RE: Status of UML 2.0

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From: Mitch Kokar (
Date: Fri 25 Oct 2002 - 20:08:33 BST

RE: Status of UML 2.0Robert,

I think a UML model defines constaraints on the programs that are consistent
with the model. And constratints don't need to be ambiguous just because
they are constraints. They describe subsets or classes of things. Is a<b
ambiguous on say natural numbers?


  -----Original Message-----
[]On Behalf Of Bauer, Robert
  Sent: Friday, October 25, 2002 12:58 PM
  To: ''
  Subject: RE: Status of UML 2.0


  Let me address the various responses in this one email.  If I forgot
something, well, sorry.

  The first thing is to understand what it means to formal specify a
programming language.  We specify
  a programming language so that we can understand what a program means.  We
describe that understanding
  by defining how the "state" (I use this in a very generic sense to
encompass not only memory, but
  registers, i/o channels, etc) is modified via the "execution" of the
program.  Irrespective of the
  mechanism of the semantics (e.g., operational, axiomatic, denotational),
determining the meaning of the
  program results in a sort of symbolic execution of the program.  As a
consequence, for specific programs,
  etc., one can determine whether two programs are equivalent in the sense
that their finals states are
  equivalent, though this problem is known to be np-complete.

  So, in a very real sense, that the specification language is undeciable,
semi-undeciable, etc., is
  not critical, because we are only interested in identifying how various
constructs in the programming language
  being described modify the state.  Hence, languages like Z and HOL are
quite beneficial.  Yet, I can
  write sentences whose truth value cannot be determined in both Z and HOL;
however and fortunately, these kinds
  of sentences do not show up to describe modifications made by constructs
in a programming language.

  So, if one were to use, say HOL to describe UML, it begs an important
questions - what about UML is being

  UML is not a programming language nor is it a semantic language that
describes how the constructs of a programming language modify the state.  At
best, UML seems to capture some information about the static

  structure of a system and it is able to capture some information about the
dynamic behaviour of the system in terms of objects that get created and
some of the communication among objects.

  So, at least to me, it appears that we understand a UML model by the
program that gets generated from the UML model.  But the UML model is not a
complete specification of that program, since to do that would require a
complete specification of the programming language in which that program is
generated as well a formal specification of the desired program (and if we
had the latter, we wouldn't need the model except as an

  example of "one" implementation of the specifcation - we know that in each
programming language there are a countably finite set of programs with
equivalent semantics).

  Following this chain of reasoning - then UML stands as sort of
meta-program that by definition is an incomplete description of the program
being represented.  This begs the question to determine what parts of the
program are represented?  And, of course, how are they being represented?
It is my contention that any such representation may be ambiguous
(unambiguity can't be proven)/inconsistent (inconsistency can't be proved).


  -----Original Message-----
  From: []
  Sent: Friday, October 25, 2002 7:55 AM
  Subject: RE: Status of UML 2.0

  > -----Original Message-----
  > From: Hubert Baumeister []
  > >
  > > For example, given some program P, I wish to determine it's
  > meaning.
  > > To
  > > do so requires that I have
  > > a formal semantics, one that is unambiguous and complete in
  > the sense
  > > that every sentence constructed
  > > in the implementation language has only one interpretation in the
  > > specification language - but that requires
  > > me to show that the specification language itself is
  > unambiguous - which
  > > in general can't be done.
  > So what your are saying is, that it is impossible to give a
  > precise mathematical semantics to
  > programming language constructs?

  Correct me if I'm wrong but I believe Modula-2 was specified using VDM.

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