I don't know if this is relevant to your discussion about kernels (most
of it goes over my head) but I thought I might mention something I would
like to implement, at some time in the future, in case there is some
requirement that is relevant?
Some time ago I implemented intuitionistic logic with a rep like this:
ILogic() : Exports == Implementation where
....
Rep := Union(_
const : Record(val : Symbol), _
var : Record(str : String), _
binaryOp : Record(typ : Symbol, c1 : %, c2 : %), _
unaryOp : Record(typ : Symbol, c1 : %)_
)
I would like to make this more general and allow many types of
propositional logic and associated algebras such as boolean, (co)Heyting
algebra and so on.
In OpenAxiom Gaby implemented PropositionalFormula using Kernel like this:
PropositionalFormula(T: SetCategory): Public == Private where
....
Rep == Union(T, Kernel %)
Would it be better if I used Kernel like this? I get the impression most
of the issues you are discussing are around casheing. I suspect there
would not be the same performance issues for discrete algebra like this?
I might even question if FriCAS/pan-axiom is the way to go for discrete
algebra? I suspect you are optimising for more numerical based algebra?
Apologies if I have misunderstood your discussion, my SPAD skills are
getting a bit rusty.
Martin
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