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 -- You received this message because you are subscribed to the Google Groups "FriCAS - computer algebra system" group. To post to this group, send email to [email protected]. To unsubscribe from this group, send email to [email protected]. For more options, visit this group at http://groups.google.com/group/fricas-devel?hl=en.
