## CHECK-SUM

assigning ``often unique'' integers to files and objects
Major Section: MISCELLANEOUS

A ``check sum'' is an integer in some fixed range computed from the
printed representation of an object, e.g., the sum, modulo `2**32`

, of
the ascii codes of all the characters in the printed
representation.

Ideally, you would like the check sum of an object to be uniquely
associated with that object, like a fingerprint. It could then be
used as a convenient way to recognize the object in the future: you
could remember the check sum (which is relatively small) and when an
object is presented to you and alleged to be the special one you
could compute its check sum and see if indeed it was. Alas, there
are many more objects than check sums (after all, each check sum is
an object, and then there's `t`

). So you try to design a check sum
algorithm that maps similar looking objects far apart, in the hopes
that corruptions and counterfeits -- which appear to be similar to
the object -- have different check sums. Nevertheless, the best you
can do is a many-to-one map. If an object with a different check
sum is presented, you can be positive it is not the special object.
But if an object with the same check sum is presented, you have no
grounds for positive identification.

The basic check sum algorithm in ACL2 is called `check-sum-obj`

, which
computes the check sum of an ACL2 object. Roughly speaking, we scan
the print representation of the object and, for each character
encountered, we multiply the ascii code of the character times its
position in the stream (modulo a certain prime) and then add (modulo
a certain prime) that into the running sum. This is inaccurate in
many senses (for example, we don't always use the ascii code and we
see numbers as though they were printed in base 127) but indicates
the basic idea.

ACL2 uses check sums to increase security in the books
mechanism; see certificate.