Modularity for making Stan more Pythonic and Rthonic

[betanalpha]

Strong agree with everything @bgoodri says here. See also TWG Definition/Roles. Call for feedback/ideas/refinement - #11 by avehtari.

@bgoodri

95% of people that Stan — and the percentage is even higher among people who are first learning Stan — do not recognize a Stan program as defining a function from the things declared in the parameters block to the real numbers that is defined by a log-kernel. This confusion is exacerbated by people continuing to write (and teach) the theta ~ normal(mu, sigma); notation rather than the target += normal_lpdf(theta | mu, sigma); notation, but even those of us who teach the latter notation find it difficult to communicate to students that a Stan program defines a function because the function it defines does not look like a function in R, Python, or whatever interface.

I’m in the “teach target += first” camp and it has been very successful in my courses. I’ve also had no problems communicating the “a Stan program defines a function” concept, but at the same time I get to that only after four hours of background on statistics and computation, so that abstraction has already been introduced and reinforced. But I definitely agree that a tighter UX/pedagogical connection will continue to improve this, and trying to turn Stan into PyTorch will not.