Lambda the Ultimate

I learned just today that Jacob Schwartz, a mathematician and computer scientist, has died on March 2. He was the designer of SETL. Here is an obituary.

I am looking for examples of what I call a "tiered" approach to higher order programming. At the base, you'd have objects (numbers, strings, etc). Above that, you'd have functions which map objects to objects. At the top, you'd have functionals which map functions to functions. Neither functions nor functionals would be first class objects, nor could you pass a function to a function or a functional to a functional.

My thinking is that this approach would offer most of the benefits of the typical higher order approach while making reasoning easier. For example, certain forms of type inference become practical that would be undecidable in a language with first class functions.

Does any language like this currently exist? Backus's FP is similar but it does not allow the definition of new functionals. FL lifts this restriction but adds first class functions. I'm looking for something in the middle.

To put it another way, I'm looking for a higher order language like Lisp or ML but with the restriction that functions can only be constructed and passed statically.

Edit: I should note that because all functions provided to functionals are statically known, programs in such a language would be trivially reducible to first order programs. The 'functionals' would be acting very much like glorified macros.