Let $L$ be a programming language, and $\cong$ a notion of equality of $L$-programs (in general $\cong$ will be undecidable). Let $syntax(n)$ be the number of $L$-programs of size $n$ (for some reasonable notion of program size), and $semantics(n)$ denotes the number of $\cong$-equivalence classes of $L$-programs of size $n$. Now define
$$ density(n) = semantics(n)\ /\ syntax(n)$$
So $density(n)$ tells us how many really distinct programs we can write of size $n$. What is known about the limit:
$$ \lim_{n \rightarrow \infty} density(n)?$$
I conjecture that $\lim_{n \rightarrow \infty} density(n) = 0$ for reasonable choices of $L$ and $\cong$, since the larger programs are allowed to be, the more room for redundancies like $M+N \cong N+M$.
Question. What is related work this direction?