Bill,

I apologise for not being very precise and thanks for replying anyway.

> One reason I did not reply earlier to this is because I did not
> understand what you meant by "algebra" in this context.

In my readings around the subjects of computation and category theory
I keep coming across terms like \Omega-Algebras, F-Algebras and T-
Algebras, I haven't found a precise definition of these and I think
different sources use these terms differently but my interpretation of
these terms would be:

\Omega-Algebra A set of operator symbols, each operator has an 'arity'
and
all operators act only on the elements of the algebra.

F-Algebras and F-Coalgebras are the same as \Omega-(co)algebras
except we denote all the operator signatures by a single functor.

A T-Algebra is an F-Algebra, as defined above, together with a set
of equations (axioms) built from the F-Algebra operations.

In each of these cases an 'algebra' would have a signature like this:

(%) -> %
(%,%) -> %
(%,%,%) -> %
...

and a 'co-algebra' would have a signature like this:

% -> (%)
% -> (%,%)
% -> (%,%,%)
...

So what I was trying to say is, if we are building an instance of an
'algebra' signature in FriCAS we would tend to have a representation
like:

Rep:=Record(....

But if we are building an instance of an 'co-algebra' signature in
FriCAS we would tend to have a representation like:

Rep:=Union(....

That is: the first is a datatype and the second is a co-datatype.

In the computation framework the domains appear to be of the second
type (co-datatypes) but I was thinking of Kernel (and I've probably
completely misunderstood here) as something that takes an 'algebra'
signature and allows us to solve equations in that algebra.

So I was just trying to understand whether the domains in the
computation framework are best thought of as 'algebras' or 'co-
algebras' in these terms.

If this still does not make sense, its probably best to leave it until
I/(we) attempt to translate the propositional logic code after which I
may understand Kernel better.

Martin

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