Function-level programming a la Backus

flp.clj

(ns flp
  "Function-level programming a la Backus; see
   http://www.stanford.edu/class/cs242/readings/backus.pdf"
  (:refer-clojure :exclude [/]))

;;; Functional Forms - combine existing functions to form new ones.

(def ^{:doc "Composition"} ° comp)

(defn / [f]
  "Insert"
  (partial reduce f))

(defn α [f]
  "ApplyToAll"
  (partial map (partial apply f)))

;;; Functions - take and return non-functions (atoms).

(defn Trans [coll]
  "Transpose"
  (apply map vector coll))

;;; Compute the inner product.

(def IP (° (/ +) (α *) Trans))

(comment
  (IP [[1 2 3] [6 5 4]]) ;=> 28
)

I think that's the point: (comp f g) is not "creating", while (define f (lambda ...)) must be. FLP does not allow the latter.