🚀 go-pugleaf

In article <BEVAN.92Apr14015933@panda.cs.man.ac.uk> bevan@cs.man.ac.uk (Stephen J Bevan) writes:
| In article <STEPHEN.92Apr13034706@estragon.uchicago.edu> stephen@estragon.uchicago.edu (Stephen P Spackman) writes:
|    In article <BEVAN.92Apr10173700@panda.cs.man.ac.uk> bevan@cs.man.ac.uk (Stephen J Bevan) writes:
|    [ type is a "hidden value" that is optimised away in most languages
|	with static typing ]
|
|    Nononono! If this were an accurate description, then the type would be
|    stored in a field (possibly optimisaed away!) whose type was described
|    by a field of type ?
|
| Why do I have to give the "type" field a "type" using the same
| construction mechanism?  Trying to do so obviously results in the same
| sort of problem as trying to define the set of all sets.  Why can't I
| punt on the issue and call the type field an instance of special
| "type" which itself can't appear in the "type" field?  (Forgive me if
| this is straying too far, but isn't a similar "trick" done in category
| theory, where there are "small" and "large" categories?)

(1) there are perfectly sound type theories with type: type (even if I
don't personally understand why), as has been known for many years.

(2) you were claiming that every value has a type field associated
with it, and the value of the type field is optimised out. So the
content of a type field is a value. So it has a type field, which has
a value. It was your idea, not mine....

It happens that I think your analysis is perfectly reasonable on an
intuitive level, and I normally think about it in almost this way, but
I think it's crucial to insist that the process is founded somewhere:
at some point there is static typing and the system a priori knows the
object's type. It just happens that in lisp or smalltalk or APL there
is only ONE type that is known to the system (unless you worry about
functions, anyway).
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stephen p spackman         Center for Information and Language Studies
stephen@estragon.uchicago.edu                    University of Chicago
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