Re: Composition vs. inheritance

From: (Stefan Ram)
26 Apr 2008 15:03:35 GMT
Patricia Shanahan <> writes:

Circle-ellipsis could be a problem. I think that OO and math
may have slightly different definitions of is-a.

Isn't this just a matter of the immutable vs. mutable issue?


  (The relation to mathematics is, that in mathematics, there is
  no concept of time and no concept of storage and nothing
  changes, so one can not argue about mutability in mathematics.)

  I have posted this some days ago, and repeat it here:


  The whole rectangle square discussion only stems
  from insufficiant care to distinguish between
  value and storage objects.

  Let Q be the set of ?quarternary digits? {0,1,2,3},
  its subset {0,1} is called B; B is ?the set of
  binary digits?. The inclusion

      B c Q (B is a subset of Q)

  is valid.

  A quartary storage q* can store a quartary digit. It
  also might be used to store a binary digit. However, one
  can not use any binary storage to store any quartenary digit.

  So, for the set of binary storages B* and the set of
  quartary storages Q*:

      Q* c B* (Q* is a subset of B*)

  In general, if every B value is a Q value, then every Q storage
  is a B storage.

  If one now does not care to distinguish between values and
  memories, this would be worded as ?If every B is a Q, then
  every Q is a B?, which is false.

  The rectangle square problem only exists as long as one does
  not make it clear whether one wants to model rectangle and
  square /values/ or rectangle and square /storages/.

                                                   end of quotation

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