-evaluates to? Well, the right-hand side of the second binding will evaluate to `(1, 2)`, because it uses the outer binding of `x` to `0` for the right-hand side of its own binding `x match x + 1`. That gives us a new binding of `x` to `1`, which is in place when we evaluate `(x, 2*x)`. That's why the whole right-hand side of the second binding evaluates to `(1, 2)`. So `y` gets bound to `1` and `z` to `2`. But now what is `x` bound to in the final line? The binding of `x` to `1` was in place only until we got to `(x, 2*x)`. After that its scope expired, and the original binding of `x` to `0` reappears. So the final line evaluates to `([1, 2], 0)`.
+evaluates to? Well, consider the right-hand side of the second binding:
+
+ let
+ x match x + 1
+ in (x, 2*x)
+
+This expression evaluates to `(1, 2)`, because it uses the outer binding of `x` to `0` for the right-hand side of its own binding `x match x + 1`. That gives us a new binding of `x` to `1`, which is in place when we evaluate `(x, 2*x)`. That's why the whole thing evaluates to `(1, 2)`. So now returning to the outer expression, `y` gets bound to `1` and `z` to `2`. But now what is `x` bound to in the final line,`([y, z], x)`? The binding of `x` to `1` was in place only until we got to `(x, 2*x)`. After that its scope expired, and the original binding of `x` to `0` reappears. So the final line evaluates to `([1, 2], 0)`.
+
+This is very like what happens in ordinary predicate logic if you say: ∃ `x. F x and (` ∀ `x. G x ) and H x`. The `x` in `F x` and in `H x` are governed by the outermost quantifier, and only the `x` in `G x` is governed by the inner quantifier.
+
+### That's enough ###
+
+This was a lot of material, and you may need to read it carefully and think about it, but none of it should seem profoundly different from things you're already accustomed to doing. What we worked our way up to was just the kind of recursive definitions of `factorial` and `length` that you volunteered in class, before learning any programming.
+
+You have all the materials you need now to do this week's [[assignment|assignment1]]. Some of you may find it easy. Many of you will not. But if you understand what we've done here, and give it your time and attention, we believe you can do it.