尾递归函数将元素追加到列表 [英] tail-recursive function appending element to list

问题描述

我已经看到了几个将元素实现 append 到列表中的示例，但是都没有使用 tail recursion .如何以功能样式实现这种功能?

i've seen several examples of implementing append an element to a list, but all are not using tail recursion. how to implement such a function in a functional style?

 (define (append-list lst elem)
    expr)

推荐答案

以下是 tail递归模态优化优化，从而生成完全尾部递归代码.它复制输入结构，然后以自上而下的方式通过突变将新元素附加到该结构上.由于此突变是针对其内部新创建的数据完成的，因此它在外部仍然可以使用(不更改传递给它的任何数据，除了产生其结果外，没有可观察到的效果):

The following is an implementation of tail recursion modulo cons optimization, resulting in a fully tail recursive code. It copies the input structure and then appends the new element to it, by mutation, in the top-down manner. Since this mutation is done to its internal freshly-created data, it is still functional on the outside (does not alter any data passed into it and has no observable effects except for producing its result):

(define (add-elt lst elt)
  (let ((result (list 1)))
    (let loop ((p result) (lst lst))
      (cond 
        ((null? lst) 
           (set-cdr! p (list elt)) 
           (cdr result))
        (else 
           (set-cdr! p (list (car lst)))
           (loop (cdr p) (cdr lst)))))))

我喜欢使用头部前哨"技巧，它大大简化了代码，但只分配了一个额外的cons单元.

I like using a "head-sentinel" trick, it greatly simplifies the code at a cost of allocating just one extra cons cell.

此代码使用低级突变原语来完成某些语言(例如Prolog)由编译器自动完成的操作.在TRMC优化假设方案中，我们将能够编写以下尾递归 modulo cons 代码，并让编译器自动将其翻译为与上述代码等效的代码:

This code uses low-level mutation primitives to accomplish what in some languages (e.g. Prolog) is done automatically by a compiler. In TRMC-optimizing hypothetical Scheme, we would be able to write the following tail-recursive modulo cons code, and have a compiler automatically translate it into some equivalent of the code above:

(define (append-elt lst elt)              ;; %% in Prolog:
  (if (null lst)                          ;; app1( [],   E,R) :- Z=[X].
    (list elt)                            ;; app1( [A|D],E,R) :-
    (cons (car lst)                       ;;  R = [A|T], % cons _before_
          (append-elt (cdr lst) elt))))   ;;  app1( D,E,T). % tail call

如果不执行 cons 操作，则 append-elt 将为尾递归.这就是TRMC优化发挥作用的地方.

If not for the cons operation, append-elt would be tail-recursive. This is where the TRMC optimization comes into play.

2021更新:当然，具有 tail-recursive 函数的全部要点是表示一个循环(以函数样式，是的)，因此例如，例如常见的Lisp(在CLISP实现中)，循环表达式

2021 update: of course the whole point of having a tail-recursive function is to express a loop (in a functional style, yes), and so as an example, in e.g. Common Lisp (in the CLISP implementation), the loop expression

(loop for x in '(1 2) appending (list x))

(这是一种高级规范-y甚至没有以其自身非常特定的方式起作用)被翻译成相同的尾部约束单元跟踪和更改样式:

(which is kind of high-level specification-y if not even functional in its own very specific way) is translated into the same tail-cons-cell tracking and altering style:

[20]> (macroexpand '(loop for x in '(1 2) appending (list x)))
(MACROLET ((LOOP-FINISH NIL (SYSTEM::LOOP-FINISH-ERROR)))
 (BLOCK NIL
  (LET ((#:G3047 '(1 2)))
   (PROGN
    (LET ((X NIL))
     (LET ((#:ACCULIST-VAR-30483049 NIL) (#:ACCULIST-VAR-3048 NIL))
      (MACROLET ((LOOP-FINISH NIL '(GO SYSTEM::END-LOOP)))
       (TAGBODY SYSTEM::BEGIN-LOOP (WHEN (ENDP #:G3047) (LOOP-FINISH))
        (SETQ X (CAR #:G3047))
        (PROGN
         (LET ((#:G3050 (COPY-LIST (LIST X))))
          (IF #:ACCULIST-VAR-3048
           (SETF #:ACCULIST-VAR-30483049
            (LAST (RPLACD #:ACCULIST-VAR-30483049 #:G3050)))
           (SETF #:ACCULIST-VAR-30483049
            (LAST (SETF #:ACCULIST-VAR-3048 #:G3050))))))
        (PSETQ #:G3047 (CDR #:G3047)) (GO SYSTEM::BEGIN-LOOP) SYSTEM::END-LOOP
        (MACROLET
         ((LOOP-FINISH NIL (SYSTEM::LOOP-FINISH-WARN) '(GO SYSTEM::END-LOOP)))
         (RETURN-FROM NIL #:ACCULIST-VAR-3048)))))))))) ;
T
[21]>

(所有结构变异基元的母亲都拼写为 R.P.L.A.C.D.)，所以这是Lisp系统(不仅是Prolog)的一个示例，它实际上做了类似的事情.

(with the mother of all structure-mutating primitives spelled R.P.L.A.C.D.) so that's one example of a Lisp system (not just Prolog) which actually does something similar.

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