You know how in Python, if v is a list or a dictionary, it's quite common to write functions that modify v in place (instead of just returning the new value). I'm wondering if it is possible to write a checker that identifies such functions.

For simplicity, say you have a function f, which only takes one argument - a and returns in finite time (the return value is actually irrelevant). Assume also that for any input value v, f(v) always does the same thing (i.e. the logic inside of f does not depend on any context or environment values - it's a pure computation on a).

Is it possible to write a function m, such that m(f, v) returns True if and only if f(v) actually changes the original value of v?

No; this is equivalent to the Halting problem. If such an m did exist, then I could just write:

def f(a):if m(f, a):return aelse:# Modify `a` somehowreturn a

and we get a contradiction.