Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Gabriel Dos Reis
> 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... I believe I fixed this some time ago, and I also thin the fix propag

Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Gabriel Dos Reis
On Wed, May 28, 2008 at 8:29 PM, Bill Page <[EMAIL PROTECTED]> wrote: > Gaby, e. al. > > Although the type system of OpenAxiom has some improvements over Axiom > and FriCAS, I still find some of the fundamentals confusing (or > confused :-) > > I would be very interested in your opinions on the fol

Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Bill Page
Francois, Thank you for reading and considering this list. To some people this exercise may seem a little pointless - being concerned with mostly "abstract nonesense" as opposed to "real" programming problems. But I think the situation is rather similar here to category theory in mathematics: It s

Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Ralf Hemmecke
On 05/29/2008 02:48 PM, Francois Maltey wrote: > Ralf wrote : > > >> In this last case I must be able to recognize the domain : > >> Expression Complex Integer or Expression Complex YYY, as > >> Expression Fraction Complex Integer and Expression Complex Fraction > >> Integer or others

Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Francois Maltey
Ralf wrote : >> In this last case I must be able to recognize the domain : >> Expression Complex Integer or Expression Complex YYY, as >> Expression Fraction Complex Integer and Expression Complex Fraction >> Integer or others. > What does "Expression(X)" actually tell you? Why the

Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Ralf Hemmecke
> In this last case I must be able to recognize the domain : > Expression Complex Integer or Expression Complex YYY, as > Expression Fraction Complex Integer and Expression Complex Fraction > Integer or others. What does "Expression(X)" actually tell you? Why the X at all? Is the imagin

Re: [open-axiom-devel] OpenAxiom semantics

2008-05-29 Thread Francois Maltey
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

[open-axiom-devel] OpenAxiom semantics

2008-05-28 Thread Bill Page
Gaby, e. al. Although the type system of OpenAxiom has some improvements over Axiom and FriCAS, I still find some of the fundamentals confusing (or confused :-) I would be very interested in your opinions on the following claims and questions. Which of these are true "by definition" and which mig