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    <h2>What <code>let*</code> expands to</h2> <p>This:</p> <pre><code>(let* ([a 1] [b (* 2 a)]) (cons a b)) </code></pre> <p>expands to this:</p> <pre><code>((lambda (a) ((lambda (b) (cons a b)) (* 2 a))) 1) </code></pre> <p>Here's a nice way to think of what <code>lambda</code> means in Scheme (nice because it's both simple and accurate): it's both a label for a place in the program <em>and</em> a scope for bound variables. In Scheme, a label for a place in the program (like what you can <code>goto</code> to in other languages or branch to in machine language) always goes with a scope for bound variables. You can only "goto" a place in the program by supplying values to bind to the variables bound within its scope. </p> <p>Scheme's <code>let</code> is a way of saying, "I want to make a scope where these variables are bound, but I don't want to wait until later to tell their values. I want to specify their values right here." So, <code>let</code> is just a macro that makes the lambda and then supplies the values right there.</p> <p>If you want the values of one of the variables to be an expression that uses another of the variables, like the way <code>b</code> is expressed in terms of <code>a</code> above, then <code>b</code> has to be defined within the scope of <code>a</code>. Hence the <code>let*</code> macro, which defines each successive variable in a scope that includes the previous variable. Since we have a bunch of nested scopes, they are implemented by a bunch of nested lambdas.</p> <h2>The macro</h2> <p>Here's how to tell Scheme how to rewrite a <code>let*</code> as a bunch of nested lambdas and function applications:</p> <pre><code>(define-syntax let* (syntax-rules () [(__ () body ...) (begin body ...)] [(__ ([v e] [v* e*] ...) body ...) ((lambda (v) (let* ([v* e*] ...) body ...)) e)])) (let* ([a 1] [b (* 2 a)]) (cons a b)) =&gt; (1 . 2) </code></pre> <p>In <a href="http://www.scheme.com/petitechezscheme.html" rel="nofollow">Chez Scheme</a>, you can play around with this in the REPL by typing <code>(expand '(let* ([a 1] [b (* 2 a)]) (cons a b))</code> and seeing what comes out. Here's what comes out when I try it:</p> <pre><code>(let ([#:a 1]) (let ([#:b (#2%* 2 #:a)]) (#2%cons #:a #:b))) </code></pre>
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