Problem implementing Zipf (power law) distribution -- external C++

Interfaces RStan
22

OK. I have the problem surrounded. This works, i.e. just declare real zeta(real alpha); but don’t define a power_law function that calls it:

functions{
    real zeta(real s);
    /*TODO: implement rng for prior and posterior predictive checks*/
}
data{
  int<lower=0> K; // number of unique values
  int values[K];
  int<lower=0> frequencies[K];
}
parameters{
  real <lower=1> alpha;
}
model{
  real constant = log(zeta(alpha));
  for (k in 1:K) {
    target += frequencies[k] * (-alpha * log(values[k]) - constant);
  }
}

That is actually better (iff alpha is a scalar) because it only evaluates the zeta function once. But it does not answer the question (for @Bob_Carpenter or @seantalts) of why you can declare a zeta function, define it in an external C++ file, but not call it from another Stan function without incurring a linker error. In other words, the original Stan program fails to link, even though it should inline to the same thing

functions{
    real zeta(real s);
    real power_law_lpmf(int x, real alpha){
     return (-alpha * log(x) - log(zeta(alpha)) );
    }
    /*TODO: implement rng for prior and posterior predictive checks*/
}
data{
  int<lower=0> K; // number of unique values  
  int values[K];
  int<lower=0> frequencies[K]; 
}
parameters{
  real <lower=1> alpha;
}
model{
  for (k in 1:K) target += frequencies[k] * power_law_lpmf(values[k] | alpha);
}

with errors like

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