Le samedi 07 avril 2007 à 02:07 -0400, Bill Page a écrit :
> On April 6, 2007 12:30 PM Gregory Vanuxem wrote:
> >
> > At the boot level I want to know if a given type is valid.
> > By type I mean a category or a domain (parametrised if
> > they must be). So for example I want to know that
> > 'Matrix(Character)' and 'Fields' are invalid but not
> > Matrix(Ring) and Matrix(Integer)
>
> You implied that Matrix(Ring) is valid, but it is not. Perhaps
> this was a typo?
No this is not a typo, I was not very clear, here I consider
Matrix(Ring) as a valid type. Something on which I can work at the boot
level (this is probably different than a "real" domain, I don't know,
this is in part why I first want to know if I'm working on a valid
type). When I say parametrised I consider a category as a valid
parameter. I can not rely on the interpreter and what it returns or on
some parts of the functions available in the src/interp directory (there
are also 'new' and 'old' functions).
(8) -> DirectProduct(3,IntegerNumberSystem)
(8) DirectProduct(3,IntegerNumberSystem)
Type: Domain
(9) -> [1,2,3]::%
>> System error:
NIL is not of type CONS.
The interpeter considers DirectProduct(3,IntegerNumberSystem) as a valid
domain (type ?) :-(
> The definition of Matrix is
>
> Matrix(R:Ring)
>
> I wonder if you mean something like: since both
>
> Integer has Ring
> Field has Ring
>
> are true, why not both
>
> Matrix(Integer)
> Matrix(Field)
>
> Field of course, is a category while Integer is a domain.
> > There are several functions in the interpreter for that but
> > they are 'interactive' functions (in the sense that they will
> > throw an error if the type is not valid) or they do not accept
> > all possible categories. There is, for example, the function
> > 'isValidType' but it seems to only accept domains and simple
> > categories.
>
> Can you give an example of a valid category for which isValidType
> does not return T?
No, I thought, but I was wrong :-(, thanks for pointing this out.
Think of a category, here, as the set of matrices over a ring
(Ring being a category in the Axiom sense).
> isValidType seems to work for me (of course this is just the
> interpreter but the equivalent must work in Boot):
>
> (1) -> mytype1:=["Matrix"::Symbol::SEX, ["Integer"::Symbol::SEX]::SEX]::SEX
>
>
> (1) (Matrix (Integer))
>
> Type: SExpression
> (2) -> mytype2:=["Matrix"::Symbol::SEX,
> ["Character"::Symbol::SEX]::SEX]::SEX
>
> (2) (Matrix (Character))
> Type: SExpression
>
> (3) -> mytype3:=["FiniteSetAggregate"::Symbol::SEX,
> ["Integer"::Symbol::SEX]::SEX]::SEX
>
> (3) (FiniteSetAggregate (Integer))
> Type: SExpression
>
> (4) -> isValidType(mytype1)$Lisp
>
>
> (4) T
> Type: SExpression
>
> (5) -> isValidType(mytype2)$Lisp
>
> (5) ()
> Type: SExpression
>
> (6) -> isValidType(mytype3)$Lisp
>
> (6) T
> Type: SExpression
Yes, I was not clear. I do not have a clear overview of what Axiom
does behind the scene but I suspect some error from my part and
I must put out some simple mistakes.
> > The nirvana would be a function that accepts things like
> > Matrix(Join(Foo,Bar)) [1].
>
> I do not understand what you mean by this.
I want to know if I can extract information from what I call a
valid type, i.e:
)bo Matrix(Join(Field(),ConvertibleTo(InputForm())))
(|Matrix| (|Join| (|Field|) (|ConvertibleTo| (|InputForm|))))
Value = #<(SIMPLE-VECTOR 72) {10053B01FF}>
I'm interested by this vector :-).
[...]
> >
> > Am I thinking wrong ?
I was...
Greg
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