尾递归版本列表附加功能 [英] a tail-recursion version list appending function

问题描述

我看到了几个将append元素实现到列表中的示例，但都没有使用 tail递归.如何以功能风格实现这样的功能?

i see 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"head-sentinel"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)                          ;; app([], X, Z) :- Z=[X].
    (list elt)                            ;; app([A|B], X, Z) :-
    (cons (car lst)                       ;;   Z=[A|Y],         % cons _before_
          (append-elt (cdr lst) elt))))   ;;   app( B, X, Y).   % tail call

如果不执行cons操作，则append-elt 将进行尾部递归.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.

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