#lang racket
(define (nock-eval nock k)
    (match nock
      ; Cell at head of formula, evaluate both formulae and return as cell
      ([cons (var a) (cons (cons (var b) (var c)) (var d))]
       (nock-eval (cons a (cons b c)) (nock-cell-1 a d k)))
      ; literal tree index into subject
      ([cons (var a) (cons 0 b)] (nock-tree-find a b k))
      ; literal
      ([cons _ (cons 1 b)] (apply-k k b))
      ; evaluate b with subject a
      ; evaluate c with subject a
      ; evaluate result of c with result of b as subject
      ([cons (var a) (cons 2 (cons (var b) (var c)))]
        (nock-eval (cons a b) (nock-2-1 a c k)))
      ; evaluate b with a as subject, return 0 if cell and 1 if atom
      ([cons (var a) (cons 3 (var b))]
       (nock-eval (cons a b) (nock-3-1 k)))
      ; evaluate b with a as subject, return atom-value of result incremented by 1
      ([cons (var a) (cons 4 (var b))]
       (nock-eval (cons a b) (nock-4-1 k)))
      ; Test for structural equality between 2 nouns
      ([cons (var a) (cons 5 (cons (var b) (var c)))]
       (nock-eval (cons a b) (nock-5-1 a c k)))
      ; Here we deviate from slavishly following the spec to a symbolically-evaluated reduction of the spec
      ; Evaluate b with subject a. If 0 then evaluate c with subject a, else evaluate d with subject a
      ;
      ; Note that in the CPS transformation we do *not* evaluate the branches first and then
      ; test for which result to feed the continuation.
      ([cons (var a) (cons 6 (cons (var b) (cons (var c) (var d))))]
       (nock-eval (cons a b) (nock-6-1 a c d k)))
      ; Evaluate b with subject a, use result as subject and evaluate c
      ([cons (var a) (cons 7 (cons (var b) (var c)))]
       (nock-eval (cons a b)) (nock-7-1 c k))
      ; Evaluate b with subject a, add result to subject a and evaluate c
      ([cons (var a) (cons 8 (cons (var b) (var c)))]
       (nock-eval (cons a b) (nock-8-1 a c k)))
      ; Evaluate c with subject a to get a core, look up address b in the core and use it as a formula with the core
      ; as the subject
      ([cons (var a) (cons 9 (cons (var b) (var c)))]
       (nock-eval (cons a c) (nock-9-1 b k)))
      ; Replace the address specified by b in the result of c with subject a with the result of d with subject a
      ([cons (var a) (cons 10 (cons (cons (var b) (var c)) (var d)))]
       (nock-eval (cons a c) (nock-10-1 a b d k)))
      ; Cell hint, compute then discard
      ([cons (var a) (cons 11 (cons (cons (var b) (var c)) (var d)))]
       (nock-eval (cons b c) (nock-11-1 a d k)))  
      ; Atom hint, discard
      ([cons (var a) (cons 11 (cons _ (var c)))]
       (nock-eval a c k))
      ; Atom, return
      ([var a] (apply-k k a))))

; continuation definitions for the cell-formula case
(define (nock-cell-1 a d k)
 (lambda (abc) (nock-eval (cons a d) (nock-cell-2 abc k))))

(define (nock-cell-2 abc k)
 (lambda (ad) (apply-k k (cons abc ad))))

; continuation definitions for nock 2
(define (nock-2-1 a c k)
 (lambda (ab) (nock-eval (cons a c) (nock-2-2 ab k))))

(define (nock-2-2 ab k)
 (lambda (ac) (nock-eval (cons ab ac) k)))

; continuation definition for nock 3
(define (nock-3-1 k)
  (lambda (ab) (if (pair? ab) (apply-k k 0) (apply-k k 1))))

; continuation definition for nock 4
(define (nock-4-1 k)
  (lambda (ab) (apply-k k (+ 1 ab))))

; continuation definitions for nock 5
(define (nock-5-1 a c k)
  (lambda (ab) (nock-eval (cons a c) (nock-5-2 ab k))))

(define (nock-5-2 ab k)
  (lambda (ac) (if (= ab ac) (apply-k k 0) (apply-k k 1))))

; continuation definitions for nock 6
(define (nock-6-1 a c d k)
 (lambda (ab) (if (= ab 0) (nock-eval (cons a c) k) (nock-eval (cons a d) k))))

; continuation definitions for nock 7
(define (nock-7-1 c k)
 (lambda (ab) (nock-eval (cons ab c) k)))

; continuation definitions for nock 8
(define (nock-8-1 a c k)
  (lambda (ab) (nock-eval (cons (cons ab a) c) k)))

; continuation definitions for nock 9
(define (nock-9-1 b k)
 (lambda (core) (nock-tree-find core b (nock-9-2 core k))))

(define (nock-9-2 core k)
 (lambda (arm) (nock-eval (cons core arm) k)))

; continuation definitions for nock 10
(define (nock-10-1 a b d k)
 (lambda (ac) (nock-eval (cons a d) nock-10-2)))

(define (nock-10-2 ac b k)
 (lambda (ad) (nock-tree-edit ac b ad k)))

; continuation definitions for nock 11
(define (nock-11-1 a d k)
  (lambda (_) (nock-eval (cons a d) k)))

; / operator in nock spec: tree addressing
(define (nock-tree-find tree address k)
    (if (= address 1) (apply-k k tree)
        (nock-tree-find (if (even? address) (car tree) (cdr tree)) (quotient address 2) k)))

; # operator in nock spec: tree editing
(define (nock-tree-edit subtree address tree k)
    (if (= address 1) (apply-k k subtree)
      (if (even? address)
          (nock-tree-edit subtree (quotient address 2) (car tree) (nock-tree-edit-even tree k))
          (nock-tree-edit subtree (quotient address 2) (cdr tree) (nock-tree-edit-odd tree k)))))

(define (nock-tree-edit-even tree k) (lambda (x) (k (cons x (cdr tree)))))
(define (nock-tree-edit-odd tree k) (lambda (x) (k (cons (car tree) x))))

(define (apply-k k^ v)
  (k^ v))

(define tree23 (cons 2 3))
(define (get x) (cons 0 x))
(define (const x) (cons 1 x))
(define (call x y) (cons 9 (cons x y)))
(define (declare x y) (cons 8 (cons x y)))

(nock-eval (cons tree23 (get 1)) identity)
(nock-eval (cons 4 (declare (const tree23) (get 4))) identity)
(nock-eval (cons (declare (const tree23) (get 4)) (call 1 (get 1))) identity)