Applicative functors analysis

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I've been trying to learn about static analysis of applicative functors. Many sources say that an advantage of using them over monads is the susceptibility to static analysis.

However, the only example I can find of actually performing static analysis is too complicated for me to understand. Are there any simpler examples of this?

Specifically, I want to know if I can performing static analysis on recursive applications. For example, something like:

y = f <$> x <*> y <*> z

When analyzing the above code, is it possible to detect that it is recursive on y? Or does referential transparency still prevent this from being possible?

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