subtyping (was: Re: [E-Lang] Operators #2: Comparison)

[Mark S. Miller]

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At 06:57 AM Saturday 4/7/01, zooko@zooko.com wrote:
>Hm.  Note that you are assuming nominative typing here instead of structural.
>It is nominative because it is based on typed declared by the programmer.

I'm glad you raised that, because E hasn't taken a stance on this issue, and 
isn't ready to.  There are good arguments on both sides.


>Unless we really need to specify this behaviour now, I would suggest leaving it
>until later, when we'll have a better idea of what we want.

Agreed.  "type op__cmp(type)" is hereby withdrawn.  Turns out it conflicts 
with another use of op__cmp that we'd agreed to, but which I forgot to list. 
For example, we agreed that

    integer < 3

(rather than the current "any < 3") should be the way to form the region of 
all integers less than three.  

So, for those types whose instances respond to op__cmp, and for which one 
can form regions representing non-enumerable sets of these instances, we 
consider these types to also represent the coordinate-space in which these 
instances are positions, where the type-as-coordinate-space provides the 
following region formation operators:

    space < positionX  ->  region of all positions in space < positionX

and similarly for the other comparison operators.  Note that the region

    float64 <=> 0.0

evaluates to the singleton region containing all positions equivalent to 
0.0.  This includes both 0.0 and -0.0, but the region is still considered a 
singleton region.

Likewise

    float64 <=> NaN

evaluates to the empty region of float64s, not a singleton region, since no 
positions in this space are equivalent to NaN.


        Cheers,
        --MarkM

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At 06:57 AM Saturday 4/7/01, zooko@zooko.com wrote:

> Hm.  Note that you are
> assuming nominative typing here instead of structural.
> It is nominative because it is based on typed declared by the
> programmer.


I'm glad you raised that, because E hasn't taken a stance on this issue,
and 

isn't ready to.  There are good arguments on both sides.



> Unless we really need to specify
> this behaviour now, I would suggest leaving it
> until later, when we'll have a better idea of what we
> want.


Agreed.  "type op__cmp(type)" is hereby withdrawn. 
Turns out it conflicts 

with another use of op__cmp that we'd agreed to, but which I forgot to
list. 

For example, we agreed that


    integer < 3


(rather than the current "any < 3") should be the way to
form the region of 

all integers less than three.  


So, for those types whose instances respond to op__cmp, and for which one

can form regions representing non-enumerable sets of these instances, we

consider these types to also represent the coordinate-space in which
these 

instances are positions, where the type-as-coordinate-space provides the

following region formation operators:


    space < positionX  ->  region of all
positions in space < positionX


and similarly for the other comparison operators.  Note that the
region


    float64 <=> 0.0


evaluates to the singleton region containing all positions equivalent to

0.0.  This includes both 0.0 and -0.0, but the region is still
considered a 

singleton region.


Likewise


    float64 <=> NaN


evaluates to the empty region of float64s, not a singleton region, since
no 

positions in this space are equivalent to NaN.



        Cheers,

        --MarkM


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