] = g()+f().
But you’re right. In order to use this, I have to be able to calculate evaluations and comparisons on arbitrary pieces of code, not just the ones existing in U()...