王垠四十行代码mark

最近接触到一些关于CPS编程风格的东西，就去看了看曾今轰动一时的王垠四十行代码，看完有种隔行如隔山的感觉。目前只知道这些代码能够自动把一个递归函数转化成尾递归的形式，其他的就一窍不通了，只能先把代码本身保存下来以后再研究了

;; A simple CPS transformer which does proper tail-call and does not
;; duplicate contexts for if-expressions.

;; author: Yin Wang ([email protected])


(load "pmatch.scm")


(define cps
  (lambda (exp)
    (letrec
        ([trivial? (lambda (x) (memq x '(zero? add1 sub1)))]
         [id (lambda (v) v)]
         [ctx0 (lambda (v) `(k ,v))]      ; tail context
         [fv (let ([n -1])
               (lambda ()
                 (set! n (+ 1 n))
                 (string->symbol (string-append "v" (number->string n)))))]
         [cps1
          (lambda (exp ctx)
            (pmatch exp
              [,x (guard (not (pair? x))) (ctx x)]
              [(if ,test ,conseq ,alt)
               (cps1 test
                     (lambda (t)
                       (cond
                        [(memq ctx (list ctx0 id))
                         `(if ,t ,(cps1 conseq ctx) ,(cps1 alt ctx))]
                        [else
                         (let ([u (fv)])
                           `(let ([k (lambda (,u) ,(ctx u))])
                              (if ,t ,(cps1 conseq ctx0) ,(cps1 alt ctx0))))])))]
              [(lambda (,x) ,body)
               (ctx `(lambda (,x k) ,(cps1 body ctx0)))]
              [(,op ,a ,b)
               (cps1 a (lambda (v1)
                         (cps1 b (lambda (v2)
                                   (ctx `(,op ,v1 ,v2))))))]
              [(,rator ,rand)
               (cps1 rator
                     (lambda (r)
                       (cps1 rand
                             (lambda (d)
                               (cond
                                [(trivial? r) (ctx `(,r ,d))]
                                [(eq? ctx ctx0) `(,r ,d k)]  ; tail call
                                [else
                                 (let ([u (fv)])
                                   `(,r ,d (lambda (,u) ,(ctx u))))])))))]))])
      (cps1 exp id))))




;;; tests

;; var
(cps 'x)
(cps '(lambda (x) x))
(cps '(lambda (x) (x 1)))


;; no lambda (will generate identity functions to return to the toplevel)
(cps '(if (f x) a b))
(cps '(if x (f a) b))


;; if stand-alone (tail)
(cps '(lambda (x) (if (f x) a b)))


;; if inside if-test (non-tail)
(cps '(lambda (x) (if (if x (f a) b) c d)))


;; both branches are trivial, should do some more optimizations
(cps '(lambda (x) (if (if x (zero? a) b) c d)))


;; if inside if-branch (tail)
(cps '(lambda (x) (if t (if x (f a) b) c)))


;; if inside if-branch, but again inside another if-test (non-tail)
(cps '(lambda (x) (if (if t (if x (f a) b) c) e w)))


;; if as operand (non-tail)
(cps '(lambda (x) (h (if x (f a) b))))


;; if as operator (non-tail)
(cps '(lambda (x) ((if x (f g) h) c)))


;; why we need more than two names
(cps '(((f a) (g b)) ((f c) (g d))))



;; factorial
(define fact-cps
  (cps
   '(lambda (n)
      ((lambda (fact)
         ((fact fact) n))
       (lambda (fact)
         (lambda (n)
           (if (zero? n)
               1
               (* n ((fact fact) (sub1 n))))))))))

;; print out CPSed function
(pretty-print fact-cps)
;; =>
;; '(lambda (n k)
;;    ((lambda (fact k) (fact fact (lambda (v0) (v0 n k))))
;;     (lambda (fact k)
;;       (k
;;        (lambda (n k)
;;          (if (zero? n)
;;            (k 1)
;;            (fact
;;             fact
;;             (lambda (v1) (v1 (sub1 n) (lambda (v2) (k (* n v2))))))))))
;;     k))


((eval fact-cps) 5 (lambda (v) v))
;; => 120

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