Bill Page wrote : > 1) Categories and domains are types. > 2) Domains satisfy categories only by assertion, > 3) It is possible to construct domains that contain types > 4) 'Void' is a domain that satisfies no categories except 'Type' > 5) Objects /1 are members of 'Domains' > 6) In the interpreter the type (domain) of variables can be declared > 7) Categories can be passed as arguments > 8) But at the present time the type of a variable cannot be a category > 9) Is 'Category' the domain of all categories > 10) or is 'Category' a category? > For 6) and 1) I never see x:CategoryXX := ... So it seems that variable has ONE value in ONE domain
x :=Integer claims that Integer is a member of a domain : Domains. x : Domains := Integer x :Category:= ThisCategory means that Category is also a domain. I feel that no axiom can hold any category. A category adds functions to an "object". And I'm waiting about functions : what are the type/domain of functions f (x) == 2*x g(x:Integer) : Integer==3*x h := x +-> 4*x --- an anonymous function k: Integer -> Integer := x +->5*x -- not yet possible... Last related question : Imagine I want to have rewrite functions over every trigonometric expressions, not only Expression Integer, nor Expression DomainXXX, but over all sort of expressions. The place of this rewrite/expand/combine function is in TrigonometricFunctionCategory (see trigcat.spad file). In this case I must be able to pick up the x in sin x, and play with this x even if I don't know the domain of x... How is it possible ? I have 2 examples in mind. How can I expand (sin (3*x)) ? and how can I expand (exp (a+%i*b)) in exp a * (cos b + %i * sin b). In this last case I must be able to recognize the domain : Expression Complex Integer or Expression XXXX Complex YYYYYYY, as Expression Fraction Complex Integer and Expression Complex Fraction Integer or others. Have a nice day ! F. ------------------------------------------------------------------------- This SF.net email is sponsored by: Microsoft Defy all challenges. Microsoft(R) Visual Studio 2008. http://clk.atdmt.com/MRT/go/vse0120000070mrt/direct/01/ _______________________________________________ open-axiom-devel mailing list open-axiom-devel@lists.sourceforge.net https://lists.sourceforge.net/lists/listinfo/open-axiom-devel
