Refactor: encapsulate variadic functions in typechecking

[WardBrian]

In anticipation of #576 and potential future variadic higher-order functions, I decided it was worth taking a good look at cleaning up the shared code between existing variadic functions.

The DAE and ODE functions, and the future solve_newton etc are completely described by a few rules:

1. What type does the higher-order function itself return?
2. What arguments are for this function, rather than passed to the first argument (I named these the control_args)?
3. What return type do we require for the function passed in?
4. What, if any, arguments do we require for the function passed in?

This PR reorganizes the existing code around this to remove current duplication and prevent more going foward.

Note that the above are not sufficient to capture reduce_sum, since item 4 is actually dynamic depending on the first argument. So, for now at least, this is left as a special case.

This would also let us try to print these as part of --dump-stan-math-signatures eventually, if we wanted to.

Finally, I'd like to note that it would eventually be nice to also clean up the code gen for these higher-order functions, which is currently also very special cased due to the differing positions of arguments, different requirements for functors being generated, etc.

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