On Wed, Jul 9, 2008 at 3:31 PM, Bill Page <[EMAIL PROTECTED]> wrote:
> 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?
Symbolic Float -- as explained in the `computing with unknowns' paper.
> What operation is represented
> by '+'?
The `+' there is the modemap for the + that operates on Floats. Note that
x + 1.0 is not a Float, therefore, the code that implements the `+' operation
is not called, until x is actually substituted with a Float value.
The value x + 1.0 -- which is of type Symbolc Float, is internally
a typed AST, with the node trhe modemap for `+', and leaves, the
Float value 1.0 and the symbol x.
> What are the types of it's arguments?
See above.
>
>>>
>>> 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)
No, that is absolutely false. Not declaring `x' results in the
interpreter evaluating the *expression* `x' to a value of type
Variable x with internal representation the symbol x.
The key is to distinguish declaration from the evaluation of an
identifier as an expression.
>
> There are no untyped expressions in Axiom.
True, but irrelevant.
In the augmented OpenAxiom interpreter, not giving a
value to x in
x:Float
results in the evaluation of the *expression* `x' to evaluate to
a value of type Symbolic Float with internal representation
the symbol x.
-- Gaby
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