+Next we'll add aliasing as described at the end of [[week9]]. We'll also add the ability to pass (implicit) reference cells as arguments to a function, which lets changes made within the function body to be effective in the outside environment. When we discussed this in [[week9]], we proposed a different syntactic form for the function values that get called in this way. Instead of:
+
+ let f = lambda (y) -> ...
+ ...
+ in f x
+
+one would write:
+
+ let f = lambda (alias y) -> ...
+ ...
+ in f x
+
+Real programming languages that have this ability, such as C++, do something analagous. Here the function is declared so that *all* of its applications are expected to alias the supplied argument. You can always work around that in a particular case, though, like this:
+
+ let f = lambda (alias y) -> ...
+ ...
+ in let y = x ; creates new (implicit) reference cell with x's value
+ in f y
+
+In our present framework, it will be easier to do things differently. We will
+introduce a new syntactic forms at the location where a function value is
+applied, rather than in the function's declaration. So we will say instead:
+
+ Let ('f',
+ Lambda ('y', ...),
+ ...
+ Apply(Variable 'f', Variable 'x')...)
+
+for the familiar, passing-by-value behavior, and:
+
+ Let ('f',
+ Lambda ('y', ...),
+ ...
+ Applyalias(Variable 'f', 'x')...)
+
+for the proposed new, passing-by-reference behavior. (Besides being easier to implement here, this strategy also has the advantage of more closely aligning with the formal system Jim discusses in his "Hyper-evaluativity" paper.) Note that the second parameter to the `Applyalias` form is just `'x'`, not `Variable 'x'`. This is because (1) only variables are acceptable there, not arbitrary expressions, and (2) we don't need at that point to compute the variable's present value.
+
+Here is our expanded language:
+