On Wed, Jul 9, 2008 at 3:49 PM, Gabriel Dos Reis wrote:
>
> And I don't think anybody claimed that x:Float to be of type
> "symbolic value".
>

If you expect to be able to write:

  x:Float
  x+1.0

what is the possible type of the result? What operation is represented
by '+'? What are the types of it's arguments?

>>
>> 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.
>

In the Axiom interpreter, not specifying any type for x is equivalent
to declaring

  x:Variable(x)

There are no untyped expressions in Axiom.

Because of the function selection process in the interpreter and
because a coercion path from 'Variable(x)' to Expression Integer
exists, the result of writing 'sin(x)' is of type 'Expression
Integer'.

Regards,
Bill Page.

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