Iteration - Revised(5) Scheme

— library syntax: (do ((<variable1> <init1> <step1>)

...) (<test> <expression> ...) <command> ...) Do is an iteration construct. It specifies a set of variables to be bound, how they are to be initialized at the start, and how they are to be updated on each iteration. When a termination condition is met, the loop exits after evaluating the <expression>s.
Do expressions are evaluated as follows: The <init> expressions are evaluated (in some unspecified order), the <variable>s are bound to fresh locations, the results of the <init> expressions are stored in the bindings of the <variable>s, and then the iteration phase begins.
Each iteration begins by evaluating <test>; if the result is false (see section see Booleans), then the <command> expressions are evaluated in order for effect, the <step> expressions are evaluated in some unspecified order, the <variable>s are bound to fresh locations, the results of the <step>s are stored in the bindings of the <variable>s, and the next iteration begins.
If <test> evaluates to a true value, then the <expression>s are evaluated from left to right and the value(s) of the last <expression> is(are) returned. If no <expression>s are present, then the value of the do expression is unspecified.
The region of the binding of a <variable> consists of the entire do expression except for the <init>s. It is an error for a <variable> to appear more than once in the list of do variables.
A <step> may be omitted, in which case the effect is the same as if (<variable> <init> <variable>) had been written instead of (<variable> <init>).
(do ((vec (make-vector 5))
          (i 0 (+ i 1)))
         ((= i 5) vec)
       (vector-set! vec i i))               ==>  #(0 1 2 3 4)
     
     (let ((x '(1 3 5 7 9)))
       (do ((x x (cdr x))
            (sum 0 (+ sum (car x))))
           ((null? x) sum)))                ==>  25
     
— library syntax: let <variable> <bindings> <body>
“Named let” is a variant on the syntax of let which provides a more general looping construct than do and may also be used to express recursions. It has the same syntax and semantics as ordinary let except that <variable> is bound within <body> to a procedure whose formal arguments are the bound variables and whose body is <body>. Thus the execution of <body> may be repeated by invoking the procedure named by <variable>.
(let loop ((numbers '(3 -2 1 6 -5))
                (nonneg '())
                (neg '()))
       (cond ((null? numbers) (list nonneg neg))
             ((>= (car numbers) 0)
              (loop (cdr numbers)
                    (cons (car numbers) nonneg)
                    neg))
             ((< (car numbers) 0)
              (loop (cdr numbers)
                    nonneg
                    (cons (car numbers) neg)))))
               ==>  ((6 1 3) (-5 -2))
     

4.2.4 Iteration