Re: Scalars & atomic values & variables
Date: Sat, 3 Jan 2004 15:09:01 -0600
Message-ID: <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.
So talking about lists, for example, these are all non-atomic except for
the empty list. Which makes sense. On the other hand, you could also say
by my definition that all types are non-atomic except for the type with
Of course I haven't actually studied any formal type theories yet so I'm just talking out of my ass. Received on Sat Jan 03 2004 - 22:09:01 CET