Re: Partial type specifications and their ordering

[Eric Hughes <eric.eh9@gmail.com>]

On Mar 18, 2:40 am, "Dmitry A. Kazakov" <mail...@dmitry-kazakov.de>
wrote:
> Your draft does not explain why certain sets of types (called partial here)
> cannot form a proper class.

No code.  No subprogram definitions.  Nothing to execute.  The name
"partial type" can be taken as an abbreviation for "partial
specification of a type".  Pretty much every definition of types that
I've seen, starting with Godel's 1957 _Dialectica_ paper, uses some
kind of algorithm expression to define types.  A partial type strips
out algorithm expressions and focuses only on assumptions and results
of operations and on invariants about data.

> My guess is that any set of types can be associated with a class.

Any set of partial types can be associated with a least common
superclass.  That's what a lattice is.  See http://en.wikipedia.org/wiki/Lattice_%28order%29.

> Consequently, generic types (not Ada term, but the meaning is obvious) are
> fully equivalent to classes.

Please go find out what Alonzo Church meant by a lambda constructor
(which became Lisp, but is far broader than Lisp).  Barring
degeneracies, a generic type has a higher minimal lambda recursion
level than an ordinary type.  If you'd rather use a programming
language that treats type recursion as basic, try a functional
language such as Haskell.

Partial types specification are a notion orthogonal to generics.

Eric