Re: an idea about possreps

From: David BL <davidbl_at_iinet.net.au>
Date: Sun, 3 Feb 2008 18:46:20 -0800 (PST)
Message-ID: <9e1d980f-4837-4858-b18f-5b90fe249ca4_at_b2g2000hsg.googlegroups.com>


On Feb 3, 11:59 pm, Jan Hidders <hidd..._at_gmail.com> wrote:
> On 3 feb, 05:31, Marshall <marshall.spi..._at_gmail.com> wrote:
>
> > I just had this idea about possreps.
>
> > In another context, someone discussing methods, or functions
> > that are bound very closely to a specific type, commented
> > that he thought that such functions should be extremely
> > limited, rather than the grab-bag that OOP usually produces.
> > I thought this a rather interesting comment, and after thinking
> > about it for a long time decided it was a good comment,
> > but that I didn't really know how to measure how well a
> > design achieved that goal.
>
> That's actually not that hard. You can formalize this by introducing a
> notion of completeness that says that a set of operations for a
> certain type / domain is complete if it holds that when we add the
> domain / type and its operations to a computationally complete
> programming or query language it stays computationally complete (*).
>
> A set of operations is then called essential for a domain if any
> proper subset of them is not complete in the above sense. Note that
> this set is not necessarily unique.
>
> (*) Computationally complete is a stronger notion than Turing
> complete. In many cases the two coincide, but here their difference
> matters. Roughly it means that for all types available in the language
> you can express all computable functions over these types.

I think in practice one would typically only define the set of all computable functions over a given type indirectly by defining a set of essential operators. IOW, essential operators seem to have an axiomatic character to me. Received on Mon Feb 04 2008 - 03:46:20 CET

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