🚀 go-pugleaf

fs@caesar.cs.tulane.edu (Frank Silbermann) writes:

  >	...
  >	D = (Atoms + Booleans + DxD + D->D)_bottom.

  >It is "untyped" in the sense that all expressions
  >denote objects of the same type -- domain D.
  >You can create lists of arbitrary elements,
  >and define functions which take and return arbitrary elements
  >(even copies of the function itself).
  >So it is not so rare actually to require only
  >the property of being an object!

If a functions semantic maps D->D, then the rare case 
is that it maps also D/bottom->D/bottom. In fact i have problems 
to imagine meaningful functions except identity which behave like this. 

If you view types as a model to ensure that expressions are
defined, then every expression has a type, since the 
programmer has some kind of theory wether his/her program 
is defined ( hope so :-) ). From the point of software 
engineering coming to terms with a formalized/communicatable 
type discipline seems to me very important.

I believe that variants of bounded universal and existential 
type quantification together with dynamic binding (modelling
whats called message passing in object-oriented languages) can make
untyped languages obsolet in future in sense of giving a unique 
framework ranging infinitely variable from "untyped" to "strong-typed"
programming style. 

--
Wolfgang Grieskamp 
wg@opal.cs.tu-berlin.de tub!tubopal!wg wg%opal@DB0TUI11.BITNET