> On Wed, Jul 9, 2008 at 12:22 AM, Bill Page wrote:
>> The multiplication of a Float and some unknown symbolic value must
>> produce a symbolic expression of some kind. If we know that the
>> currently unknown symbolic value can only take values from Float,
>> then we can deduce from knowledge of multiplication in Float that
>> the value of the symbolic expression representing the multiplication
>> of a Float with this unknown symbolic value must also only take
>> values from Float.
On Wed, Jul 9, 2008 at 7:24 AM, Gabriel Dos Reis wrote:
>
> This is a fundamental observation. The way I read
>
> x: Float
> x + 1
>
> is that the declaration x:Float asserts that x can only take Float
> values, when it has a value.
>
I agree but the trouble is that contrary to naive expectations,
x:Float
does not declare 'x' as a "symbolic value" - in fact just the opposite!
In Axiom as it exists today if we want 'x' to be symbolic we must
write something like:
x:Polynomial Float
Only then can we use 'x' as a generator of such polynomials. E.g.
(1) -> x:Polynomial Float
Type: Void
(2) -> p:=x^2+2.0
2
(2) x + 2.0
Type: Polynomial Float
But there is no apriori requirement that symbolic values like 'p'
evaluate to Float when a value is given for 'x'.
(3) -> p1:=eval(p,x=1)
(3) 3.0
Type: Polynomial Float
But Axiom does have the concept of 'retract' so one can write, albeit
rather awkwardly,
(4) -> p2:=retractIfCan(p1)@Union(Float,"failed")
(4) 3.0
Type: Union(Float,...)
(5) -> p2 case Float => p2::Float
(5) 3.0
Type: Float
For more general expressions can use 'Expression Float' and some other
symbolic domains in a similar manner. But I think that all of this
machinery is probably quite "unnatural" to the new user of Axiom.
Regards,
Bill Page.
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