On Wed, Jul 9, 2008 at 10:17 AM, Bill Page <[EMAIL PROTECTED]> wrote:
>> 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!
And I don't think anybody claimed that x:Float to be of type
"symbolic value".
>
> In Axiom as it exists today if we want 'x' to be symbolic we must
> write something like:
>
> x:Polynomial Float
I strongly disagree with that. When I write
integrate(sin(x)^3,x)
I have no declaration to supply for 'x', in order for it to be
interpreted as symbolic value -- a value of type Expression Integer.
-- Gaby
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