[racket] Nested scope in D vs Racket

This brings up an interesting moment in PLAI that always elicits totally blank stares: the moment in lecture that matches this part of the book, on page 34 of the current online version:


"Hopefully we can agree that the value of this program is 8 (the left x in the addition evaluates to 5, the right x is given the value 3 by the inner with, so the sum is 8). The refined substitution algorithm, however, converts this expression into

{with {x 5} {+ 5 {with {x 3} 5}}}

which, when evaluated, yields 10. What went wrong here? Our substitution algorithm respected binding instances, but not their scope.
In the sample expression, the with introduces a new scope for the inner x. The scope of the outer x is shadowed or masked by the inner binding. Because substitution doesn’t recognize this possibility, it incorrectly substitutes the inner x.
"

Many students say to me, "but... you're not allowed to define the same name twice!"  

At a minimum, then, this discussion has an interesting association with the definition of substitution (and the teaching thereof).

John

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