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    <p>From some of Kent's students, I have learned the following: <code>letrec</code> is implemented in terms of <code>let</code> using macro expansion. It expands the <code>letrec</code> into a <code>let</code> that uses <code>set!</code> inside. So your first example would expand to this:</p> <pre><code>(let ([sum (void)]) (set! sum (lambda (x) (if (zero? x) 0 (+ x (sum (- x 1)))))) (sum 5)) </code></pre> <p>Your second, similarly (note that the nested <code>let</code>s are a result of the <code>let*</code> - also, this may not be a completely correct expansion, but is my best guess):</p> <pre><code>(let ([sum (void)] (set! sum (lambda (x) (if (zero? x) 0 (+ x (sum (- x 1)))))) (let [f (void)] (set! f (lambda () (cons n n-sum))) (let [n (void)] (set! n 15) (let [n-sum (void)]) (set! n-sum (sum n)) (f)) </code></pre> <p>I am not 600% sure how the named <code>let</code> expands, but Eli suggests that it would be implemented in terms of <code>letrec</code> itself (which makes sense and should be pretty obvious). So your named <code>let</code> moves from a named <code>let</code> into a <code>letrec</code> into an unnamed <code>let</code>. And your rewrite of the second looks almost exactly like the expansion of it anyway.</p> <p>If you are interpreting it and looking for good performance, I would lean toward the <code>letrec</code> because it is one shorter macro-expand step. Also, <code>let</code> gets turned into a lambda so you're using <code>define</code>s in your second example instead of <code>set!</code>s (which may be heavier).</p> <p>Of course, if you're compiling, it will probably all fall out in the compiler anyway so just use whichever you think looks nicer (I'm partial to <code>letrec</code> because <code>let</code> loops remind me of imperative programming but ymmv). That said, it should be up to you, stylistically (since they are more or less equivalent).</p> <p>That said, let me provide you an example that you may find worthwhile:</p> <pre><code>(letrec ([even? (lambda (n) (if (zero? n) #t (odd? (- n 1))))] [odd? (lambda (n) (if (zero? n) #f (even? (- n 1))))]) (even? 88)) </code></pre> <p>Using your internal <code>define</code> style will yield:</p> <pre><code>(let () (define even? (lambda (n) (if (zero? n) #t (odd? (- n 1))))) (define odd? (lambda (n) (if (zero? n) #f (even? (- n 1))))) (even? 88)) </code></pre> <p>So here the <code>letrec</code> code is actually shorter. And, honestly, if you're doing to do something like the latter, why not settle for <code>begin</code>?</p> <pre><code>(begin (define even? (lambda (n) (if (zero? n) #t (odd? (- n 1))))) (define odd? (lambda (n) (if (zero? n) #f (even? (- n 1))))) (even? 88)) </code></pre> <p>I suspect that <code>begin</code> is more of a built-in and, as such, will not get macro-expanded (like <code>let</code> will). Finally, <a href="https://stackoverflow.com/questions/2060744/scheme-what-are-the-benefits-of-letrec">a similar issue</a> has been raised on the Lisp stack overflow a bit ago with more or less the same point. </p>
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    1. POExample where letrec/letrec* is better than let with internal defines or named let ?
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