General shape of (1-arg) higher-order counterexample in Racket

higher-order-counterexample-template.rkt

(define L
  (λ (x)
    (cond
      ;; `x` is higher order
      [(proc? x)
       (cond ;; Send message `L_x` to `x` and transfer controll to `L_f`, with `L_f`'s shape to be decided
             [L_1 ((L_f (x L_x)) x)]
             ;; Return closure referencing `x`, with `L_g`'s shape to be decided
             ;; Shu-Hung pointed out that this case was redundant
             ;; [L_2 (λ (y) ((L_g x) y))]
             ;; Return constant
             [else L_a])]
      ;; `x` is first-order
      [else (L' x)])))
      
;; where ...
(define L' (λ (x) #|dispatch on first-order `x`|#))
(define-values (L_f L_g L_a L_x) #|constants, first or higher-order|#)
(define-values (L_1 L_2) #|constants, only truth values matter|#)