🚀 go-pugleaf

On 26 Oct 90 15:59:37 GMT, anw@maths.nott.ac.uk (Dr A. N. Walker) said:

anw> How do I express the identity of one node with another [ie, perhaps
anw> the same node, but reached via some chain of edges]?  How do I
anw> *draw* it?

pcg> This is a thing on which I have already commented, but I love
pcg> repeating myself. The correct way to implement identity is by
pcg> contents, not location.

anw> But why should I have to invent a contents, just so that I can
anw> avoid referring to location?

You are not inventing a content -- what you call "location" here is part
of the contents, it is the relationship between a content and another.
It is also a content, at some higher level of abstraction.

anw> If I draw a graph with lots of nodes, and put some information
anw> (perhaps a colour, RED, GREEN, BLUE, ...)  in each, I don't
anw> necessarily want the contents to be unique.

By definition, if two entities have the same contents they are the same
entity, unless they are elementary particles and Bell's Theorem applies
:-). What actually happens is that then you put only part of the
contents in the actual data storage.

anw> On the other hand, if I'm explaining my drawing to you, I can point
anw> to nodes: "Look, *this* node connects to *that*, and so there's a
anw> path from *here* to *there*".  There's nothing wrong with location!

Then part of the contents is in the location. This is just an
implementation technique, not a concept; and it is an implementation
technique that complicates matters. When I design an entity I want to be
able to know whether it is the same or different from another entity. I
want the entity to contain all information that distinguishes it from
any other. If I do not encode information in the location I can just
look at the the entities and compare them; if I encode part of the
information in the location I also have to compare their locations.

This adds a whole new world of complication, because we need no longer
just an algebra for objects, but also an algebra for locations, and we
must prove that a program not only works ok wrt to contents, but also to
locations, and that the encoding of parts of the contents in the
location is preserved correctly.

This is worth the while if we are working close to the machine, because
that is how the machine is built. It is crazy if we are using an high
level language, like SQL or APL or whatever else like it.
--
Piercarlo "Peter" Grandi           | ARPA: pcg%uk.ac.aber.cs@nsfnet-relay.ac.uk
Dept of CS, UCW Aberystwyth        | UUCP: ...!mcsun!ukc!aber-cs!pcg
Penglais, Aberystwyth SY23 3BZ, UK | INET: pcg@cs.aber.ac.uk