User blog:Ubersketch/Homomorphism between Cantor's normal form of finite degree and primitive sequence system

Let + denote function composition. A homomorphism is a function F between notations A to B such that for all functions f and g in A and all objects a in A, F(f+g(a))=F(f(a))+F(g(a))

Let | denote concatenation
 * F(0)=(empty string)
 * F(w^0)=(0)
 * F(w^(a+w^0))=b such that b[n]=F(w^a)|F(w^a)|F(w^a)... with n F(w^a)
 * F(a+b)=F(a)|F(b)

It seems that constructing homomorphisms between ordinal notations provides a promising new way of doing analysis without being informal, as well as a way to generalize ordinal notations by generalizing the homomorphism, such as generalizing a homomorphism PrSS -> CNF to BMS -> ???