Dr Scheme example

This thread began with @mister-fett’s small DrScheme GUI sketch and later includes two practical requests: @bexta87 asked for decimal→binary conversion and @nwest posted an attempted routine for list nesting depth. The two compact, idiomatic Scheme snippets below (portable across PLT/Racket and most R5RS-compatible interpreters with only minor name differences) provide correct behavior and clarify common pitfalls found in the earlier posts.

Decimal → binary (returns a list of bits, MSB first; zero yields '(0); negative inputs signal an error):

(define (decimal->binary n)
  (cond ((< n 0) (error "decimal->binary: negative input"))
        ((= n 0) '(0))
        (else
         (let loop ((q n) (acc '()))
           (if (= q 0)
               acc
               (loop (quotient q 2) (cons (remainder q 2) acc)))))))

(define (binary->string bits)
  (apply string-append (map number->string bits)))

Notes: decimal->binary is tail-recursive and runs in O(log n) time and space (number of bits). The helper binary->string is convenience for display in implementations that provide string-append and number->string.

Corrected list-depth (definition used here: atoms have depth 0; the empty list counts as depth 1; a non-empty list has depth 1 + max depth of its elements):

(define (list-depth x)
  (letrec ((max2 (lambda (a b) (if (> a b) a b)))
           (elem-depth
            (lambda (y)
              (cond ((null? y) 1)
                    ((pair? y) (+ 1 (max-elems y)))
                    (else 0))))
           (max-elems
            (lambda (s)
              (if (null? s) 0
                  (max2 (elem-depth (car s)) (max-elems (cdr s)))))))
    (elem-depth x)))

Clarification: @nwest’s original attempt treated the empty list specially but only recursed on one branch; the corrected version inspects both car and cdr and computes the maximum depth across elements. These routines are small, explicit, and suitable to paste into an old DrScheme/PLT environment (modern Racket may accept them unchanged).