Dear John,

> 1. Is there a way to catch overflow exceptions within an entire 
>    computation?
> 2. Is there a way to tell OCaml that ints really are either 
>    (a) bignums or
>    (b) overflow-protected ints (as in SML/NJ, for instance)

Solution (a) is problematic because of literals.  It's easy to
redefine the infix `+' operator to mean "bignum addition", and
similarly for other arithmetic operators, but OCaml has no syntax for
bignum literals, e.g. to get the bignum 123 one needs to type
Int 123 or num_of_string "123".  A Camlp4 syntax extension could
possibly do the job, however.

Solution (b) is much easier, provided you don't care much for
performance (probably true for an intro course).  Stick the following
definitions in, say, CS101.ml

  exception Overflow

  let ( + ) a b =
    let c = a + b in
    if (a lxor b) lor (a lxor (lnot c)) < 0 then c else raise Overflow

  let ( - ) a b =
    let c = a - b in
    if (a lxor (lnot b)) lor (b lxor c) < 0 then c else raise Overflow

  let ( * ) a b =
    let c = a * b in
    if Int64.of_int c = Int64.mul (Int64.of_int a) (Int64.of_int b)
    then c else raise Overflow

  let ( / ) a b =
    if a = min_int && b = -1 then raise Overflow else a / b

[Note that the definition of ( * ) above assumes a 32-bit processor.
 Something even less efficient is required to work both on 32- and 64-bit
 architectures.]

Compile this source to CS101.cmo and make sure that the module CS101 is
linked and opened in the students' code.  For instance, with the
interactive toplevel loop, make them stick

   #load "/path/to/CS101.cmo";;
   #directory "/path/to";;
   open CS101;;

in $HOME/.ocamlinit, and voila, every time they start ocaml, they get
overflow-protected integers.

Don't even think of modifying the OCaml bytecode interpreter so that
the arithmetic operations of the abstract machine perform overflow
detection: some code in the standard library and the compilers rely on
modulo arithmetic.

Hope this helps,

- Xavier

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