What is a type error?

[Joe Marshall]

Marshall wrote:
>
> I am having a hard time with this very broad definition of aliasing.

How about this definition:  Consider three variables, i, j, and k, and
a functional equivalence predicate (EQUIVALENT(i, j) returns true if
for every pure function F, F(i) = F(j)).  Now suppose i and j are
EQUIVALENT at some point, then a side effecting function G is invoked
on k, after which i and j are no longer equivalent.  Then there is
aliasing.

This is still a little awkward, but there are three main points:
  1.  Aliasing occurs between variables (named objects).
  2.  It is tied to the notion of equivalence.
  3.  You can detect it when a procedure that has no access to a value
can nonetheless modify the value.

In a call-by-value language, you cannot alias values directly, but if
the values are aggregate data structures (like in Java), you may be
able to modify a shared subcomponent.