Re: Scalars & atomic values & variables

"Adrian Kubala" <adrian_at_sixfingeredman.net> wrote in message news:slrnbvebrd.ta3.adrian_at_sixfingeredman.net...
> Dawn M. Wolthuis <dwolt_at_tincat-group.com> schrieb:
> > Scalar value (mathematics): An object in a space for which there is no
> > operation in that space that takes a single operand and maps that object
to
> > two or more other objects (decomposes the object), which can then be
rebuilt
> > into the original object with another operation in the space.
>
> I don't understand what it means for a function to return two values in
> any other way then via some non-atomic type like a tuple, so I'm going
> to interpret your definition to read: given some set of agreed-upon
> non-atomic values, a value is non-atomic if there is an isomorphism
> between it and some subset of that set.
>
> In that case, even integers are not scalars since they are isomorphic to
> the assumed-non-atomic set of ordered pairs <x, x> where x is an
> integer.
>
> The definition I proposed elsewhere (for types the values of which are
> atomic), is that subtypes are non-atomic. What constitutes a subtype
> depends on the type system, I guess. Using the "set of values and
> associated functions" definition, my original guess is that A is a
> subtype of B if its values and functions are supersets of those of B.

Nope. A is a subtype of B if its values are a subset and its operations are a superset. A is a proper subtype of B if its values are a proper subset and its operations are a proper superset.

> Of course I haven't actually studied any formal type theories yet so I'm
> just talking out of my ass.

I appreciate your intellectual honesty. Received on Sat Jan 03 2004 - 23:41:52 CET