Re: patenting colimits?

[Steve Vickers <s.j.vickers@cs.bham.ac.uk>]

Toby Bartels wrote:
> ...
> Certainly much of what is in the patent application is obvious,
> but perhaps not all of it; were these diagrams of diagrams a new idea?,
> or was applying them to computer system specifications a new idea?.
> ...

Dear Toby,

The idea of treating specifications as colimits is a few decades old
now. Burstall and Goguen used it in their categorical account of their
specification language Clear, with a specification used to construct a
new theory as colimit of others.

The hierarchical step, diagrams of diagrams, was studied by Catherine
Oriat in her thesis and (I believe) a TCS paper in 2000. My own student
Gillian Hill investigated a variant of this (PhD Thesis 2002; also two
papers with me, 2001, 2006), replacing the category of finite diagrams
over a base category C by the equivalent category of finitely presented
presheaves. Both are finite cocompletions, but a presheaf presentation
by generators and relations comes over neatly as a "configuration by
components and sharing". For obvious reasons the iterated construction
"flattens" back down to the single one (the construction is a KZ-monad
in the 2-category of categories). Gillian also investigated a
multi-level configuration language that maintains the hierarchical
structure without flattening (configurations of configurations of
configurations of ...) and includes cross-level specification morphisms.
However, we did not persevere to work out the categorical semantics of
this, nor did we make a computer implementation.

Regards,

Steve Vickers.


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