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Arnold Neumaier wrote:
Nate Hayes wrote:Arnold Neumaier wrote:Nate Hayes wrote:For those that may be interested, attached is the current draft of the position paper John referred to.Nate Hayes wrote: > we propose an > alternative, including by Proposition 1 (Motion 18) to make the distinction > between 1/0 and 1/Empty with decorations D_1 and D_0, But your scheme fails to make a distinction between 1+1/0 and 1+1/Empty, so your decorations for this distinction cannot be relied upon in a longer calculation.My scheme reports that both 1+1/0 and 1+1/Empty are ill-formed, as it should be:1/0 is undefined, and 1+undefined is ill-formed (as is 1/Empty).Under these circumstances, what's the point of distinguishing between undefined and ill-formed?
A user may want to trap the undefined operation in 1+1/0 to pinpoint the location inside the lengthy computation where the evaluation ceased to be real. Your scheme would not allow this.
The functions f(x):=1/x and g(x)=1+1/x are both defined everywhere except at x=0, so f(0) and g(0) should both be undefined, or both be ill-formed. But it doesn't make sense to label f(0) undefined and g(0) ill-formed, just because your scheme yields this artificial distinction.
Well, that is your opinion, and I don't accept it is a fact.In my view, IEEE 1788 is a hardware-oriented computational standard focusing on the individual arithmetic operations, and my scheme provides information that is lost in your scheme. Users can safely ignore the distinction if it is not useful to them, as demostrated in the example of Section 5.3 of my paper. So it incurs no penalty to users that may feel the way you do. However, if P1788 standardizes your scheme, users will have no choice, since the relevant information will always be lost.
Nate