Scans and reduction functions

Related to #3339, there are also common higher-order functions that return a different type than their input.

Some common options are:

• fold_left(F, T, ...) => f(f(f(f(T[0], T[1]), T[2]), ...), T[3]) (sometimes, rather than starting at T[0], an extra 'init' argument is passed)
• fold_right, which is the same idea but with the opposite association f(T[0], f(T[1], ...f(T[N], init)))
• reduce, which is defined such that it is equivalent to the above when the f is associative but does not explicitly state an order of evaluation. The cool thing about reduce is it can be parallelized, c.f. foldl and foldr Considered Slightly Harmful, and More Fun with Moniods
• scan, which returns a cumulative evaluation scan(f, T, ...) => [T[1], f(T[1], T[2]), f(f(T[1], T[2]), T3), ...]. Note that scan can also be parallelized when f is associative, c.f. Prefix Sums and their Applications. (Note: even though reduce(f, T, ...) == scan(f, T, ...)[N], the ideal parallelization algorithms actually differ)

There are other functions of questionable value to Stan in this family, like folding_map which returns both a carry and a mapped container (this is, confusingly, what JAX calls scan. Scans a-la Blelloch as described above are called associative_scan in JAX)

Start with the related issue #3339, then review the proposed semantics for fold_left, fold_right, reduce, and scan and the linked references on parallel algorithms. Before implementation, clarify which functions Stan should support and their API and evaluation requirements; done means the scope is agreed and the selected functions are implemented consistently.